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Nonlinear dynamics and comparative analysis of hybrid piezoelectric-inductive energy harvesters subjected to galloping vibrations
Abstract
Modeling and comparative analysis of galloping-based hybrid piezoelectric-inductive energy harvesting systems are investigated. Both piezoelectric and electromagnetic transducers are attached to the transverse degree of freedom of the prismatic structure in order to harvest energy from two possible sources. A fully-coupled electroaeroelastic model is developed which takes into account the coupling between the generated voltage from the piezoelectric transducer, the induced current from the electromagnetic transducer, and the transverse displacement of the bluff body. A nonlinear quasi-steady approximation is employed to model the galloping force. To determine the influences of the external load resistances that are connected to the piezoelectric and electromagnetic circuits on the onset speed of galloping, a deep linear analysis is performed. It is found that the external load resistances in these two circuits have significant effects on the onset speed of galloping of the harvester with the presence of optimum values. To investigate the effects of these transduction mechanisms on the performance of the galloping energy harvester, a nonlinear analysis is performed. Using the normal form of the Hopf bifurcation, it is demonstrated that the hybrid energy harvester has a supercritical instability for different values of the external load resistances. For well-defined wind speed and external load resistance in the electromagnetic circuit, the results showed that there is a range of external load resistances in the piezoelectric circuit at which the output power generated by the electromagnetic induction is very small. On the other hand, there are two optimal load resistances at which the output power by the piezoelectric transducer is maximum. Based on a comparative study, it is demonstrated the hybrid piezoelectric-inductive energy harvester is very beneficial in terms of having two sources of energy. However, compared to the classical piezoelectric and electromagnetic energy harvesters, the results show that, considering a hybrid energy harvester leads to an increase in the onset speed of galloping and a decrease in the levels of the harvested power in both the piezoelectric and electromagnetic circuits which is explained by the additional resistive shunt damping effects in the hybrid energy harvester.
... It has several advantages in renewable energy development (Tang et al., 2019) and is widely adopted in various technological fields (Bibo and Daqaq, 2013;He et al., 2018). In the past studies, considerable effort was focused on the development of the energy harvesting from fluid-induced vibrations (FIV) (Dai et al., 2014a(Dai et al., , 2014bDunnmon et al., 2011;Javed et al., 2015;Jung and Lee, 2011). A galloping-based energy harvester is used to find the optimum value of electrical load resistance at which the power output is maximum . ...
... Dunnmon et al. (2011) utilized the limit cycle oscillation to generate the piezoelectric power from the aerodynamic force. The modeling and performance of galloping-based hybrid piezoelectric-inductive energy harvesting systems are investigated by Javed et al. (2015). Theoretical and experimental analyses are performed for a simple cantilever-type vibration energy harvester (Elvin et al., 2001) and found that the bending of a beam can provide the self-power source for the energy sensor. ...
This paper deals with the impact of uncertain input parameters on the electrical power generation of galloping-based piezoelectric energy harvester (GPEH). A distributed parameter model for the system is derived and solved by using Newmark beta numerical integration technique. Nonlinear systems tend to behave in a completely different manner in response to a slight change in input parameters. Due to the complex manufacturing process and various technical defects, randomness in system properties is inevitable. Owing to the presence of randomness within the system parameters, the actual power output differs from the expected one. Therefore, stochastic analysis is performed considering uncertainty in aerodynamic, mechanical, and electrical parameters. A polynomial neural network (PNN) based surrogate model is used to analyze the stochastic power output. A sensitivity analysis is conducted and highly influenced parameters to the electric power output are identified. The accuracy and adaptability of the PNN model are established by comparing the results with Monte Carlo simulation (MCS). Further, the stochastic analyses of power output are performed for various degrees of randomness and wind velocities. The obtained results showed that the influence of the electromechanical coefficient on power output is more compared to other parameters.
... The concept of energy harvesting by prismatic shaped cylinders prone to galloping oscillations due to incoming wind flow is relatively new [19][20][21][22][23][24][25]. High amplitude oscillations and a wide range of wind speeds over which energy can be harvested make this phenomenon an excellent choice for localized energy production. ...
... Each inclined energy harvester's bifurcation diagram is plotted in Figs. [16][17][18][19][20]. The plotted curves in Figs. ...
