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Modeling and nonlinear analysis of piezoelectric energy harvesting from transverse galloping
Abstract
A model for harvesting energy from galloping oscillations of a bar with an equilateral triangle cross-section attached to two cantilever beams is presented. The energy is harvested by attaching piezoelectric sheets to cantilever beams holding the bar. The derived nonlinear distributed-parameter model is validated with previous experimental results. The quasi-steady approximation is used to model the aerodynamic loads. The power levels that can be generated from these vibrations, and the variations of these levels with the load resistance and wind speed, are determined. Linear analysis is performed to validate the onset of galloping speed with experimental measurements. The effects of the electrical load resistance on the onset of galloping are then investigated. The results show that the electrical load resistance affects the onset speed of galloping. A nonlinear analysis is also performed to determine the effects of the electrical load resistance and the nonlinear torsional spring on the level of the harvested power. The results show that maximum levels of harvested power are accompanied by minimum transverse displacement amplitudes. It is also demonstrated that there is an optimum load resistance that maximizes the level of the harvested power.
... Nonlinear elasticity's influence on GEH performance is extensively studied [11,12]. It is found to enhance efficiency at low flow rates, albeit potentially reducing operating speeds [13,14]. ...
... Therefore, in the following part of the work notation 1 = has been adopted. Returning now to the general definition of efficiency (5) and substituting the expressions (6b), (10), (12) into it, we obtain: Figure 1 illustrates the efficiency characteristics of the system under discussion. The efficiency is depicted as the ratio / and such representation maintained throughout the study. ...
... The reason for this discrepancy lies in the fact that in the cited work, the operating conditions of the compared systems were not standardized -the devices had different critical speeds and, consequently, different nominal speeds. Despite the unquestionable value of this article, the conclusion stated therein can be subject to 12 Funding: This research was funded by Polish Ministry of Higher Education, grant number 0612/SBAD/3628. ...
This paper examines the energy efficiency of three variations of the two-degree-of-freedom transverse galloping energy harvester. These variants differ in the number and placement of electromechanical transducers. By utilizing the harmonic balance method, limit cycles of mathematical models of devices were determined. Analytical expressions derived from models were then used to formulate the efficiency of the systems. It was demonstrated that efficiency depends on flow speed and can be comprehensively characterized by four criteria parameters: peak efficiency, denoting the maximum efficiency of the system, and high efficiency bandwidth, which describes the range of flow velocities within which the efficiency remains at no less than 90% of peak efficiency. The values of these parameters are heavily reliant on the speed at which the system achieves peak efficiency—referred to as the nominal speed nominal speed, which in turn is related to the critical speed of the system. Comparative analysis revealed that only the two-degree-of-freedom device equipped with two electromechanical transducers can potentially outperform a simple one-degree-of-freedom system in terms of efficiency.
... In the area of small-scale wind energy harvesting, aeroelastic energy harvesting has become one of the most promising technologies [2]. Recently, several flow-induced-vibration mechanisms [3][4][5][6][7][8][9][10], such as vortex-induced vibration [3][4], flutter [5][6], galloping [7][8], and wake galloping [9][10], have been introduced into aeroelastic energy harvesting. Among these mechanisms, the galloping-based energy harvester has high energy harvesting efficiency as a result of the large structural response during the induced limit cycle oscillation when galloping takes place, leading to a large output power [7][8]. ...
... In the area of small-scale wind energy harvesting, aeroelastic energy harvesting has become one of the most promising technologies [2]. Recently, several flow-induced-vibration mechanisms [3][4][5][6][7][8][9][10], such as vortex-induced vibration [3][4], flutter [5][6], galloping [7][8], and wake galloping [9][10], have been introduced into aeroelastic energy harvesting. Among these mechanisms, the galloping-based energy harvester has high energy harvesting efficiency as a result of the large structural response during the induced limit cycle oscillation when galloping takes place, leading to a large output power [7][8]. ...
... Recently, several flow-induced-vibration mechanisms [3][4][5][6][7][8][9][10], such as vortex-induced vibration [3][4], flutter [5][6], galloping [7][8], and wake galloping [9][10], have been introduced into aeroelastic energy harvesting. Among these mechanisms, the galloping-based energy harvester has high energy harvesting efficiency as a result of the large structural response during the induced limit cycle oscillation when galloping takes place, leading to a large output power [7][8]. ...
... It is considered that the adoption of energy harvesters can be an innovative approach to achieve smart building if the airflow energy from low-velocity wind can be harvested effectively to power indoor wireless sensors, as described in [9]. To date, many studies have been conducted on harvesting wind energy by exploiting aeroelastic instabilities such as vortex-induced vibrations (VIVs) [11][12][13], galloping [14][15][16][17], flutter [18,19], and wake galloping [20][21][22]. Among these phenomena, we mainly concentrate on a survey of the galloping phenomenon utilized in this study. ...
... In this study, the Krylov-Bogoliubov method was used to obtain approximate solutions by considering the system as a weakly nonlinear oscillator. Abdelkefi et al. [15] presented a coupled nonlinear distributed parametric model of a galloping energy harvester composed of a cantilever beam and a bluff body with an equilateral triangle cross-section. In addition, they experimentally investigated the effects of electrical load resistance on the onset of galloping and on efficiency. ...
... As shown in Fig. 5(a), the drag forces measured with the two bluff bodies were proportional to the wind velocity squared; this is in agreement with the existing formula for drag forces [15]. The drag force coefficient can be computed using the measured drag force values and Eq. ...
In this study, a novel galloping-based piezoelectric energy harvester adaptable to external wind velocity (GPEHAW) is proposed. The purpose of developing the GPEHAW is two-fold: (1) improve the power density in a high wind velocity regime and (2) lower the critical wind velocity for galloping in a low wind velocity regime. The bluff body in the GPEHAW is designed to be movable, under an elastic constraint, in axial direction on a flexible beam, and a set of springs is mounted between them. The dynamics of this bluff body are governed by the unbalance between the drag, centrifugal, spring, and friction forces. A nonlinear aero-electro-mechanical model is derived using the extended Hamilton principle, and its analytical solution is obtained using a perturbation technique: the method of multiple scales. The moving mechanism of the bluff body is thoroughly investigated under various force conditions, followed by a numerical analysis and preliminary experimental validation. Subsequently, the mathematically obtained coupled behavior of the GPEHAW system is compared with the experimental results. Furthermore, a comprehensive study is performed to investigate the influence of the distance traveled by the bluff body (equivalent to the effective beam length) on the behavior of the GPEHAW system, with a special focus on the critical wind velocity for galloping, transverse displacement, average power, and power density. The results show that the proposed system exhibits an excellent energy performance, an increase in power density by 70.2%, and a mean power density improvement rate (MPDR) of 23.4%, compared with the conventional system (equipped with a fixed bluff body). We consider that the findings in this study provide a useful guideline for designing efficient galloping-based piezoelectric energy harvesters, which would be particularly effective in an urban environment.
... In the area of small-scale wind energy harvesting, aeroelastic energy harvesting has become one of the most promising technologies [2]. Recently, several flow-induced-vibration mechanisms [3][4][5][6][7][8][9][10], such as vortex-induced vibration [3][4][5], flutter [6,7], galloping [8,9], and wake galloping [10,11], have been introduced into aeroelastic energy harvesting. Among these mechanisms, the galloping-based energy harvester has high energy harvesting efficiency as a result of the large structural response during the induced limit cycle oscillation when galloping takes place, leading to a large output power [8,9]. ...
... In the area of small-scale wind energy harvesting, aeroelastic energy harvesting has become one of the most promising technologies [2]. Recently, several flow-induced-vibration mechanisms [3][4][5][6][7][8][9][10], such as vortex-induced vibration [3][4][5], flutter [6,7], galloping [8,9], and wake galloping [10,11], have been introduced into aeroelastic energy harvesting. Among these mechanisms, the galloping-based energy harvester has high energy harvesting efficiency as a result of the large structural response during the induced limit cycle oscillation when galloping takes place, leading to a large output power [8,9]. ...
... Recently, several flow-induced-vibration mechanisms [3][4][5][6][7][8][9][10], such as vortex-induced vibration [3][4][5], flutter [6,7], galloping [8,9], and wake galloping [10,11], have been introduced into aeroelastic energy harvesting. Among these mechanisms, the galloping-based energy harvester has high energy harvesting efficiency as a result of the large structural response during the induced limit cycle oscillation when galloping takes place, leading to a large output power [8,9]. ...
In the past decade, galloping-based energy harvesters (GPEH) connected with various interface circuits have been developed and analytical models have been built. However, the power performances of these advanced structures and circuits are always treated separately, and a general model is missing to gain insights at a system level. To tackle this issue, this paper proposes a unified analysis framework for GPEHs. Its results are consistent with validated (but disconnected) results in the literature. The method provides an integrated view of the physics of linear GPEHs in multiple domains at the system level, and elucidates the similarities and differences among power behaviors of GPEHs connected with various interface circuits. The framework is based on two major elements: an equivalent circuit that represents the entire system, and an equivalent impedance that represents the interface circuit. Firstly, the electromechanical system is linearized and modeled in the electrical domain by an equivalent self-excited circuit with a negative resistive element representing the external aerodynamic excitation, and a general load impedance representing the interface circuit. Then, a closed-form, analytical expression of the harvested power is obtained based on the Kirchhoff’s Voltage Law, from which the optimal load, maximum power, power limit, and critical electromechanical coupling (minimum coupling to reach the power limit) are determined. In this unified analysis, the exact type of energy harvesting interface circuit is not assumed. After that, the power characteristics of a GPEH connected with five representative interface circuits are analytically derived and discussed, by using the particular equivalent impedance of the interface circuit of interest. It is shown that they are subjected to the same power limit. However, the critical electromechanical coupling depends on the type of circuit. Throughout the discussions, impedance plots are used to illustrate the relationship between the internal system characteristics and external load impedance, facilitating the understanding of system power behavior.
... Firstly, the effect of electrical load resistance or incoming flow velocity on the energy harnessing and harvested voltage of an equilateral triangular prismatic oscillator was explored in Refs. [69,70]. Authors mainly used the piezoelectric transducers to produce power. ...
... Being similar to the research on square oscillator [57], another study used a piezoelectric energy converter to convert the mechanical energy of an equilateral triangular prism's transverse galloping to electric energy ( Fig. 21) [70]. The effectiveness of the energy harvester was validated through a coupled nonlinear distributed-parameter model with a linear or nonlinear torsional spring. ...
... Refs. [58,59] replaced the equilateral triangular section with an isosceles triangle with two different base angles, namely δ = 30 • and 53 • . It can be observed that the function of changing the value of electrical load resistance or flow velocity for the corresponding oscillation displacement or harvested power were similar to Ref. [70]. ...
A comprehensive review of hydrokinetic energy converters based on alternating lift
technology (ALT) is provided. Emphasis is on nonlinear oscillators based on Flow Induced Vibration (FIV) or Oscillation (FIO). Due to strong coupling in Fluid-Structure Interaction (FSI), and in order to maximize the hydrokinetic harnessed energy,
the design of nonlinear oscillators and analysis by model tests or computational fluid dynamics dominates this area. Research confirmed that the nonlinear oscillator can harvest energy from a stochastic excitation modeled by a generic wide spectrum, and overcome the most severe oscillator limitations: specifically, the need for continuous frequency tuning due to the narrow bandwidth response, and low efficiency outside the narrow bandwidth oscillator response. This review covers the following aspects of nonlinear oscillators in ALT converters: (1) Geometric changes in oscillator cross-section; e.g., circular, square, rectangular, or trilateral shapes. (2) Passive turbulence control of FIV/FIO. (3) Position based nonlinear stiffness. (4) Multi-cylinder synergistic FIV/FIO. (5)
Mechanically linked oscillators. (6) Velocity-based, nonlinear, adaptive harnessing damping.