... Dai et al. [17] developed the lumped-parameter model of a bluff-body galloping electromagnetic generator, and observed the harvesting performances after the eigenvalue analysis giving the coupled frequency, coupled damping and the onset speed of galloping. Using the same analysis procedures, Javed et al. [30] conducted the performance comparisons between a hybrid piezoelectric-inductive energy harvester subjected to galloping vibration with its piezoelectric and electromagnetic counterparts. It was demonstrated that the hybrid harvester led to an increase in the onset speed of galloping and a decrease in the levels of the power in both the piezoelectric and electromagnetic circuits. ...
... In the aforementioned works, the electromagnetic induction has been exploited to harvest energy from the aeroelastic flutter [18,22,44], the vortex-induced vibration [12], the transverse galloping [12,17,30], and the wake induced oscillation [31]. Instead of regarding as an energy conversion mechanism, the magnetic force has been applied for improving the broadband vibration energy harvesting. ...
A new energy harvester by coupling the electromagnetic induction and the pitch vibration of a rigid wing is built up in this paper. It is aimed: (1) to harvest energy from the pitch limit cycle oscillation (LCO) of the wing due to the preloaded free-play nonlinearity; (2) to introduce a theoretical analysis scheme based on the equivalent linearized method into the design of this harvester. With the equivalent linearized method, the domains of the single stable LCO and double stable LCOs are respectively obtained. Combining the analytical and numerical solutions, the single stable LCO along with the stable limit cycle amplitude greater than its corresponding unstable one is recognized as the better mode for harvesting, since the larger limit cycle domain is induced and the more energy are yielded. Based on such chosen mode, analyses of varying parameters are conducted with respect to the plunge stiffness, pitch stiffness, distance of elastic axis from center of gravity, distance of geometric center from elastic axis, load resistance and magnetic flux density. Meanwhile, three indicators are applied to reveal their effects on the harvesting performances: (1) the size of limit cycle domain, (2) the onset velocity of LCO, and (3) the energy output.
... They considered linear and cubic coefficients as constants because of high Reynolds number condition. The quasi-steady approach of Hartog and Parkinson and Brooks has been followed by other researchers as well, and massive contributions have been made to understand the dynamics of different galloping systems for energy harvesting and control purposes [30,31,[41][42][43][44][45][46]. ...
... One of the main factors when designing galloping energy harvesters is the electrical load resistance. It was shown in several research studies [31,41] that there is an optimum value of the electrical load resistance where maximum levels of the harvested power are obtained. Another essential factor is optimizing the design for a welldefined range of wind speeds depending on the location of the energy harvester. ...
One of the challenging tasks in the analytical modeling of galloping systems is the representation of the galloping force. In this study, the impacts of using different aerodynamic load representations on the dynamics of galloping oscillations are investigated. A distributed-parameter model is considered to determine the response of a galloping energy harvester subjected to a uniform wind speed. For the same experimental data and conditions, various polynomial expressions for the galloping force are proposed in order to determine the possible differences in the variations of the harvester’s outputs as well as the type of instability. For the same experimental data of the galloping force, it is demonstrated that the choice of the coefficients of the polynomial approximation may result in a change in the type of bifurcation, the tip displacement and harvested power amplitudes. A parametric study is then performed to investigate the effects of the electrical load resistance on the harvester’s performance when considering different possible representations of the aerodynamic force. It is indicated that for low and high values of the electrical resistance, there is an increase in the range of wind speeds where the response of the energy harvester is not affected. The performed analysis shows the importance of accurately representing the galloping force in order to efficiently design piezoelectric energy harvesters.
... refer to the electric field and electrical displacement vectors, (ε, e) signify the dielectric and piezoelectricity matrices, respectively, and φ is the electric potential. Also, the electric current across the upper and lower electrodes of each layer in the bimorph piezoelectric splitter plate (I p ) can be found based on the Gauss law by integrating over the electroded area (Γ s ) in the form [58]: ...
... The simulations followed by the experimental verifications in this study were explained with emphasis on improving the energy conversion efficiency of an electromagnetic converter, which gives a power gain of 27 compared to the DC power obtained with standard silicon diodes. Javed et al. 16 investigated the hybrid energy harvester by creating an aeroelastic-based structure. Their theoretically modeled work performed detailed bifurcation analysis using different air velocities and different resistive loads. ...