... (2) using a distributed parameter model with Rayleigh-Ritz discretization [252]; and (3) using a Euler-Bernoulli distributed parameter model [253]. A mathematical model can also be derived for the piezoelectric energy harvester based on other types of FIV response, such as a flutter converter [253] and a wake-galloping converter [254]. ...
... (2) using a distributed parameter model with Rayleigh-Ritz discretization [252]; and (3) using a Euler-Bernoulli distributed parameter model [253]. A mathematical model can also be derived for the piezoelectric energy harvester based on other types of FIV response, such as a flutter converter [253] and a wake-galloping converter [254]. As a final note, the use of a SDOF mass-spring-damper system [250,251] mentioned here involves simply using an odd-order polynomial approximation for F y in Equation (39) which results in ...
A comprehensive review of modelling techniques for the flow-induced vibration (FIV) of bluff bodies is presented. This phenomenology involves bidirectional fluid-structure interaction (FSI) coupled with nonlinear dynamics. In addition to experimental investigations of this phenomenon in wind tunnels and water channels, a number of modelling methodologies have become important in the study of various aspects of the FIV response of bluff bodies. This paper reviews three different approaches for the modelling of FIV phenomenology. Firstly, we consider the mathematical (semi-analytical) modelling of various types of FIV responses: namely, vortex-induced vibration (VIV), galloping, and combined VIV-galloping. Secondly, the conventional numerical modelling of FIV phenomenology involving various computational fluid dynamics (CFD) methodologies is described, namely: direct numerical simulation (DNS), large-eddy simulation (LES), detached-eddy simulation (DES), and Reynolds-averaged Navier-Stokes (RANS) modelling. Emergent machine learning (ML) approaches based on the data-driven methods to model FIV phenomenology are also reviewed (e.g., reduced-order modelling and application of deep neural networks). Following on from this survey of different modelling approaches to address the FIV problem, the application of these approaches to a fluid energy harvesting problem is described in order to highlight these various modelling techniques for the prediction of FIV phenomenon for this problem. Finally, the critical challenges and future directions for conventional and data-driven approaches are discussed. So, in summary, we review the key prevailing trends in the modelling and prediction of the full spectrum of FIV phenomena (e.g., VIV, galloping, VIV-galloping), provide a discussion of the current state of the field, present the current capabilities and limitations and recommend future work to address these limitations (knowledge gaps).
... Initially, the researches of the VIV PWEHs and galloping PWEHs (hereinafter referred to as PWEHs) mainly focused on the conversion mechanism of the piezoelectric transducers [31][32][33][34]. Sivadas et al. discussed a preliminary study on harnessing energy from piezoelectric transducers by using bluff body and vortex-induced vibration phenomena [31]. ...
... It showed that the harvester could produce approximately 0.1 mW of non-rectified output power at a flow speed of 1.192 m⋅s − 1 in a wind tunnel [32]. Abdelkefi et al. proposed a model for harvesting energy from galloping oscillations of a bar with an equilateral triangle cross-section attached to two cantilever beams, which was validated with some experimental results [33]. Mutsuda et al. proposed a highly flexible piezoelectric energy device to harvest flow-induced vibration such as energy of ocean, current and wind [34]. ...
Energy harvesting from wind-induced vibration energy using piezoelectric materials has received great attention because of the self-powered demand for wireless sensor networks. To improve the reliability, output performance and environmental adaptability (or designability of the structure), a piezoelectric wind energy harvester excited indirectly by a coupler via magnetic-field coupling (MC-PWEH) is proposed in this paper. The MC-PWEH is mainly composed of a piezoelectric transducer and a coupler consisting of a flexible beam, a cylinder, some exciting magnets and added coupler mass. By introducing the interaction of the piezoelectric transducer sealed in the chamber and the cylinder via the magnetic coupling, the interactive vortex-induced vibration (VIV) and galloping is realized and the composite vibration energy is transformed into electric energy. The feasibility of the structure and principle of the MC-PWEH is proved through theoretical simulations and experiments. The results indicated that the piezoelectric transducer began to oscillate strongly and generate fairly high output voltage when the wind speed exceeded a low critical wind speed, accompanied by a coupling phenomenon of VIV and galloping, and then finally converged to a stable value when the wind speed exceeded a high critical value. Moreover, the critical wind speeds, bandwidth of wind speed, natural frequency and power generation performance of the MC-PWEH could be adjusted by changing the structural parameters. Under the transducer proof mass of 50 g, the optimal wind speed bandwidth for the MC-PWEH to output voltage greater than 3.5 V obtained was 25.84 m⋅s⁻¹ that occupies 86.12% of the experimental wind speed bandwidth. The achieved maximum output power was 4.73 mW at the optimal external load resistance of 1000 kΩ and wind speed of 24 m⋅s⁻¹.
... Converting the inexhaustible energy into electric energy would reduce carbon emission. Among the fluid-structure interaction mechanism, the response amplitude of galloping increases dramatically as the incoming wind speed exceeds the critical cut-in one, and thus it has an advantage in the operational wind speed range [37][38][39][40][41][42][43] . Dai et al. [44][45] established a theoretical model of a nonlinear energy harvester based on the Euler-Lagrange method, and investigated the influence of electromagnetic coupling analytically. ...
In the practical environment, it is very common for the simultaneous occurrence of base excitation and crosswind. Scavenging the combined energy of vibration and wind with a single energy harvesting structure is fascinating. For this purpose, the effects of the wind speed and random excitation level are investigated with the stochastic averaging method (SAM) based on the energy envelope. The results of the analytical prediction are verified with the Monte-Carlo method (MCM). The numerical simulation shows that the introduction of wind can reduce the critical excitation level for triggering an inter-well jump and make a bi-stable energy harvester (BEH) realize the performance enhancement for a weak base excitation. However, as the strength of the wind increases to a particular level, the influence of the random base excitation on the dynamic responses is weakened, and the system exhibits a periodic galloping response. A comparison between a BEH and a linear energy harvester (LEH) indicates that the BEH demonstrates inferior performance for high-speed wind. Relevant experiments are conducted to investigate the validity of the theoretical prediction and numerical simulation. The experimental findings also show that strong random excitation is favorable for the BEH in the range of low wind speeds. However, as the speed of the incoming wind is up to a particular level, the disadvantage of the BEH becomes clear and evident.
... Under harmonic excitation, the optimal resistance of the NES-piezoelectric vibration energy harvester could be determined by the harmonic balance method [151,152]. The aerodynamic loads were modeled using the quasisteady approximation approach, through which the relation between the load resistance and the output power, jump frequency, and bandwidth could be obtained [153]. When considering weak electromechanical coupling, different load resistances could affect the performance of the energy harvester-NES system. ...
Vibration control has been of great interest to scientists and engineers for many years. Although linear vibration absorbers have been shown to be effective in mitigating vibrations at specific frequencies, their vibration reduction effect is usually limited to a narrow frequency bandwidth. Nonlinear energy sinks have attracted attention due to their better vibration reduction effect over a wider frequency bandwidth. In practical applications, the nonlinear energy sink devices can effectively absorb, dissipate, and convert energy from broadband excitation, so as to achieve vibration reduction and energy harvesting. However, research on energy harvesting based on the nonlinear energy sink is less mature than in linear systems. Multiple parameters of device design (e.g., damping size) affect the actual performance of the nonlinear energy sinks, but there is no exact method to simplify the design of the multiparameter nonlinear energy sinks. Since it is more difficult to implement electromagnetic and electrostatic energy harvesters, more research has focused on piezoelectric energy harvesters. This paper summarizes the research on the nonlinear energy sink and energy harvesting technology, including the introduction of the nonlinear energy sink, energy harvesting based on the nonlinear energy sink, and its application in various fields of energy harvesting. The paper also summarizes some important methods for solving the dynamical equations, as well as their advantages and disadvantages. The conclusions provide an outlook on the subsequent research of the nonlinear energy sink technology, such as the introduction of piezoelectric materials with high energy density, the benefits of balanced vibration suppression and harvesting of vibration energy, and the self-tuning of parameters in complex environments. It provides a powerful reference for the popularization and application of energy harvesting technology based on nonlinear energy sinks.
... Piezoelectric energy harvesters in the turbine structure are widely used in aerostatic structures where the principle of aerodynamic instability is applied, such as vortex-induced vibrations [35,36], flutter [37], wake-induced oscillation [38][39][40] and galloping [35,41] to convert mechanical energy into electrical energy. With the thought that changing the bluff structure of the turbine blade will increase the energy generation performance, Abdelkefi et al. [42] proposed square, triangle, equilateral triangle, and D-shaped bluff structures for energy harvesting mechanisms. To improve the energy efficiency of wind speed in the forked bluff structure, Liu et al. [43] reported experimental and simulation results at length ratios of different blades. ...
In this study, an approach is proposed to examine hybrid piezoelectric energy harvesting performances from vibrations induced by thermal and angular velocity loads in order to generate energy from the smart turbine blade. In the proposed method, a smart turbine blade is formed by patching the piezoelectric material to the root surface of the turbine blade. A finite element (FE) model of the smart turbine blade is established and then it is validated with a smart blade model in a reference study to test the reliability and accuracy of the FE method. The defined loads are applied to the smart blade to obtain energy from mechanical vibrations induced by thermal and angular velocity loads. Temperature distribution, voltage, and vibration results obtained from energy harvesting analysis under different thermal and angular velocity loads are presented. In order to investigate the energy conversion efficiency of the energy obtained from the system, the energy harvesting circuit is tested in terms of battery discharge times and power output values. The results show that while the maximum energy conversion in the thermally induced smart turbine blade is 11.9 W, a power output of 12.3 W is obtained from the hybrid energy harvesting mechanism under angular velocity and heat flux loads.
... We denote the Heaviside step function as 'H(x)', and utilize it to define the spatial region associated with each piezoelectric element, represented by 'H(x a ) − H(x a − l PD ).' Prior research on piezoelectric effects has widely adopted such mathematical approaches to ensure the inclusion of piezoelectricity-related terms during spatial differential processes. Indeed, some analytical models, particularly those addressing longitudinal waves and transverse vibrations, have appealed remarkable agreement with finite-element-method results [25,26,47,48]. ...
Extensive prior research has delved into the localization of elastic wave energy through defect modes within phononic crystals (PnCs). The amalgamation of defective PnCs with piezoelectric materials has opened new avenues for conceptual innovations catering to energy harvesters, wave filters, and ultrasonic receivers. A recent departure from this conventional paradigm involves designing an ultrasonic actuator that excites elastic waves. However, previous efforts have mostly focused on single-defect scenarios for bending wave excitation. To push the boundaries, this re-search takes a step forward by extending PnC design to include double piezoelectric defects. This advancement allows ultrasonic actuators to effectively operate across multiple frequencies. An analytical model originally developed for a single-defect situation via Euler-Bernoulli beam theory is adapted to fit within the framework of a double-defect setup, predicting wave-excitation performance. Furthermore, a comprehensive study is executed to analyze how changes in input voltage configurations impact the output responses. The ultimate goal is to create ultrasonic transducers that could have practical applications in nondestructive testing for monitoring structural health and in ultrasonic imaging for medical purposes.
... Since wind energy is a suitable electricity source for a clean environment, studies on piezoelectric wind energy harvesting have been focused on converting wind energy into electrical energy [35][36][37]. A piezoelectric energy harvesting mechanism is presented to collect electrical energy via wind energy from an arc-shaped elastic beam in the unidirectional and narrow wind speed range [38]. ...
Energy consumption and control of electrical devices in flying electric vehicles with propellers such as drones are important for the continuity of the movement process. With this motivation, the piezoelectric energy harvesting performances of the smart drone propeller and smart wind blades are evaluated in order to obtain electrical energy from lead zirconate titanate (PZT) material placed on the propellers. Initially, the effect of smart wind blades with different blade angles on energy harvesting analysis is examined. The energy harvesting performances of the converse (z polarization) and shearing movements (y polarization) of the PZT material placed on the wind blades are compared under different angular rotational velocities. Then, the power outputs obtained depending on the sensor responses of the smart drone propeller with different resistance gains are evaluated according to the polarization directions. The maximum and minimum power output values obtained from the smart drone propeller at 12,000 rpm rotation velocity are measured as about 0.086 and 0.008 W, respectively. The results show that the energy harvesting performance of the z-polarized smart propeller is more effective than the y polarization, and the amount of energy obtained with the increase in the endpoint vibration amplitudes increases as the rotation speed increases.
... Tan et al., in a recent study, looked into the benefits of coupling piezoelectric galloping energy harvesting with the natural environment [20]. By utilizing vortex-induced vibrations [20][21][22][23][24][25][26] and galloping, the harvesters generated more energy [21,[27][28][29][30][31]. Furthermore, PEH have been studied for their possible application in devices that harness energy from human movements [32][33][34][35][36][37]. ...
Given its versatility in drawing power from many sources in the natural world, piezoelectric energy harvesting (PEH) has become increasingly popular. However, its energy harvesting capacities could be enhanced further. Here, a mathematical model that accurately simulates the dynamic behavior and energy harvested can facilitate further improvements in the performance of piezoelectric devices. One of the goals of this study is to create a dependable reduced-order model of a multi-purpose gyroscope. This model will make it possible to compute the harvested voltage and electrical power in a semi-analytical manner. The harvested voltage is often modeled as an average value across the whole electrode surface in piezoelectric devices. We propose a model which provides practical insights toward optimizing the performance of the system by considering a spatially varying electric field across the electrode surface length. Our framework allows investigation of the limits of applicability of the modeling assumptions across a range of load resistances. The differential quadrature method (DQM) provides the basis for the suggested numerical solution. The model is also employed to examine energy harvesting under various resistance loads. The newly developed spatially varying model is evaluated for open- and closed-circuit conditions and is proved to be accurate for various values of load resistance that have not previously been considered. The results show that using a spatially varying model is more versatile when modeling the performance of the piezoelectric multifunctional energy harvester. The performance may be accurately captured by the model for load resistances ranging between 103 Ω and 108 Ω. At optimum load resistance and near 65 KHz, the maximum power output predicted by the spatially varying (SV) model is 1.3 mV, 1.5 mV for the open-circuit (OC) model, and 2.1 mV for the closed circuit (CE) model. At a high-load resistance, the SV and OC models all predict the maximum power output to be 1.9 mV while the CE model predicted the maximum voltage to be 3 mV.
... is the rth modal coordinate and / r x ð Þ is the mass-normalized eigenfunction of the rth mode, which can either be explicitly expressed using a transcendental equation incorporating all boundary conditions 13,33,34 or numerically obtained using the finite element method. 6 Introducing the expanded w(x, t) and considering the first two modes (r ¼ 1,2), one obtains the modal aero-electro-mechanical model, given by ...
Vortex-induced vibration (VIV) and wake galloping are two aeroelastic instability phenomena with similar underlying mechanisms related to vortex shedding. Inspired by this common feature, a two-degree-of-freedom (2DOF) piezoelectric aeroelastic energy harvester (PAEH) is proposed, which employs VIV and wake galloping mechanisms with their respective benefits to improve the wind energy harvesting performance in a wide wind speed range. The proposed 2DOF PAEH overcomes the limitations of conventional one-degree-of-freedom VIV and wake galloping energy harvesters, with the former being only effective in a single and narrow lock-in wind speed range and the latter failing to work at low wind speeds. The modal frequencies of the 2DOF PAEHs are easily manipulated, and the twin mechanisms improve power generation over two lock-in regions at low wind speeds by the VIV mechanism and a third power generation region at relatively higher wind speeds due to wake galloping. A coupled aero-electro-mechanical model is developed and verified by wind tunnel experiments on a prototype. The results show that the proposed harvester efficiently extracts wind energy in a wide wind speed range from 1.1 to 6 m/s. The influence of the distance between the two parallel bluff bodies, in which distance is a critical parameter, on the voltage output is experimentally investigated, revealing three distinct aerodynamic behaviors at different distances.
... When air flow is the only source of energy generating the vibration, changing the shape of the bluff body is an appealing option to enhance performance. Abdelkefi et al. [104] suggested a galloping collecting model for an equilateral triangular bluff body and investigated the notion of energy harvesting for bluff bodies with various cross-sections (square, D-shaped, and triangular). Wang et al. [105] examined the energy harvesting of various top-angle cross-sections in a triangular cross-section bluff body and proved that obtuse isosceles triangles may be employed to effectively gather galloping energy. ...
Microelectromechanical systems (MEMS) powered by conventional batteries are disadvantaged in terms of scope of application and environmental friendliness because their power sources need to be replaced regularly and have the risk of polluting the environment. Piezoelectric technology provides a solution for harvesting clean energy such as wind energy from the environment, achieving self-supply of electrical energy for MEMS, and meeting the requirement of without management and maintenance after installation. An overview of piezoelectric wind energy harvesting can help to connect the MEMS field and meet its self-supply needs. This paper presents a comprehensive review of state-of-the-art advances in piezoelectric wind energy harvesters (PWEH). The classification of piezoelectric materials is briefly introduced. The principle of its operation is introduced. It is divided into five categories by structure: bluff body, airfoil, flag, wind concentrator, and wind turbine structures. The research status of harvester has been discussed from four perspectives: structure, application, theoretical modeling, and signal processing. The existing literature is integrated, and the future development directions in three aspects: expanding application area, improving adaptive capabilities, and application-oriented system design are proposed. This paper provides references for people in the industry who are committed to structural innovation and performance enhancement.
... When air flow is the only source of energy generating the vibration, changing the shape of the bluff body is an appealing option to enhance performance. Abdelkefi et al. [104] suggested a galloping collecting model for an equilateral triangular bluff body and investigated the notion of energy harvesting for bluff bodies with various cross-sections (square, D-shaped, and triangular). Wang et al. [105] examined the energy harvesting of various top-angle cross-sections in a triangular cross-section bluff body and proved that obtuse isosceles triangles may be employed to effectively gather galloping energy. ...
Due to the great potential of rotary piezoelectric energy harvesters in environmental monitoring and energy harvesting, a great deal of research has been conducted by scholars. This paper presents a comprehensive review of the recent research progress of rotary piezoelectric energy harvesters in terms of literature background, excitation principles, practical applications and interface circuits. According to the different excitation methods, we divide the rotary piezoelectric energy harvester into centrifugal, impact, tensile (compression), magnetic and compound types, and describe and evaluate the different research results. Meanwhile the current potential applications of rotating piezoelectric energy harvesters can be divided into three categories: wearable devices, vehicle wheels and other applications, and the corresponding research progress is reviewed. Through the review and analysis of different excitation modes, application scenarios and the back-end energy interface circuits, the reference is improved for the design and research of the rotary piezoelectric energy harvester with high output performance. In addition, this paper also proposes future research directions and challenges.
... Unlike the lock-in phenomenon of VIV, the vibration intensity of a galloping system monotonically increases with the wind-speed increase. However, galloping normally occurs when a bluff body with sharp corners is under a moderate to high wind flow [19,[43][44][45]. In other words, the cut-in wind speed of a galloping system is usually high, making it not suitable for low wind-speed energy harvesting. ...
Small-scale wind energy harvesting based on flow-induced vibration mechanisms has attracted lots of research interest in recent years. Vortex-induced vibration (VIV) and galloping energy harvesters usually outperform each other in different wind speed ranges. To combine the advantages of VIV and galloping harvesters, this paper explored the idea of using a hybridized bluff body constituted of two cylindrical and one cuboid segment for wind energy harvesting. The total length of the hybridized bluff body was fixed. The cuboid segment length was varied to investigate the effect on the flow-induced vibration behavior of the bluff body. The results show that when the cuboid segment length is small, the bluff body exhibits VIV-like behavior in the low wind speed range and galloping-like behavior in the high-speed range. In the medium wind speed range, there appears galloping-VIV coupling. However, if the cuboid segment becomes large, the galloping-VIV coupling phenomenon disappears; the hybridized bluff body behaves just like a cuboid one and only exhibits galloping motion. In addition to experiments, CFD simulations were also conducted to provide more insights into the aerodynamics of the hybridized bluff body. The simulation results reveal that introducing hybridization into the bluff body changes the vorticity flow behind it and the vortex shedding behavior. The vortex shedding effect, in turn, affects the vibration of the bluff body, as well as the performance of the harvester.
... Abdelkefi et al. [15] presented an experimentally validated distributed-parameter GLM for galloping PWEHs and investigated the effects of the load resistance. Galloping PWEHs experience large amplitude oscillations, resulting in relatively large errors for these GLMs which neglect the effects of geometrical nonlinearity. ...
The interaction between vortex-induced vibration (VIV) and galloping could enhance the performance of wind energy harvesters. Though VIV-galloping interaction may cause large amplitude wind-induced vibrations, the effects of geometrical nonlinearity were not considered in the modeling of VIV-galloping interactive piezoelectric wind energy harvesters (PWEHs). In this work, based on the extended Hamilton’s principle, a geometrically nonlinear model (GNM) of cantilevered PWEHs with VIV-galloping interaction was derived. The model includes both the transverse and axial aerodynamic forces, and considers the effect of the rotation of the bluff body on the aerodynamic forces. The aerodynamic coefficients were extracted by a piecewise polynomial fitting in a relatively large range of angle of attack for the square cross-sectional bluff body. Two flexible PWEH prototypes were fabricated and tested in a small wind tunnel to verify the proposed model. After the mechanical damping ratio of the low-coupling piezoelectric energy harvester prototypes were identified based on purely electrical measurements, the steady-state root mean square voltages of the prototypes with increasing wind speed were worked out using geometrically linear model (GLM) and the proposed GNM, respectively, and then compared with experiments. Both models can accurately predict the VIV-galloping interaction, but GNM is much more accurate than GLM at a relatively high wind speed. The proposed GNM provides a powerful tool to develop VIV-galloping interactive PWEHs.
... C p = ε s 33 bl 1 /h p is the total capacitance of the piezoelectric patch. Θ = −2e 31 b(h s + h p + h ps ) is the electromechanical coupling coefficient [Abdelkefi et al., 2013b]. The total effective mass M can be expressed by M = (33/140)M m + M h , where M m and M h are the mass of the piezoelectric beam and the angle section head, respectively. ...
A high-performance wind-induced vibration energy harvester with an angle section head is designed. Experimental results show that the harvester has a wide frequency-locked/operating wind speed range. Experiments are carried out for the harvester with different angles and lengths of the angle section head. It is found that the reasonable design of the angle section head can benefit wind energy harvesting. In this study, the widest operating wind speed range of 13.4 m/s (from 6.6 m/s to 20 m/s) is experimentally demonstrated, and the maximum output power is 214.6 μW.
... For example, carbon nanotubes (CNTs), which possess unique thermal, electrical, and mechanical properties that are magnified at the nanoscale have been modeled as beam-like structures (Ceballes and Abdelkefi, 2021a). In modeling CNTs as nanobeams and beam-based systems, researchers have been able to analyze their static and/or dynamic responses under various axial and thermal loading conditions or other boundary conditions (Ceballes and Abdelkefi, 2021a;Ghaffari et al., 2019;Kong et al., 2009;Abdelkefi et al., 2013). For instance, Ghaffari et al., 2018, 2019 studied nanoscale mass sensors modeled as CNTs subjected to a thermal environment. ...
This research considers different methods in sensitivity analysis and uncertainty quantification applied to cylindrical tubes subject to three types of thermal load representation, namely, uniform, linear, and nonlinear in the radial direction. Sensitivity analysis techniques are used to quantify and rank the parameters that are most influential in altering the critical buckling temperatures, the post-buckled configuration amplitudes, and the natural frequencies in the pre- and post-buckling regimes. The uncertainty quantification and sensitivity analysis strategies show a great potential and usefulness in terms of determining the most influential input parameters for cylindrical tubes subject to thermal loads. Based on the set of nominal parameters in this study, it is shown that the length is the most sensitive parameter in altering the critical thermal buckling load. Additionally, it is demonstrated how uncertainty in the thermal load representation can lead to over or underestimation in both sensitivity analysis and uncertainty quantification findings. The outcome of this analysis can be utilized by other researchers in the design and optimization of cylindrical tubes in thermal environment.