In this study, hybrid energy harvesting based on electromagnetic induction (EM) and piezoelectric transduction (PZT) is experimentally investigated under different conditions of flow-induced vibrations. The energy harvesting performance of the system is examined when the electromagnetic and piezoelectric mechanisms are used both separately and simultaneously. In this regard, firstly, only electromagnetic induction harvesting structure is attached to a beam, and time-dependent voltage and displacement are experimentally investigated. Then, PZT has adhered to the beam, and voltage outputs are measured in both the PZT and EM circuits. The third scenario is based on removing the electromagnetic harvesting structure and only the piezoelectric energy harvesting performance is studied. The mentioned cases are investigated under different excitation circumstances, that is, distinct bluff-body geometries and flow velocities. While the square bluff-body geometry is connected to the structure, both PZT and EM harvested power are determined by considering different electrical load resistances. It is mainly revealed that the total energy amount is higher in the hybrid configuration. After determining the hybrid structure is the most effective, elements with different splitters geometry are attached to the bluff-body geometry of the harvesting structure. Finally, the vibration enhancement potential of these new types of splitters on the harvesting structure is experimentally investigated. For the solo electromagnetic harvester, the maximum power is obtained at an external load resistance value of 10 kΩ, while for the solo PZT harvester, the maximum power is observed at the resistance value of 330 kΩ. Among the three types of splitter geometries examined, the highest voltage was obtained from type-1 as 14.168 V.
... The model with quasi-steady aerodynamics was validated through experimentation using a bluff body with airflow and base excitation with a shaker. Considering a hybrid energy harvester leads to an increase in the onset speed of galloping and a decrease in the levels of the harvested power [12,13]. Galloping has been used in a wide range of applications including two-degree-offreedom systems [14,15]. ...
The effects of freeplay and multi-segmented nonlinearities in the pitch degree of freedom on the dynamical responses of a two-degree-of-freedom piezoaeroelastic energy harvesting system are investigated. The nonlinear governing equations of the considered piezoaeroelastic energy harvesting system are derived along with the use of the unsteady representation based on the Duhammel formulation to model the aerodynamic loads. The nonlinear piezoaeroelastic response is carried out in the presence of freeplay and multi-segmented nonlinearities before and after the linear onset of flutter. Such nonlinearities can be introduced to piezoaeroelastic energy harvesters for performance enhancement through the possible existence of sudden jumps and chaotic responses due to the grazing bifurcation. It is shown that the existence of discontinuous effects results in the possibility of harvesting energy at lower speeds than the linear onset speed of instability. Additionally, the increase of the strength of the multi-segmented nonlinearities leads to the presence of aperiodic responses with the presence of several bifurcations limiting the system’s dynamics at low pitch angles.
... The piezoelectric transduction mechanism was used to flow energy (Vocca et al. 2012;Roshani et al. 2016;Xiong and Wang 2016) as a vibration source. Out of all fluid-induced vibrations galloping show promising practical applications (Sirohi and Mahadik 2011;Abdelkefi, Hajj, and Nayfeh 2012;Yang, Zhao, and Tang 2013;Zhao, Tang, and Yang 2013;Bibo and Daqaq, 2014;Javed, Dai, and Abdelkefi 2015). The galloping effect was first noticed by Den Hartog (1956) and he used quasisteady approximation to find the condition for onset speed of galloping. ...
A finite element model is proposed for a galloping based piezoelectric energy harvester (GPEH) with an inclined square prism. The absence of any numerical model to capture the effects of inclinations of the bluff body on the performance of GPEH system necessitate the present study. The proposed model is solved in MATLAB environment and validated using the available experimental data. Dynamic stability analysis of the system is done at various vertical inclinations. A substantial decrease in power generation is noticed with the increment of the forward inclination angle. Again, large backward inclinations reduce the power output but perform well compared to forward inclinations. The present work aims to enhance the probability of power generation (GPEH system) in extreme natural flow conditions with negligible structural damage.
... The model with quasi-steady aerodynamics was validated through experimentation using a bluff body with airflow and base excitation with a shaker. Considering a hybrid energy harvester leads to an increase in the onset speed of galloping and a decrease in the levels of the harvested power [12,13]. Galloping has been used in a wide range of applications including two-degree-offreedom systems [14,15]. ...