... Originally, the researchers focused on the mechanism of conversion between wind-induced vibration energy of the piezoelectric transducers and electrical energy [34,35]. Recently, more and more scholars start to work on improving the energy harvesting performance, environmental adaptability, and structural reliability of the PWEHs. ...
The indirect-excitation piezoelectric wind energy harvesters have shown great potential in providing power to sensor network nodes as well as wireless electronic devices. To improve the weak power generation performance of the existing indirect-excitation harvesters, this paper proposes a joint-nested structure piezoelectric energy harvester (JNS-PWEH) for high-performance wind-induced vibration energy harvesting. The joint-nested structure is composed of a piezoelectric transducer, a cylindrical shell, and a rectangle-shaped spoiler. Unlike the most existing approaches adopted to enhance the energy harvesting via modifying the structural configuration of the shell, this JNS-PWEH realized a transition of poor-performance vortex-induced vibration to high-energy galloping vibration by introducing a downstream rectangle-shaped spoiler to interfere with the vortices induced by the shell. In this way, the vibration-enhanced shell will drive the piezoelectric transducer mounted inside to oscillate significantly, thus achieving indirect excitation and performance enhancement. The feasibility of the structure and principle of the JNS-PWEH was demonstrated via experimental studies. The results showed that the maximum overall voltage output performance of the JNS-PWEH was significantly improved by 1040% compared to the conventional single-cylinder PWEH due to the introduction of the joint nesting structure. At this point, the JNS-PWEH could output power of 2.22 mW at 300 kΩ and easily lit up at least 126 LEDs in 6.6 m/s, as well as displayed excellent charging speed in charging capacitors. On the other hand, it was demonstrated that the output performance of the JNS-PWEH could be enhanced by adjusting the width of the rectangle-shaped spoiler and the gap length between the joint-nested structure. In general, it illustrates a great benefit of the joint nested structure in enhancing the indirect-excitation PWEHs, which is expected to accelerate the practical application of the indirect-excitation PWEHs.
... To establish a mathematic model, the piezoelectric cantilever is usually assumed to follow the Euler-Bernoulli beam theory. A common method for modeling the VIV energy harvesting system utilizes the distributed parameter model considering the first mode of vibration based on mode shape discretization [56,57]. Compared with the single-degree-offreedom lumped parameter model, the distributed parameter model considers the distribution of piezoelectric layers and the rotational inertia of the attached cylinder and thus has higher accuracy. ...
Low-speed wind energy has potential to be captured for powering micro-electro-mechanical systems or sensors in remote inaccessible place by piezoelectric energy harvesting from vortex-induced vibration (VIV). Conventional theory or finite-element analysis mostly considers a simple pure resistance as interface circuit because of the complex fluid-solid-electricity coupling in aeroelastic piezoelectric energy harvesting. However, the output alternating voltage should be rectified to direct voltage to be used in practical occasions, where the theoretical analysis and finite-element analysis for complex interface may be cumbersome or difficult. To solve this problem, this paper presents an equivalent circuit modeling (ECM) method to analyze the performance of vortex-induced energy harvesters. Firstly, the equivalent analogies from the mechanical and fluid domain to the electrical domain are built. The linear mechanical and fluid elements are represented by standard electrical elements. The nonlinear elements are represented by electrical non-standard user-defined components. Secondly, the total fluid-solid-electricity coupled mathematical equations of the harvesting system are transformed into electrical formulations based on the equivalent analogies. Finally, the entire ECM is established in a circuit simulation software to perform system-level transient analyses. The simulation results from ECM have good agreement with the experimental measurements. Further parametric studies are carried out to assess the influences of wind speed and resistance on the output power of the alternating circuit interface and the capacitor filter circuit. At wind speed of 1.2 m/s, the energy harvester could generate an output power of 81.71 μW with the capacitor filter circuit and 114.64 μW with the alternating circuit interface. The filter capacitance is further studied to ascertain its effects on the stability of output and the settling time.
... Abdelkefi et al investigated energy harvester from transverse wake galloping [8], and they attached a piezoelectric transducer on the harvester to generate energy from the air. Abdelkefi and Zhimiao Yan et al [9,10] employed piezomagnetic transduction mechanisms to improve output power and broadband resonance frequency, which was verified by experiments in the wind tunnel. ...
Efficient energy use to be transformed into electricity for small power devices has drawn increasing attention. A piezoelectric energy harvester is proposed to convert flow energy underwater to electrical energy. The harvester consists of the connecting device, springs, base, bluff body, piezoelectric cantilever beam and displacement sensor. The output voltage is derived from the flow-solid-electric coupling equations, including a nonlinear van der Pol equation, a linear equation of structural vibration and a piezoelectric equivalent circuit. Vibration response and output performance are obtained based on the finite central difference method. The theoretical results show that the vibration frequency, amplitude and average power increase with the limited water velocity. Furthermore, it is demonstrated that a proper selection of structure mass and load resistance can improve average harvested power for the available water velocity. Finally, the experimental prototype is fabricated to test piezoelectric generator performance at different water speeds, which shows good agreement with the theoretical results. This work provides a significant guide for the underwater use of piezoelectric energy harvesters.
... Also, a two-degree-of-freedom (2DOF) piezoelectric energy harvester with magnetic interaction is found to better perform than the conventional single-degree-of-freedom (SDOF) harvesters [33]. The output power is found to be inversely proportional to the transverse displacement amplitudes [34]. ...
A triboelectric vibration energy harvester under rotational magnetic excitation for wind energy harvesting applications is developed. The triboelectric beam generates electricity using the magnetic impact-induced vibration. The triboelectric energy harvester consists of a clamped-clamped (CC) beam embedded in an outer case. The lower side of the CC-beam acts as an upper electrode that will undergo a contact-separation motion with another lower electrode with a bonded Polydimethylsiloxane (PDMS) insulator. A permanent magnet will be attached to the CC-beam's upper side and will face another magnet attached to a rotation rigid shaft blade at the same polarity. While the fan rotates, a repulsive magnetic force will be created between the two magnets that will excite the CC-beam, lead to the contact-separation motion, and generation of electricity. A single degree of freedom model is presented and simulated to extract the dynamic behavior and the generated electrical signal. The relationship between the output voltage and excitation rotational frequency is analyzed. The relationship between the output voltage and the distance between magnets and its effect on the bandwidth is also discussed. The effect of the surface charge density on the generated output voltage signal is examined. The rotational wind triboelectric energy harvester can effectively scavenge wind energy.
... Polynomial representation of the galloping force. co-authors [15,23,[35][36][37][38] highlighted experimentally and numerically the influences on the effectivenesses of galloping energy harvesters of the tip body shape, the flow features (e.g., the Reynolds number), the accuracy of the aerodynamic force coefficients, and the inclined angle of the tip body relative to wind flow. Yang et al. [25] presented wind tunnel experiments to study the effectiveness of energy harvesters with several different cross-sections (e.g., square, rectangular, and triangular) as galloping bluff bodies. ...
Energy harvesting based on transverse galloping of a square cylinder has been widely studied while the effects of angle of attack and corner shape remain unclear. This study proposes to explore the impacts of these two parameters on the characteristics and effectiveness of square-based galloping energy harvesting systems using a coupled fluid–structure-electrical model. It is demonstrated that the onset speed of instability is dependent on the electrical load resistance. Additionally, the load resistance value corresponding to the maximum onset speed of galloping is inversely proportional to the natural frequency of the energy harvester. Further, the onset wind speed of instability and the dynamic response of the energy harvester are largely affected by the angle of attack and corner shape. The rounded corners make the onset velocity less sensitive to the angle of attack. The considered square cylinders with different corner shapes exhibit the largest transverse displacements at the angle of attack α0 = 0°, while the displacements at α0 = 2° are only slightly lower than those at α0 = 0°. In general, the rounded corners slightly decrease the displacements and power outputs of the harvester. However, the rounded corners enhance the robustness of the harvester by making its performance less sensitive to the angle of attack within α0 = 0° ~ 6°. It is also shown that the type of instability is strongly dependent on the angle of attack and corner shape which may result in the presence of unexpected bifurcations, such as the subcritical and saddle-node ones.
This paper presents a magnetically coupled double cantilever beam-based piezoelectric energy harvester. Two square-shaped bluff bodies are attached to the tip of the beams to induce galloping-based oscillation in the proposed system. Spatio-temporal electro-mechanical equations of motion are developed using the Lagrange principle and discretized to their temporal form using generalized Galerkin’s method. 4th order Runge-Kutta method-based MATLAB solver (ode45) is used to solve these equations of motion and obtain numerical results. A prototype of the system is developed and experimented in a wind tunnel to support the numerical findings. Three wind speed regions (light air, light breeze, and gentle breeze) based on the Beaufort wind force scale are considered for getting a detailed insight into the system dynamics. Periodic, quasi-periodic, and chaotic oscillations are observed depending on different coupling conditions and wind speeds. Typical hopf bifurcation, Torus 3 bifurcations occur in the system due to galloping and magnetic repulsive force. Parametric studies are conducted for each wind speed region considering the load resistances and distance between the permanent magnets. Significant improvement in power output can be found for light air and gentle breeze regions with the magnetically coupled system than the uncoupled system (without magnetic interaction), whereas the uncoupled system performs better in the light breeze region.
With the increase of low-powered electronic devices, there is growing social interest in environmentally friendly energy sources capable of replacing batteries. In this study, a flutter-driven piezoelectric nanogenerator (FD-PENG) using electrospun PVDF nanofiber was fabricated to create a wind-energy harvesting device. The FD-PENG was composed of a PVDF nanofiber mat (active layer) and Al foil (electrodes), with these components encapsulated by polyethylene terephthalate (PET) film using an ordinary coating machine. The short-circuit current generated from the FD-PENG during a bending test was significantly enhanced by optimizing the electrospinning process and with the proper alignment of the PVDF nanofibers. The dynamic behavior of the FD-PENG with respect to various wind speeds was systematically analyzed by categorizing its motion into four distinct modes. The flapping mode, in which the FD-PENG displays the largest amplitude of oscillation, was induced when wind speed was in the range of \(3-4~\mathrm{ m}/{\text{s}}\). The FD-PENG generated open-circuit voltage of approximately 10 V at a wind speed of \(4~\mathrm{ m}/{\text{s}}\) and exhibited excellent durability over 10,000 cycles. Using a single FD-PENG, maximum power approaching 14.66 μW was achieved under an external load of 1.1 MΩ. Furthermore, the wind speed inducing the flapping mode was modulated by the shape of the FD-PENG. The results here show that the wind energy harvester can be applied at a wide range of wind speeds by modifying the shape of the FD-PENG.
Piezoelectric energy harvester (PEH) is being world widely studied by many researchers due to their excellent advantages over batteries. Therefore, how to improve the capability of energy harvesting has become a hot research topic. In this study, based on the theory that the electromechanical coupling coefficient is proportional to the difference of mode shape slopes at the two ends of a piezoelectric sheet made of macro fiber composite, a modified cantilever structure consisting of two segments is proposed. The piezoelectric sheet is affixed on the segment close to the fixed end, while the segment containing the free end is rotated by 90° along its axial direction. The mode shape of the cantilever structure is calculated based on the Euler-Bernoulli beam theory. Prototypes of the conventional and modified PEHs are fabricated and tested. Compared to the conventional one, the experimental result of the modified PEH demonstrates that the electromechanical coupling coefficient is enhanced by 600%, and the output power is increased by more than 300%. The proposed PEH is simple, highly efficient, and easy-realized.
Wind-induced vibration energy harvesters have attracted increasing attention due to their unique dynamic characteristics and excellent energy harvesting performance. In this study, two types of magnetic energy harvesters, namely the magnetic attraction energy harvester (A-GEH) and the coupled magnetic attraction and repulsion energy harvester (A&R-GEH), were designed and their electromechanical coupling analysis models were established. The results showed that the magnetically coupled energy harvesters can adjust the operating wind speed range and increase the energy harvesting capability by varying the placement of the magnetic poles and the magnetic moment. Furthermore, the established analysis model accurately predicted the results of the wind tunnel experiments. The output power of the energy harvesters was evaluated by illuminating LED bulbs, demonstrating the potential for self-powering small wireless sensors. Under an experimental wind speed of 5.1 m s ⁻¹ and a vertical distance Δ y = 12 mm between the magnets, the A-GEH and A&R-GEH showed an increase in output power of 356.854% and 365.488%, respectively, compared to a general energy harvester without magnetism. In conclusion, this study provides a framework for the analysis and design of magnetic-coupled wind-induced vibration energy harvesters.
The development of smart Internet-of-Things (IoT) solutions requires sensor nodes to be placed at different locations of monitored structures. Wireless solutions are quite attractive because of their simplicity although requiring for local energy supply. In this context, this study investigates the influences of the predefined angle of attack on the piezoelectric energy harvesting based on transverse galloping of different bluff bodies. The investigation is based on a lumped electro-aero-mechanical model with linear electrical and mechanical properties and nonlinear aerodynamic forces evaluated using the quasi-steady theory. The performances of energy harvesters with six different bluff bodies are analyzed at various predefined angles of attack: four rectangular cross-sections with different width-to-height ratios (i.e., b/d), one trapezium section, and one equal angle section. The main purpose is to understand the sensitivity of various bluff body-based energy harvesters on the predefined angle of attack, and further suggest a bluff body-based energy harvester that is robust to the predefined angle of attack. The results show that the response is quite dependent on the characteristic of the electro-mechanical system and the bluff body cross-section and angle of attack. In all cases, the load resistance should be tuned to maximize energy production. The largest vibration amplitude (i.e., largest power output) is predicted for the rectangular bluff body with b/d = 1.0 at a 0° angle of attack. However, its performances are quite dependent on the angle of attack, resulting in a zero-power output for an angle of attack exceeding 4°. A rectangular bluff body with b/d within 1.62 to 2.5 exhibits a reduced energy production compared with b/d = 1.0 at a 0° angle of attack but better robustness varying the angle of attack. Finally, the trapezium and the angle bluff bodies are not suitable for energy harvesting due to their very high onset velocities within the considered range of angles of attack.
The technology of using galloping piezoelectric energy harvester (GPEH) to obtain low velocity hydrokinetic energy has been developed. The surface roughness of the bluff body can affect the performance of GPEH and can be designed to suit requirements. This paper investigates a GPEH with two bluff bodies in elliptical cylinder shape and different surface roughness is considered. The vorticity and pressure with different surface roughness are analyzed by numerical simulation. The quasi-steady-state assumption is applied to obtaining hydrodynamic force. A piecewise distributed parameter model of GPEH is established and the approximate analytical solutions for model is derived. The related experiments are conducted and the results verify the model. The amplitudes of elliptical cylinders with short diameters of 20 mm and 25 mm are reduced by 22.05% and 31.08%, respectively, when surface is changed from its original state to a roughness of 6.3 μm. When flow velocity increases from 0.49 m/s to 0.55 m/s, the decline ratio in maximum output power falls from 61.35% to 43.6% for short diameter of 20 mm and from 88.15% to 54.55% for short diameter of 25 mm. Additionally, the surface roughness is positively correlated with the onset velocity and has an effect on optimal resistance.
This chapter focuses on the fluid‐induced piezoelectric energy harvesters and introduces the types of fluid‐induced piezoelectric energy harvesters, mainly including rotating‐type, flutter‐type, galloping‐type, and vortex‐excited vibration types. Then, this chapter highlights water vortex shedding‐induced and aeroacoustics‐driven jet‐stream piezoelectric energy harvesters and discusses their working principle and output performance.
In this study, we proposed a crossing angle adjustable galloping-based piezoelectric energy harvester (CAGPEH) configured with a lambda-shaped beam to improve the energetic performance. The proposed structure can overcome the limitation of the installation capability of a conventional galloping energy harvester with a single cantilever beam by varying the crossing angle. This structure can change the crossing angle between primary and secondary beams so that the bluff body always faces the changing wind direction to ensure an efficient harvesting performance. A distributed parameter model was established using Euler-Bernoulli beam theory and Lagrange method, and a series of numerical analyses was performed to uncover the dynamical behaviors of the aero-electromechanical coupled system. The first two modes were considered to obtain a comprehensive understanding of the dynamic behaviors at different crossing angles. We validated the theoretical model through amplitude and output voltage comparisons between numerical and experimental results. The results show that a larger crossing angle and a smaller length proportional factor of the primary and secondary beams help reduce the critical wind velocity. The results show that a significant increase rate of 103% in the overall average output power (OAOP) can be achieved with a crossing angle of 30° and a proportional factor of 0.6. It is expected that the CAGPEH can help develop self-power systems for applications in wireless sensor systems.
The purpose of this paper is to investigate the effect of boundary flexibility on the performance of piezoelectric vibration energy harvester (PVEH) beam systems, which has not been studied comprehensively in the literature despite its importance. The coupled electromechanical equations of motion of a piezoelectric cantilever beam with a tip mass are established, with the base boundary constrained by translational and rotational springs. An exact closed-form solution of the frequency response function (FRF) of the PVEH is obtained by the distributed transfer function method (DTFM). The DTFM is a systematic powerful tool for the dynamic analysis of distributed parameter continua with non-classical boundary conditions, intermediate constraints, coupled fields, and non-proportional damping without adding much complexity to the solution formulation. Moreover, the DTFM computes the derivatives of the response, that is, the strains, which are required in the electromechanical coupling formulation, simultaneously without any differentiation. Numerical results showing the effects of boundary flexibility on energy harvesting efficiency are presented. A first-order rational function relating the boundary stiffness parameters and the harvesting efficiency is determined by nonlinear curve fitting of the calculated data. Physical insights and applicability of this analytical function for end-of-line quality check of the boundary of PVEH are discussed.
For the last few decades, piezoelectric materials have been playing a fundamental role in the field of energy harvesting. These materials are capable of driving micro-electromechanical systems by absorbing the energy from the surroundings thanks to their properties to generate a voltage differential once exposed to a deformation or stress field.
The increasing interest in the industrial world for a very large and distributed network of sensors for monitoring and IoT representations of systems and processes have brought energy harvesting in a central role for those applications where the energy supply can be a critical issue because of operative conditions, system complexity and a strict limit on the weight that harnessing and batteries can add to the specific system.
Thus, the strict requirements in the aerospace industry lead to the formulation of various novel energy harvesting mechanisms, one of which is the piezoelectric energy harvesting mechanism.
Piezoelectric transducers are used to describe the phenomenon of energy generation as the energy transformation from the operating environment into electric energy that can be used on the premises for actuation or deposited in batteries for use in the future. Due to lightweight engineering designs, leading to micro-/nano-powered electronic circuits, the world is changing to low-powered electronic devices. Many researchers concentrated on the self-powered use of the piezoelectric energy harvester over battery use. These harvesters are suitable for use in microelectronic systems, smart buildings, tracking of structural health, and as wireless sensor systems for sub-orbital missions during recent technical progress.
Many scientists have highlighted the relevance of piezoelectric device modeling. In linear and non-linear situations, for 3D solids, as well as structural elements, such as plate and shell, numerous technologies have been developed. By taking energy from the surroundings, they can harvest valuable electricity that can be used for electronics or deposited in batteries for later purposes. A piezoelectric aeroelastic energy harvester consumes airflow energy and transforms it into usable electrical energy, which is analyzed in this book.
When the Fluid–Structure Interaction (FSI) problem is considered it is necessary to consider the entire dynamics of the structure and flow together leading to the concept of the aeroelastic system later introduced in this book. From a mathematical point of view, this relation happens because the state of the structural system is dictated by the flow pressure whereas the fluid state is influenced by the structural system which is seen as a
boundary condition for the flow governing equations.
This results in an inherently non-stationary and rather dynamic phenomenon and cannot be studied anymore by separate consideration of the structure and flow. It is self-evident that the mean velocity of the flow plays a critical role in the dynamics of an aeroelastic system where different kind of structural excitation and instability phenomena can happen. Both the flow excitation of the structures and the dynamical aeroelastic instability phenomena can be used for energy harvesting purposes by means of PZT
devices and this will be deeply analyzed in the present book.
Thus, in this book, different strategies to harvest useful electrical energy by absorbing the energy from the surroundings via PZT materials are discussed in detail with a particular focus on those where the energy is gathered from a fluid–structure interaction. Particular emphasis is placed on demonstrating correct modeling for the unsteadiness of aerodynamics. Indeed, the aerodynamic model is a critical ingredient for a sound prediction of the linear behavior of an aeroelastic system: without correct aerodynamic
modeling is not possible a correct evaluation of the nonlinear behavior which is at the base of most of the energy harvesters that will be analyzed.
These harvesters can be deployed in many locations, such as urban areas, high wind areas, ventilation outlets, rivers, ducts of buildings, lifting components in aircraft structures, etc. These harvesters can be used to power small electronic devices including health monitoring sensors, medical implants, data transmitters, wireless sensors, and cameras.
Energy harvesting has seen increasing concern over the last few years and the research volume has continued to rise over the last few decades. In this chapter, mechanisms for energy harvesting are elaborated in detail. Moreover, different sources of energy harvesting are analyzed. These techniques and methodologies are widely used in self-powered electronic devices, i.e., wireless sensors, biomedical devices, calculators, bluetooth devices, military control facilities, and built-in instrumentation.
In an aeroelastic system, the fluid flow interacts with the structure/body of the system, also known as fluid–structure interaction. When an aeroelastic system is subjected to axial flow, it starts oscillating abruptly at a certain velocity called flutter velocity; this phenomenon is known as limit cycle oscillations (LCOs). In this chapter, mechanisms and physics behind LCOs are studied as well. Moreover, the aeroelastic systems based on LCOs are analyzed in this chapter.
In fluid mechanics (dynamics), vortex-induced vibrations are motions induced on structures interacting with an external fluid flow, produced by or motion producing periodical irregularities on this flow. In this chapter, the physics behind the vortex-induced vibrations is elaborated. Different mechanisms for this phenomenon are studied in detail. Moreover, energy harvesting techniques for the systems having fluid–structure interaction based on vortex-induced vibrations are analyzed.
In fluid mechanics (dynamics), a secondary class of instabilities related to oscillations is known as galloping. Galloping in general is a low-frequency with high amplitude motion in an uncoupled mode of vibration in a plane perpendicular to the wind direction. In this chapter, the types and physics behind the galloping mechanisms are elaborated in detail. Moreover, aeroelastic energy harvesting based on galloping phenomena is explained as well.
In this paper, we studied the homoclinic bifurcation and nonlinear characteristics of a bistable piezoelectric energy harvester while it is concurrently excited by galloping and base excitation. Firstly, the electromechanical model of the energy harvester is established analytically by the energy approach, the Kirchhoff's law and quasi-steady hypothesis. Then, by the Melnikov method, the threshold for underlying snap-through in the system is derived, and the necessary conditions for homoclinic bifurcation and chaos are presented. The threshold is a determinant for the occurrence of high-energy oscillation. The analysis results reveal that the wind speed and the distance between magnets could affect the threshold for inter-well chaos and high energy oscillation. Finally, numerical simulation and experiments are carried out. Both results from numerical simulation and experiment support the theoretical prediction from Melnikov theory. The study could provide a guideline for the optimum design of the bi-stable piezoelectric energy harvester for wind and vibration in practice.