A comprehensive study on the design and nonlinear characterization of a two-degree of freedom piezoaeroelastic energy harvesting system with freeplay and multi-segmented nonlinearities in the pitch degree of freedom is explored and discussed. The nonlinear governing equations of the considered piezoaeroelastic energy harvesting system are derived and the unsteady representation based on the Duhamel formulation is employed to represent the aerodynamic loads. Nonlinear piezoaeroelastic response analysis is carried out in the presence of freeplay and multi-segmented nonlinearities before and after the linear onset of flutter. Such nonlinearities can be introduced to piezoaeroelastic energy harvesters for performance enhancement through the possible existence of subcritical Hopf bifurcation and aperiodic responses due to the grazing and grazing/sliding bifurcations. It is shown that the existence of discontinuous effects result in the possibility of harvesting energy at lower speeds than the linear onset speed of instability due to the activation of the subcritical Hopf bifurcation. Additionally, the increase of the strength of the multi-segmented nonlinearities leads to the existence of aperiodic responses with the presence of several bifurcations limiting the system’s dynamics at low pitch angles with limiting stall issues. It is proved that an effective design with harvesting energy at low wind speeds can be carried out for wing-based energy harvesters by carefully selecting the linear stiffness of the pitch degree of freedom, gap and type of the multi-segmented discontinuity, and electrical load resistance.
... Flow-induced vibrations (FIVs), as an important source of mechanical energy, can be a great potential in energy harvesting by designing efficient harvesters subjected to fluid or wind flows [15,16]. Typical FIV successfully applied in energy harvesting can be classified as galloping [17][18][19][20][21], flutter [22][23][24][25], and vortex-induced vibrations (VIVs) [26][27][28][29][30][31][32][33]. Galloping and VIV have received widespread attention in the last decade for piezoelectric energy harvesting applications. ...
This letter presents an idea of employing sphere as a bluff body subjected to cross flows for improving piezoelectric energy harvesting from flow-induced vibrations (FIVs). Unlike cylindrical bluff bodies used in most of previous studies, the proposed harvester with sphere configuration can be freely settled in horizontal and vertical directions without reconfiguration. Experimental results show that the aspect ratio (length of beam to diameter of sphere) and mass ratio between sphere and beam have great effects on output performance of the energy harvester. It is found that the optimal aspect ratio and mass ratio are 1.7 and 0.15 where the harvester has a broadband lock-in between 2 m s-1 and 6 m s-1 and a maximum output average power of 190 μW. This is attributed to variations of the natural frequency and aerodynamic force varying with the sphere diameter, resulting in multiple modes responses to significantly enhance the output power. Furthermore, the output comparison between sphere- and cylinder-based energy harvesters indicates that sphere is superior in the case of horizontal placement, while for the vertical placement as the wind speed is below 4 m s-1 it is better to use sphere, but beyond 4 m s-1, cylinder is superior within the considered wind speed region. The present study gives a new design for effectively harvesting energy from FIVs according to available wind speed.
... Amini et al. [15] proposes a piezoelectric vertical beam with attached end cylinder as an energy harvester in the lowspeed flows. Piezoelectric energy harvesters based on vortexinduced vibration and galloping [16][17][18][19] have been extensively studied in the past several years. Shan et al. [20] and Song et al. [21] investigated the performance of two tandem PEHs in water flow and found that the energy harvesting performance of the downstream PEH was enhanced due to the wake stimulating from the upstream PEH. ...
... Nonlinear aeroelastic systems, on the other hand, can offer persistent oscillations over ranges of airflow speeds due to the presence of concentrated or distributed structural nonlinearities as well as aerodynamic nonlinearities (Dowell & Tang 2002). Since real world applications often involve nonlinearities and in order to overcome the limitations of linear aeroelastic energy harvesters, there has been growing research interest in nonlinear aeroelastic energy harvesters over the past few years (Abdelkefi et al. 2012a, De Marqui et al. 2018, Sousa et al. 2011, Abdelkefi & Hajj 2013, Bae & Inman 2014b, De Sousa & De Marqui Junior 2015, Javed et al. 2015. ...
... Javed et al. [58] analyzed the response of a galloping MPG employing a hybrid piezoelectricelectromagnetic transduction. They noted that, a harvester with a single transduction mechanism outperforms the proposed hybrid harvester. ...