A tubular linear vibration generator applied to the energy harvester based on vortex‐induced is proposed and analyzed in this paper. First, the permanent magnet of the generator is placed on the inner side of the winding, and the outer side of the winding is improved by adding magnetically permeable housing to increase the generated power. Then, the optimal magnet magnetization method, size of the winding coil, wire diameter, and housing material are evaluated by finite element analysis. Finally, the prototype using radial magnets is fabricated and fixed on the energy harvester. The vibration displacement, the induced voltage of the coil, and the generated power at different water velocities are measured. The generators with different permeable housings are fabricated to verify the accuracy of the theory. The experiment results show the maximum average power harvested is 5.5 mW of the TVLG at the water speed of 0.7 m/s, for the coil of 0.2 mm wire diameter, 8 cm height, and 2,000 turns. Under the effective water speeds, the power obtained by the generator with magnetically permeable housing is more than 70% higher than that obtained by the generator without housing. A tubular linear vibration generator applied to the energy harvester based on vortex‐induced is proposed and analyzed in this paper. The optimal magnet magnetization method, size of the winding coil, wire diameter, and housing material are evaluated by finite element analysis. Under the effective water speeds, the experimental power obtained by the generator prototype with magnetically permeable housing is more than 70% higher than that obtained by the generator without housing.
Energy harvesting from wind-induced vibrations is considered to be a promising solution for the power requirements of wireless sensor nodes. This paper proposes an enhanced piezoelectric wind-induced vibration energy harvester (EPWEH) via the interplay between the cylindrical shell and diamond-shaped baffle to improve reliability, environmental adaptability, and power generation performance. Different from the most existing hybrid piezoelectric wind energy harvesters where the interaction of vortex-induced vibration and galloping was mainly implemented by altering the cylinder geometry, this EPWEH realized the coupling between vortex-induced vibration and galloping through introducing a downstream diamond-shaped baffle to change the aeroelastic instability of the cylinder. Besides, the pre-bending vibrator only subjected to the unidirectional compressive stress was employed and embedded inside the hollow cylinder, thus avoiding the drawbacks of bidirectional deformation of the traditional piezoelectric vibrator and direct contact between piezoelectric element and fluid. The feasibility of the structure and principle of the EPWEH was proved through a series of experiments. The experimental results demonstrated that the compound-embedded structure led to a coupling phenomenon of VIV and galloping on the cylindrical shell. Besides, it exhibited that the structural parameters brought a significant impact on the vibration characteristics, power generation performance, and wind speed bandwidth of EPWEH as well. Thanks to the performance improvement effect of the baffle, the EPWEH could reach a maximum voltage output enhancement of 910.1% and provide a maximum output power density of 5.493 mW/cm³ at an optimal load resistance of 200 kΩ. It is expected that this compound-embedded structure can provide a reference for performance improvement of the existing PWEHs.
Motion in nature is usually a low-frequency vibration such as walking, running, swinging arms, and so on, but traditional piezoelectric cantilever structures are inefficient at harvesting energy from low-frequency vibrations. T in the environment. To overcome this, a novel piezoelectric generator was designed. A cantilevered bimorph with a tip mass and a pair of preloading springs were fixed on its base to form a nonlinear piezoelectric generator. The energy transmission in the structure was analyzed. The harvester was modeled as a Euler–Bernoulli beam, and the piezoelectric material was assumed to be linear. The bending vibration was calculated using the Rayleigh–Ritz procedure, and the frequency characteristics of the output voltage were analyzed under different preloading distances. It was found that changing the preloading of the spring helped reduce the natural frequency of the cantilever, which facilitated conversion of ambient low-frequency vibrations into electrical energy. Then, the characteristics of low frequency energy harvesting were investigated experimentally. The theoretical results were consistent with the experimental data; moreover, the resonance frequency, which changes with the preloading distance, reduced from 43 to 35 Hz when the preloading distance was increased from 0 to 1 mm. In this paper, an effective structure to control the resonant frequency is proposed and its motion equation stated. The structure has potential for applications in predicting the effect of preloading distance on resonance frequency.
In this paper uncertainty-based design optimization of a micro energy reclamation device is presented. The goal is to optimally design a Microelectromechanical Systems based device to extract maximum power from externally introduced vibrations. This microstructure consists of an array of piezoelectric composite cantilever beams connected to a free standing mass. Each cantilever beam undergoes deformation when subjected to external base vibrations. This deformation induces a mechanical strain in the beam resulting in the conversion to electric voltage due to the piezoelectric effect. In case of microstructures, uncertainties in geometry as well as material properties are large and therefore may have significant effects on the mechanical behavior. In the present paper uncertainties in geometry and material properties are considered. A description of uncertainties via bounds on the uncertainty variables is adopted. Uncertainty-based design optimization is carried out using the anti-optimization technique.
The concept of harvesting energy from a circular cylinder undergoing
vortex-induced vibrations is investigated. The energy is harvested by
attaching a piezoelectric transducer to the transverse degree of
freedom. Numerical simulations are performed for Reynolds numbers (Re)
in the range 96≤Re≤118, which covers the pre-synchronization,
synchronization, and post-synchronization regimes. Load resistances (R)
in the range 500Ω≤R≤5MΩ are considered. The results
show that the load resistance has a significant effect on the
oscillation amplitude, lift coefficient, voltage output, and harvested
power. The results also show that the synchronization region widens when
the load resistance increases. It is also found that there is an optimum
value of the load resistance for which the harvested power is maximum.
This optimum value does not correspond to the case of largest
oscillations, which points to the need for a coupled analysis as
performed here.
Unmanned air vehicles (UAVs) and micro air vehicles (MAVs) constitute unique application platforms for vibration-based energy harvesting. Generating usable electrical energy during their mission has the important practical value of providing an additional energy source to run small electronic components. Electrical energy can be harvested from aeroelastic vibrations of lifting surfaces of UAVs and MAVs as they tend to have relatively flexible wings compared to their larger counterparts. In this work, an electromechanically coupled finite element model is combined with an unsteady aerodynamic model to develop a piezoaeroelastic model for airflow excitation of cantilevered plates representing wing-like structures. The electrical power output and the displacement of the wing tip are investigated for several airflow speeds and two different electrode configurations (continuous and segmented). Cancelation of electrical output occurs for typical coupled bending-torsion aeroelastic modes of a cantilevered generator wing when continuous electrodes are used. Torsional motions of the coupled modes become relatively significant when segmented electrodes are used, improving the broadband performance and altering the flutter speed. Although the focus is placed on the electrical power that can be harvested for a given airflow speed, shunt damping effect of piezoelectric power generation is also investigated for both electrode configurations.
The process of acquiring the energy surrounding a system and converting it into usable electrical energy is termed power harvesting. In the last few years, there has been a surge of research in the area of power harvesting. This increase in research has been brought on by the modern advances in wireless technology and low-power electronics such as microelectromechanical systems. The advances have allowed numerous doors to open for power harvesting systems in practical real-world applications. The use of piezoelectric materials to capitalize on the ambient vibrations surrounding a system is one method that has seen a dramatic rise in use for power harvesting. Piezoelectric materials have a crystalline structure that provides them with the ability to transform mechanical strain energy into electrical charge and, vice versa, to convert an applied electrical potential into mechanical strain. This property provides these materials with the ability to absorb mechanical energy from their surroundings, usually ambient vibration, and transform it into electrical energy that can be used to power other devices. While piezoelectric materials are the major method of harvesting energy, other methods do exist; for example, one of the conventional methods is the use of electromagnetic devices. In this paper we discuss the research that has been performed In the area of power harvesting and the future goals that must be achieved for power harvesting systems to find their way into everyday use.
Recently, piezoelectric cantilevered beams have received considerable attention for vibration-to-electric energy conversion. Generally, researchers have investigated a classical piezoelectric cantilever beam with or without a tip mass. In this paper, we propose the use of a unimorph cantilever beam undergoing bending–torsion vibrations as a new piezoelectric energy harvester. The proposed design consists of a single piezoelectric layer and a couple of asymmetric tip masses; the latter convert part of the base excitation force into a torsion moment. This structure can be tuned to be a broader band energy harvester by adjusting the first two global natural frequencies to be relatively close to each other. We develop a distributed-parameter model of the harvester by using the Euler-beam theory and Hamilton's principle, thereby obtaining the governing equations of motion and associated boundary conditions. Then, we calculate the exact eigenvalues and associated mode shapes and validate them with a finite element (FE) model. We use these mode shapes in a Galerkin procedure to develop a reduced-order model of the harvester, which we use in turn to obtain closed-form expressions for the displacement, twisting angle, voltage output, and harvested electrical power. These expressions are used to conduct a parametric study for the dynamics of the system to determine the appropriate set of geometric properties that maximizes the harvested electrical power. The results show that, as the asymmetry is increased, the harvester's performance improves. We found a 30% increase in the harvested power with this design compared to the case of beams undergoing bending only. We also show that the locations of the two masses can be chosen to bring the lowest two global natural frequencies closer to each other, thereby allowing the harvesting of electrical power from multi-frequency excitations.
The field of power harvesting has experienced significant growth over the past few years due to the ever-increasing desire to produce portable and wireless electronics with extended lifespans. Current portable and wireless devices must be designed to include electrochemical batteries as the power source. The use of batteries can be troublesome due to their limited lifespan, thus necessitating their periodic replacement. In the case of wireless sensors that are to be placed in remote locations, the sensor must be easily accessible or of a disposable nature to allow the device to function over extended periods of time. Energy scavenging devices are designed to capture the ambient energy surrounding the electronics and convert it into usable electrical energy. The concept of power harvesting works towards developing self-powered devices that do not require replaceable power supplies. A number of sources of harvestable ambient energy exist, including waste heat, vibration, electromagnetic waves, wind, flowing water, and solar energy. While each of these sources of energy can be effectively used to power remote sensors, the structural and biological communities have placed an emphasis on scavenging vibrational energy with piezoelectric materials. This article will review recent literature in the field of power harvesting and present the current state of power harvesting in its drive to create completely self-powered devices.
Power consumption is a critical concern of many sensors used in diversified applications, especially where the replacement of batteries is impossible or inconvenient. Strain energy harvesting technique is an attractive approach to solve this problem using piezoelectric materials. The feasibility of a self-powered piezoelectric microaccelerometer system using lead zirconate titanate (PZT) thin film is studied in this paper. Since the electromechanical coefficient d 33 of PZT is larger than d 31 , and the transverse (33 mode) mode is also easier to fabricate, our design and analysis are focused on the transverse mode in constructing the PZT-based self-powered microsystem. The PZT-based cantilever structure with interdigitated electrodes and silicon seismic mass at the free end are designed to have specific resonance frequencies ranging from tens to thousands of hertz. The capability of energy storage and acceleration sensitivity in the proposed microaccelerometer are concurrently evaluated. A trade-off exists between these two major functions and the desirable operating frequency of the proposed system, i.e., the compromise depends on the demands of particular applications.
This paper reviews deposition, integration, and device fabrication of
ferroelectric PbZrxTi1-xO3 (PZT) films for
applications in microelectromechanical systems. As examples, a piezoelectric
ultrasonic micromotor and pyroelectric infrared detector array are presented.
A summary of the published data on the piezoelectric properties of PZT thin
films is given. The figures of merit for various applications are discussed.
Some considerations and results on operation, reliability, and depolarization
of PZT thin films are presented.
Double blind, partial crossover.
To evaluate the analgesic activity of a novel cranial electrostimulus in people with spinal cord injury (SCI).
Hereward College, a residential centre that provides educational facilities for students with disabilities.
Subjects with SCI experiencing chronic pain were randomly assigned into two groups, one of which received sham and the other transcranial electrostimulation treatment (TCET) on two occasions daily for four successive days. After a 'wash-out' period of 8 weeks all subjects returned and received the identical stimulus that the treated cohort received on the first arm of the study.
Pain measurements applied before and after each session indicated that the pain decreased in the treated group to 51% of that reported at the commencement of treatment; reported pain intensity did not decrease significantly in the sham treated subjects. The same (sham) subject group reported experiencing 59% of the pain at the end of the second arm of the study (TCET) as on the first arm (sham). No significant differences were determined between the mood of all subjects estimated before and after each sham or TCET treatment session. The reported analgesic, and combined antidepressant and anxiolytic drug use in subjects receiving TCET on the second arm of the study, was 46% and 53% respectively of the average pre-study drug use. No similar decrease in the use of the drugs was noted in the same subjects after sham treatment on the first arm of the study. Salivary cortisol determinations made prior to and after each sham and treatment session implicated this corticoid in the pain-relieving mode of action of the treatment, but could not be associated with any changes in mood. Subjects receiving TCET had significantly higher urinary 3-methoxy-4-hydroxy-phenylglycol (MHPG) output after the TCET treatment period than sham stimulation, implicating increased central noradrenaline (NA) metabolism in the observed effects.
The subjects reported less pain during, and immediately after receiving this transcranial treatment, although they were using less medication than when receiving sham treatment.
The concept of harvesting energy from transverse galloping oscillations of a bluff body with different cross-section geometries is investigated. The energy is harvested by attaching a piezoelectric transducer to the transverse degree of freedom of the body. The power levels that can be generated from these vibrations and the variations of these levels with the load resistance, cross-section geometry, and freestream velocity are determined. A representative model that accounts for the transverse displacement of the bluff body and harvested voltage is presented. The quasi-steady approximation is used to model the aerodynamic loads. A linear analysis is performed to determine the effects of the electrical load resistance and the cross-section geometry on the onset of galloping, which is due to a Hopf bifurcation. The normal form of this bifurcation is derived to determine the type (supercritical or subcritical) of the instability and to characterize the effects of the linear and nonlinear parameters on the level of harvested power near the bifurcation. The results show that the electrical load resistance and the cross-section geometry affect the onset speed of galloping. The results also show that the maximum levels of harvested power are accompanied with minimum transverse displacement amplitudes for all considered (square, D, and triangular) cross-section geometries, which points to the need for performing a coupled analysis of the system.
We perform a sensitivity analysis of a piezoaeroelastic energy harvester consisting of a pitching and plunging rigid airfoil supported by flexural and torsional springs with a piezoelectric coupling attached to the plunge degree of freedom. We employ the nonintrusive formulation of the polynomial chaos expansion in terms of the multivariate Hermite polynomials to quantify the effects of variations in the load resistance, the eccentricity (distance between the center of mass and the elastic axis), and the nonlinear coefficients of the springs on the harvested power and the pitch and plunge amplitudes. As a first step, the normal form of the dynamics of the system near the Hopf bifurcation is used to select parameters that ensure a supercritical instability and maximize the generated power. The results show that the harvested power can be mostly affected by the eccentricity. Moreover, decreasing the nonlinear coefficient of the torsional spring results in a decrease in the pitch amplitude and an increase in the plunge amplitude and hence the harvested power. These results give guidance for optimizing and assessing the uncertainty in the performance of piezoaeroelastic energy harvesters.
We investigate energy harvesting from vortex-induced vibrations of a freely moving rigid circular cylinder with a piezoelectric transducer attached to its transverse degree of freedom. The power levels that can be generated from these vibrations and variations of these levels with the freestream velocity are determined. A mathematical model that accounts for the coupled lift force, cylinder motion, and harvested voltage is presented. Linear analysis is performed to determine the effect of the electrical load resistance of the transducer on the natural frequency of the cylinder and the onset of synchronization (the shedding frequency is equal to the cylinder oscillating frequency) region. The impact of the nonlinearities on the cylinder response and harvested energy is investigated. The results show that the load resistance shifts the onset of synchronization to higher freestream velocities. For two different system parameters, the results show that the nonlinearities result in a hardening behavior for some values of the load resistance.
The concept of exploiting galloping of square cylinders to harvest energy is investigated. The energy is harvested by attaching a piezoelectric transducer to the transverse degree of freedom. A representative model that accounts for the coupled cylinder displacement and harvested voltage is used to determine the levels of the harvested power. The focus is on the effect of the Reynolds number on the aerodynamic force, the onset of galloping, and the level of the harvested power. The quasi steady approximation is used to model the aerodynamic loads. A linear analysis is performed to determine the effects of the electrical load resistance and the Reynolds number on the onset of galloping, which is due to a Hopf bifurcation. We derive the normal form of the dynamic system near the onset of galloping to characterize the type of the instability and to determine the effects of the system parameters on its outputs near the bifurcation. The results show that the electrical load resistance and the Reynolds number play an important role in determining the level of the harvested power and the onset of galloping. The results also show that the maximum levels of harvested power are accompanied with minimum transverse displacements for both low- and high-Reynolds number configurations.
We investigate the effects of varying the eccentricity between the gravity axis and the elastic axis on the level of energy harvested from a piezoaeroelastic energy harvester consisting of a pitching and plunging rigid airfoil supported by nonlinear springs. The normal form of the dynamics of the harvester near the Hopf bifurcation is used to determine the critical nonlinear coefficients of the springs and maximize the harvested power for different eccentricities. Two configurations are evaluated in terms of the power generated from limit cycle oscillations and a range of operating wind speeds. The impact of the load resistance on the harvested power is also assessed.
We design a piezoaeroelastic energy harvester consisting of a rigid airfoil that is constrained to pitch and plunge and supported by linear and nonlinear torsional and flexural springs with a piezoelectric coupling attached to the plunge degree of freedom. We choose the linear springs to produce the minimum flutter speed and then implement a linear velocity feedback to reduce the flutter speed to any desired value and hence produce limit-cycle oscillations at low wind speeds. Then, we use the center-manifold theorem to derive the normal form of the Hopf bifurcation near the flutter onset, which, in turn, is used to choose the nonlinear spring coefficients that produce supercritical Hopf bifurcations and increase the amplitudes of the ensuing limit cycles and hence the harvested power. For given gains and hence reduced flutter speeds, the harvested power is observed to increase, achieve a maximum, and then decrease as the wind speed increases. Furthermore, the response undergoes a secondary supercritical Hopf bifurcation, resulting in either a quasiperiodic motion or a periodic motion with a large period. As the wind speed is increased further, the response becomes eventually chaotic. These complex responses may result in a reduction in the generated power. To overcome this adverse effect, we propose to adjust the gains to increase the flutter speed and hence push the secondary Hopf bifurcation to higher wind speeds.
There has been increasing interest in wireless sensor networks for a variety of outdoor applications including structural health monitoring and environmental monitoring. Replacement of batteries that power the nodes in these networks is maintenance intensive. A wind energy–harvesting device is proposed as an alternate power source for these wireless sensor nodes. The device is based on the galloping of a bar with triangular cross section attached to a cantilever beam. Piezoelectric sheets bonded to the beam convert the mechanical energy into electrical energy. A prototype device of size approximately 160 × 250 mm was fabricated and tested over a range of operating conditions in a wind tunnel, and the power dissipated across a load resistance was measured. A maximum power output of 53 mW was measured at a wind velocity of 11.6 mph. An analytical model incorporating the coupled electromechanical behavior of the piezoelectric sheets and quasi-steady aerodynamics was developed. The model showed good correlation with measurements, and it was concluded that a refined aerodynamic model may need to include apparent mass effects for more accurate predictions. The galloping piezoelectric energy-harvesting device has been shown to be a viable option for powering wireless sensor nodes in outdoor applications.
For some time, the smart materials and structures community has focused on transducer effects, and the closest advance into actually having the "structure" show signs of intelligence is implementing adaptive control into a smart structure. Here we examine taking this a step further by attempting to combine embedded computing into a smart structure system. The system of focus is based on integrated structural health monitoring of a panel which consists of a completely wireless, active sensing systems with embedded electronics. We propose and discuss an integrated autonomous sensor "patch" that contains the following key elements: power harvesting from ambient vibration and temperature gradients, a battery charging circuit, local computing and memory, active sensors, and wireless transmission. These elements should be autonomous, self contained, and unobtrusive compared to the system being monitored. Each of these elements is discussed as a part of an integrated system to be used in structural health monitoring applications.
Cantilevered beams with piezoceramic (PZT) layers are the most commonly investigated type of vibration energy harvesters. A frequently used modeling approach is the single-degree-of-freedom (SDOF) modeling of the harvester beam as it allows simple expressions for the electrical outputs. In the literature, since the base excitation on the harvester beam is assumed to be harmonic, the well known SDOF relation is employed for mathematical modeling. In this study, it is shown that the commonly accepted SDOF harmonic base excitation relation may yield highly inaccurate results for predicting the motion of cantilevered beams and bars. First, the response of a cantilevered Euler—Bernoulli beam to general base excitation given in terms of translation and small rotation is reviewed where more sophisticated damping models are considered. Then, the error in the SDOF model is shown and correction factors are derived for improving the SDOF harmonic base excitation model both for transverse and longitudinal vibrations. The formal way of treating the components of mechanical damping is also discussed. After deriving simple expressions for the electrical outputs of the PZT in open-circuit conditions, relevance of the electrical outputs to vibration mode shapes and the electrode locations is investigated and the issue of strain nodes is addressed.
Cantilevered beams with piezoceramic layers have been frequently used as piezoelectric vibration energy harvesters in the past five years. The literature includes several single degree-of-freedom models, a few approximate distributed parameter models and even some incorrect approaches for predicting the electromechanical behavior of these harvesters. In this paper, we present the exact analytical solution of a cantilevered piezoelectric energy harvester with Euler-Bernoulli beam assumptions. The excitation of the harvester is assumed to be due to its base motion in the form of translation in the transverse direction with small rotation, and it is not restricted to be harmonic in time. The resulting expressions for the coupled mechanical response and the electrical outputs are then reduced for the particular case of harmonic behavior in time and closed-form exact expressions are obtained. Simple expressions for the coupled mechanical response, voltage, current, and power outputs are also presented for excitations around the modal frequencies. Finally, the model proposed is used in a parametric case study for a unimorph harvester, and important characteristics of the coupled distributed parameter system, such as short circuit and open circuit behaviors, are investigated in detail. Modal electromechanical coupling and dependence of the electrical outputs on the locations of the electrodes are also discussed with examples.
Some elastic bluff bodies under the action of a fluid flow can experience transverse galloping and lose stability if the flow velocity exceeds a critical value. For flow velocities higher than this critical value, there is an energy transfer from the flow to the body and the body develops an oscillatory motion. Usually, it is considered as an undesirable effect for civil or marine structures but here we will show that if the vibration is substantial, it can be used to extract useful energy from the surrounding flow. This paper explores analytically the potential use of transverse galloping in order to obtain energy. To this end, transverse galloping is described by a one-degree-of-freedom model where fluid forces obey the quasi-steady hypothesis. The influence of cross-section geometry and mechanical properties in the energy conversion factor is investigated.
Energy harvesting has enabled new operational concepts in the growing field of wireless sensing. A novel energy harvesting device driven by aeroelastic flutter vibrations has been developed and could be used to complement existing environmental energy harvesters such as solar cells in wireless sensing applications. An analytical model of the mechanical, electromechanical, and aerodynamic systems suitable for designing aeroelastic energy harvesters for various flow applications are derived and presented. Wind tunnel testing was performed with a prototype energy harvester to characterize the power output and flutter frequency response of the device over its entire range of operating wind speeds. Finally, two wing geometries, a flat plate and a NACA 0012 airfoil were tested and compared.