Emergence of increasingly smaller electromechanical systems with submilli-Watt power consumption led to the development of scalable micropower generators (MPGs) that harness ambient energy to provide electrical power on a very small scale. A flow MPG is one particular type which converts the momentum of an incident flow into electrical output. Traditionally, flow energy is harnessed using rotary-type generators whose performance has been shown to drop as their size decreases. To overcome this issue, oscillating flow MPGs were proposed. Unlike rotary-type generators which rely upon a constant aerodynamic force to produce a deflection or rotation, oscillating flow MPGs take advantage of cross-flow instabilities to provide a periodic forcing which can be used to transform the momentum of the moving fluid into mechanical motion. The mechanical motion is then transformed into electricity using an electromechanical transduction element. The purpose of this review article is to summarize important research carried out during the past decade on flow micropower generation using cross-flow instabilities. The summarized research is categorized according to the different instabilities used to excite mechanical motion: galloping, flutter, vortex shedding, and wake-galloping. Under each category, the fundamental mechanism responsible for the instability is explained, and the basic mathematical equations governing the motion of the generator are presented. The main design parameters affecting the performance of the generator are identified, and the pros and cons of each method are highlighted. Possible directions of future research which could help to improve the efficacy of flow MPGs are also discussed.
... Based on their electroaeroelastic modeling and simulations, their work gave a direction for designing and optimizing airfoil-based hybrid energy harvesters. Recently, Javed et al. [27] were the first to propose and investigate a hybrid transduction mechanism for galloping energy harvesters. The transduction mechanism consisted of a piezoelectric layer and a magnet in the vicinity of a coil. ...
The vortex-induced vibrations of a circular cylinder attached as a tip mass at the end of a cantilever beam are investigated for hybrid energy harvesting using two different transduction mechanisms, namely piezoelectric and electromagnetic. The high aeroelastic oscillations generated for a range of wind speeds are translated into electrical energy by both transducers. The aerodynamic force is modeled by a modified van der Pol wake oscillator model. The Euler–Lagrange principle and Galerkin procedure are utilized to develop a nonlinear distributed-parameter model to evaluate performance of the hybrid energy harvester. The effects of the external load resistances, placement and mass of the magnet on coupled damping, frequency, and performance of the hybrid energy harvester are deeply studied. It is shown that performance of the hybrid energy harvester is highly dependent on both the external load resistances. It is demonstrated that, in the synchronous region, placement of the magnet has a huge effect on tip displacement of the harvester, generated current in the electromagnetic circuit, and generated voltage in the piezoelectric circuit. On the contrary, mass of the magnet has a negligible effect on behavior of the considered hybrid system. A comparative study between the hybrid energy harvester with the classical piezoelectric and electromagnetic counterparts is also carried out. It is indicated that, by carefully choosing the external load resistances and harvesters’ properties, energy harvesting in a hybrid configuration is an effective replacement for two different classical harvesters working separately. It is concluded that hybrid energy harvesters come out to be an effective choice for powering multiple electronic devices.
... Nonlinear aeroelastic systems offer persistent oscillations over a range of airflow speeds due to structural nonlinearities (concentrated or distributed) or aerodynamic nonlinearities . Since the nonlinear aeroelastic behavior is more realistic and also useful for airflow energy harvesting, there has been growing research interest in nonlinear aeroelastic energy harvesters over the past few years (Abdelkefi et al., 2012a;Dunnmon et al., 2011;Sousa et al., 2011;Abdelkefi et al., 2012c;Abdelkefi and Hajj, 2013;Bae and Inman, 2014;Javed et al., 2015;Sousa and De Marqui, 2015). ...
... In another work, Barrero et al. 4 modeled the aerodynamic force in terms of a cubic polynomial expression and the linear and cubic coeffcients were considered constants because of high Reynolds number. The quasi-steady approach of Den Hartog 1 and Parkinson and Brooks 2 has been followed by other researchers as well and massive contributions have been made to understand the dynamics of different important systems [5][6][7][8] . ...
... Wake-induced vibration (WIV) [4,5], vortex-induced vibration (VIV) [6][7][8], and flutter-induced vibration (FIV) [9][10][11][12] all belong to fluid-induced vibration. Piezoelectric energy harvesters based on vortex-induced vibration [13][14][15][16][17][18] and galloping [19][20][21] have been extensively studied in the past several years. Akaydin et al. [22] investigated a piezoelectric energy harvester from vortex-induced vibration in air flow. ...
This paper presents a new energy-harvesting system with two identical piezoelectric energy harvesters in a tandem configuration. Each harvester consists of a piezoelectric beam and a circular cylinder. Experiments are performed to investigate the energy-harvesting performances of this system in water. It can be found that their energy-harvesting performances are all different from that of the single harvester (without an upstream or downstream harvester). The experimental results show that the water speed and the spacing ratio have significant effects on the energy-harvesting performances of the two tandem harvesters. The output power of the upstream harvester first increases, and then decreases with the water speed increasing. The maximum output power of 167.8 μW is achieved at the water speed of 0.306 m/s and the spacing ratio (L/D) of 2.5. Increasing the water speed results in an increase in the energy performance of the downstream harvester. Compared with the single harvester, the performance of the downstream harvester is weakened in the low water speed range, but enhanced in the higher water speed range. Further, the output power of 533 μW is obtained by the downstream harvester at the water speed of 0.412 m/s and the spacing ratio of 1.7, which is 29 times more than that of the single harvester. The results indicate the superiority of the two tandem harvesters in energy-harvesting performance.
Wake-galloping energy harvesting has been extensively developed to scavenge flow energy from vortex-induced oscillations. Hence, the wake-galloping harvester only has a natural frequency which leads to a very narrow bandwidth. Therefore, it does not operate well under the wide region of shedding frequencies in variable wind speed. To overcome the vital issue, this paper we explored a novel two-degree-of-freedom nonlinear flow energy harvester to collect flow energy induced by the wake of a bluff body. The nonlinear restoring force is realized by using a repulsive magnetic force between two cuboid-shaped permanent magnets, and the electromechanical coupling equations are presented. Based on the method of harmonic balance, the electromechanical governing equations are decoupled, and the first-order harmonic solutions are implemented. The modulation equations are established, and the amplitude–frequency figures of displacement and voltage are depicted with different detuning parameters. The superiority of the presented energy harvester is contrasted with the single-degree-of-freedom linear and nonlinear cases, and the results revealed that the two-degree-of-freedom nonlinear scheme can enhance the bandwidth of flow energy capture. The effect of physical parameters on the scavenged power is discussed. The accuracy and efficiency of the approximate analytical data are examined by numerical simulations.
It is known that the displacement and stress on beams will directly affect the energy harvesting performance. For this purpose, structural changes are made on the beam elements. Behaviours of these beam structures are investigated by designing different non-classical beam geometries. This study examines vibration-based electromagnetic and piezoelectric energy harvesting from the non-classical beam structures under various conditions. Before analysing the non-classical beam structure, studies are performed for a classical beam for electromagnetic and piezoelectric energy harvesting studies. In the electromagnetic energy harvesting analysis, the effects of magnitude of magnetic field and the distance between the coil and the permanent magnet on the harvesting performance are studied by free vibration experiments. In this regard, a neodymium permanent magnet is attached to the vibrating aluminium beam endpoint. During the free vibration period, the coil and the magnet interact closely. As a result, a voltage output is obtained by inducing an electric field on the coil side. Secondly, voltage outputs of piezoelectric energy harvesting structures are experimentally evaluated for a classical beam and used for the verification of numerical simulations. Using the verified numerical simulations, new types of beam structures so-called non-classical beams are designed to obtain higher voltage outputs. Finally, by introducing the phenomenon of continuous vibration with the effect of air, the hybrid energy performance is analyzed for the proposed structure. The continuous vibration is created by the air-flow on the square galloping geometry.
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.
In the present study, a geometrically non-linear finite element (FE) method has been developed to find the dynamic characteristics of the galloping based piezoelectric energy harvesters (GPEH). The model developed deals with both structural and aerodynamic nonlinearity. Results from the present model are validated with experimental data from the literature. System bifurcations due to nonlinear damping terms are explored in detail. Further, a parametric study is done to find the effects of piezoelectric patch length, galloping force coefficients and load resistance on the power output. The current analysis emphasizes the numerical approach over conventional analytical solutions (FE) to solve complex fluid and structure problem involved in the GPEH system.