The addition of energy harvesting is investigated to determine the benefits of its integration into a small unmanned air vehicle (UAV). Specifically, solar and piezoelectric energy harvesting techniques were selected and their basic functions analyzed. The initial investigation involved using a fundamental law of thermodynamics, entropy generation, to analyze the small UAV with and without energy harvesting. A notional mission was developed for the comparison that involved the aircraft performing a reconnaissance mission. The analysis showed that the UAV with energy harvesting generated less entropy. However, the UAV without energy harvesting outperformed the other UAV in total flight time at the target. The analysis further looked at future energy harvesting technologies and their effect on the energy harvesting UAV to conduct the mission. The results of the mission using the advanced solar technology showed that the effectiveness of the energy harvesting vehicle would increase. Designs for integrating energy harvesting into the small UAV system were also developed and tests were conducted to show how the energy harvesting designs would perform. It was demonstrated that the addition of the solar and piezoelectric devices would supply usable power for charging batteries and sensors and that it would be advantageous to implement them into a small UAV.
One of the classical aeroelastic instabilities of slender structures is galloping, which can be characterized as a low-frequency, large-amplitude normal to the flow oscillations phenomenon.In this paper the effects of cross-sectional shape and mean wind angle of incidence on the transverse galloping stability (according to the Glauert–Den Hartog criterion for galloping instability) of triangular cross-section bodies has been systematically analyzed through static wind tunnel experiments. Nine triangular cross-section models were tested, the angle at the main vertex, β, ranging from 10° to 90°. In addition, three additional models having rounded corners have been tested, to check the impact of a modification in windward corners in modifying the flow pattern around the cross-section, facilitating eventually the reattachment of the boundary layer and narrowing therefore the width of the wake. Static tests confirm that the stability to transverse translational galloping of triangular cross-section cylinders are both cross-sectional geometry and angle of attack dependent, the potential unstable zones in the angle of attack–main vertex angle plane (α,β) being identified.
This paper investigates the concept of piezoaeroelasticity for energy harvesting. The focus is placed on mathematical modeling and experimental validations of the problem of generating electricity at the flutter boundary of a piezoaeroelastic airfoil. An electrical power output of 10.7 mW is delivered to a 100 kΩ load at the linear flutter speed of 9.30 m/s (which is 5.1% larger than the short-circuit flutter speed). The effect of piezoelectric power generation on the linear flutter speed is also discussed and a useful consequence of having nonlinearities in the system is addressed.
We investigate the benefits of tuning the frequencies of an energy harvester to extract more energy from a base excitation that comprises three frequency components. The energy harvester is composed of a unimorph cantilever beam with asymmetric tip masses. By adjusting the asymmetry of the tip masses, we can tune this beam–mass structure to harvest energy from multifrequency components of a base excitation. We model the beam using the Euler–Bernoulli beam theory and use the first three global mode shapes of the harvester in a Galerkin procedure to derive a reduced-order model describing its response. We derive an exact analytical solution for the tip deflection, twisting angle, voltage output, and harvested electrical power. Using this solution, we investigate the advantages of harvesting energy from a response that contains multifrequencies in comparison to a response that contains a single frequency by tuning only the fundamental frequency. The advantages of this bending–torsion energy harvester and the effect of its tuning are investigated for different short- and open-circuit configurations. The results show that, through a proper tuning of this bending–torsion harvester, the harvested power can be increased significantly and it can be made to cover a wide range of electrical load resistances.
Enabling technologies for wireless sensor networks have gained considerable attention in research communities over the past few years. It is highly desirable, even necessary in certain situations, for wireless sensor nodes to be self-powered. With this goal in mind, a vibration based piezoelectric generator has been developed as an enabling technology for wireless sensor networks. The focus of this paper is to discuss the modeling, design, and optimization of a piezoelectric generator based on a two-layer bending element. An analytical model of the generator has been developed and validated. In addition to providing intuitive design insight, the model has been used as the basis for design optimization. Designs of 1 cm3 in size generated using the model have demonstrated a power output of 375 µW from a vibration source of 2.5 m s−2 at 120 Hz. Furthermore, a 1 cm3 generator has been used to power a custom designed 1.9 GHz radio transmitter from the same vibration source.
The available power in a flowing fluid is proportional to the cube of its velocity, and this feature indicates the potential for generating substantial electrical energy by exploiting the direct piezoelectric effect. The present work is an experimental investigation of a self-excited piezoelectric energy harvester subjected to a uniform and steady flow. The harvester consists of a cylinder attached to the free end of a cantilevered beam, which is partially covered by piezoelectric patches. Due to fluid–structure interaction phenomena, the cylinder is subjected to oscillatory forces, and the beam is deflected accordingly, causing the piezoelectric elements to strain and thus develop electric charge. The harvester was tested in a wind tunnel and it produced approximately 0.1 mW of non-rectified electrical power at a flow speed of 1.192 m s−1. The aeroelectromechanical efficiency at resonance was calculated to be 0.72%, while the power per device volume was 23.6 mW m−3 and the power per piezoelectric volume was 233 W m−3. Strain measurements were obtained during the tests and were used to predict the voltage output by employing a distributed parameter model. The effect of non-rigid bonding on strain transfer was also investigated. While the rigid bonding assumption caused a significant (>60%) overestimation of the measured power, a non-rigid bonding model gave a better agreement (<10% error).
This paper describes the analysis, simulation and testing of a microengineered motion-driven power generator, suitable for application in sensors within or worn on the human body. Micro-generators capable of powering sensors have previously been reported, but these have required high frequency mechanical vibrations to excite a resonant structure. However, body-driven movements are slow and ir-regular, with large displacements, and hence do not effectively couple energy into such generators. The device presented here uses an alternative, non-resonant operating mode. Analysis of this generator shows its potential for the application considered, and shows the possibility to optimise the design for particular conditions. An experimental prototype based on a variable parallel-plate capacitor operat-ing in constant charge mode is described which confirms the analysis and simulation models. This prototype, when precharged to 30 V, develops an output voltage of 250 V, corresponding to 0.3 J per cycle. The experimental test procedure and the instrumentation are also described.
Piezoelectric transduction has received great attention for vibration-to-electric energy conversion over the last five years. A typical piezoelectric energy harvester is a unimorph or a bimorph cantilever located on a vibrating host structure, to generate electrical energy from base excitations. Several authors have investigated modeling of cantilevered piezoelectric energy harvesters under base excitation. The existing mathematical modeling approaches range from elementary single-degree-of-freedom models to approximate distributed parameter solutions in the sense of Rayleigh–Ritz discretization as well as analytical solution attempts with certain simplifications. Recently, the authors have presented the closed-form analytical solution for a unimorph cantilever under base excitation based on the Euler–Bernoulli beam assumptions. In this paper, the analytical solution is applied to bimorph cantilever configurations with series and parallel connections of piezoceramic layers. The base excitation is assumed to be translation in the transverse direction with a superimposed small rotation. The closed-form steady state response expressions are obtained for harmonic excitations at arbitrary frequencies, which are then reduced to simple but accurate single-mode expressions for modal excitations. The electromechanical frequency response functions (FRFs) that relate the voltage output and vibration response to translational and rotational base accelerations are identified from the multi-mode and single-mode solutions. Experimental validation of the single-mode coupled voltage output and vibration response expressions is presented for a bimorph cantilever with a tip mass. It is observed that the closed-form single-mode FRFs obtained from the analytical solution can successfully predict the coupled system dynamics for a wide range of electrical load resistance. The performance of the bimorph device is analyzed extensively for the short circuit and open circuit resonance frequency excitations and the accuracy of the model is shown in all cases.
A nonlinear analysis of an energy harvester consisting of a multilayered cantilever beam with a tip mass is performed. The
model takes into account geometric, inertia, and piezoelectric nonlinearities. Acombination of the Galerkin technique, the
extended Hamilton principle, and the Gauss law is used to derive a reduced-order model of the harvester. The method of multiple
scales is used to determine analytical expressions for the tip deflection, output voltage, and harvested power near the first
global natural frequency. The results show that one- or two-mode approximations are not sufficient to produce accurate estimates
of the voltage and harvested power. A parametric study is performed to investigate the effects of the nonlinear piezoelectric
coefficients and the excitation amplitude on the system response. The effective nonlinearity may be of the hardening or softening
type, depending on the relative magnitudes of the different nonlinearities.
KeywordsPiezoelectric material–Energy harvesting–Nonlinear distributed parameter model–Nonlinear analysis–Method of multiple scales
A global nonlinear distributed-parameter model for a piezoelectric energy harvester under parametric excitation is developed.
The harvester consists of a unimorph piezoelectric cantilever beam with a tip mass. The derived model accounts for geometric,
inertia, piezoelectric, and fluid drag nonlinearities. Areduced-order model is derived by using the Euler–Lagrange principle
and Gauss law and implementing a Galerkin discretization. The method of multiple scales is used to obtain analytical expressions
for the tip deflection, output voltage, and harvested power near the first principal parametric resonance. The effects of
the nonlinear piezoelectric coefficients, the quadratic damping, and the excitation amplitude on the output voltage and harvested
electrical power are quantified. The results show that a one-mode approximation in the Galerkin approach is not sufficient
to evaluate the performance of the harvester. Furthermore, the nonlinear piezoelectric coefficients have an important influence
on the harvester’s behavior in terms of softening or hardening. Depending on the excitation frequency, it is determined that,
for small values of the quadratic damping, there is an overhang associated with a subcritical pitchfork bifurcation.
KeywordsPiezoelectric material–Energy harvesting–Distributed parameter model–Nonlinear analysis–Method of multiple scales
This work investigates the influence of structural and aerodynamic nonlinearities on the dynamic behavior of a piezoaeroelastic
system. The system is composed of a rigid airfoil supported by nonlinear torsional and flexural springs in the pitch and plunge
motions, respectively, with a piezoelectric coupling attached to the plunge degree of freedom. The analysis shows that the
effect of the electrical load resistance on the flutter speed is negligible in comparison to the effects of the linear spring
coefficients. The effects of aerodynamic nonlinearities and nonlinear plunge and pitch spring coefficients on the system’s
stability near the bifurcation are determined from the nonlinear normal form. This is useful to characterize the effects of
different parameters on the system’s output and ensure that subcritical or “catastrophic” bifurcation does not take place.
Numerical solutions of the coupled equations for two different configurations are then performed to determine the effects
of varying the load resistance and the nonlinear spring coefficients on the limit-cycle oscillations (LCO) in the pitch and
plunge motions, the voltage output and the harvested power.
KeywordsEnergy harvesting–Piezoaeroelastic–Nonlinear analysis–Normal form
This paper discusses the history, current state of the art, and ongoing challenges for compact (less than a few cubic centimeters) magnetic power generation systems in the microwatts to tens of watts power range. These systems are of great interest for powering sensor networks, robotics, wireless communication systems, and other portable electronics. The paper considers the following topics. 1) The theoretical and practical implications of miniaturizing magnetic power generators. 2) The design and performance of previously demonstrated devices, which are summarized and compared. 3) Ongoing challenges for implementation, including integrated high-performance hard magnetic materials, microscale core laminations, low-friction bearings, high-speed rotor dynamics, and compact, high-efficiency power converters.
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Priya S, Popa D and Lewis F 2006 Energy efficient mobile
wireless sensor networks Proc. ASME Int. Mechanical
Engineering Congr. Exposition (Chicago, IL)
Analysis design of a self
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- W Liao
- W J Li
Zhou W, Liao W H and Li W J 2005 Analysis design of a
self-powered piezoelectric microaccelerometer Smart
Structures and Materials Conf.; Proc. SPIE 5763 233-40
Energy efficient mobile wireless sensor networks Proc
- S Priya
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Priya S, Popa D and Lewis F 2006 Energy efficient mobile
wireless sensor networks Proc. ASME Int. Mechanical
Engineering Congr. Exposition (Chicago, IL)
Investigation of energy harvesting small unmanned air vehicle Smart Materials and Structures: Active and Passive Smart Structures and Integrated Systems II
- K C Magoteaux
- Sanders B Sodano
Magoteaux K C, Sanders B and Sodano A H 2008
Investigation of energy harvesting small unmanned air
vehicle Smart Materials and Structures: Active and Passive
Smart Structures and Integrated Systems II (Proceedings of
the SPIE) vol 6928 (San Diego, CA)