To realize the self-power of the vehicle micro-sensors, a piezo-electromagnetic hybrid vehicle-mounted energy harvester is proposed to recover the wind and vibration energy generated during driving. This energy harvester includes a flutter piezoelectric energy harvesting structure (FPEH) and an electromagnetic vibration energy harvester structure (EVEH). The combination of the two structures can improve the energy harvesting effect and reduce the cut-in wind speed. The coupled vibration mathematical model is established to predict the output performance of the wind energy harvesting effect. The effects of the different distances between magnets on the output are discussed. And the vibration characteristics of piezoelectric and electromagnetic vibrators are analyzed. Results show that the energy-harvesting effect is the best when the distance between magnets is 30mm. At the same time, the numerical simulation proves that the wind energy harvesting effect of the hybrid structure is better than the classic flutter structure. The experimental verification is carried out, and the experimental results are consistent with the theoretical prediction results, which verified the correctness of the theory. The optimal load of FPEH is 70kΩ , and the optimal load of EVEH is 60Ω. Under these conditions, when the wind speed is 18m/s, the peak output power of FPEH is 14.5mW, and that of EVEH is 31.8mW.
In the present work, a non-linear electromechanical distributed parameter model is proposed for galloping
based piezoelectric energy harvester (GPEH) and the impact of different order polynomial representation of
aerodynamic force coefficient on the dynamic behavior of the system is investigated. Both geometric and
aerodynamic nonlinearity (till9thorder polynomial) is introduced in the proposed model. The derived model
is universally valid for both series and parallel connection of piezoelectric bimorph patches. The dynamic
responses of the system, for different order representations of aerodynamic force, are extensively studied
and then compared with experimental results from the literature. It is shown that a minimum till 7th order
polynomial should be chosen for representing the galloping force coefficient in order to get a good agreement
with experimental results. It is also shown from the model that the overall efficiency of the system is highest
near the onset of galloping speed and decreases with an increase in wind speed. Further, a parametric study
is done to find the effect of load resistance on the dynamic behavior of the system. It is seen that the error
between experimental and predicted power decreases with an increase in the order of polynomial at a particular
value of load resistance. The present analysis based on the proposed model emphasizes the importance of
representation of aerodynamic force coefficients and geometric nonlinearity in predicting the accurate response
for GPEH.
To improve the performance of the wind galloping energy harvester, the piezoelectromagnetic synergy design is proposed. Hamilton's principle and Euler–Bernoulli beam assumptions, quasi-steady hypothesis, Gauss law and Faraday's law are adopted to establish an electromechanical coupled distributed parameter model for the hybrid energy harvesting system. Using the harmonic balance method, the approximate analytical solutions of the dynamic response and electric output are derived. Wind tunnel experiments validate the nonlinear results of the proposed model including the Hopf bifurcation and unsteady response. The load resistances are optimized via finding the extreme of the power binary function. For the wind speed smaller than the critical wind speed, the piezoelectric module works with switched-off electromagnetic module. For the wind speed larger than the critical wind speed, piezoelectric and electromagnetic modules work concurrently to realize the synergistic effect. The piezoelectromagnetic galloping energy harvester is demonstrated to be superior than the piezoelectric galloping energy harvester and the electromagnetic energy harvester for higher harvested power from smaller galloping oscillations.
In this paper, for the first time, a new design for a MEMS cantilever-based energy harvester (EH) has been proposed which takes advantage of two engineered piezoelectric layers. The output voltage of the EH has been increased by the aid of making grooves in the piezoelectric layers. By application of the grooves in the piezoelectric layers, the sensitivity of the cantilever as the vibration sensor or the EH has been improved. Results have shown that these grooves can increase the output voltage and decrease the resonance frequency which are desired changes in designing EHs. The single and double groove bimorph cantilevers have been compared and discussed. The position, length and depth of the grooves have been used as optimization parameters and consequently an optimal design has been proposed at the end of the paper. In the optimal design the top and the bottom piezoelectric layers have not covered the entire beam and have different lengths to produce maximum voltage. By means of groove engineering, we could rise the voltage from 5.395 V to 28.35 V which is considered a great improvement compared to other structures reported previously.
Energy harvesting technology may be considered an ultimate solution to replace batteries and provide a long‐term power supply for wireless sensor networks. Looking back into its research history, individual energy harvesters for the conversion of single energy sources into electricity are developed first, followed by hybrid counterparts designed for use with multiple energy sources. Very recently, the concept of a truly multisource energy harvester built from only a single piece of material as the energy conversion component is proposed. This review, from the aspect of materials and device configurations, explains in detail a wide scope to give an overview of energy harvesting research. It covers single‐source devices including solar, thermal, kinetic and other types of energy harvesters, hybrid energy harvesting configurations for both single and multiple energy sources and single material, and multisource energy harvesters. It also includes the energy conversion principles of photovoltaic, electromagnetic, piezoelectric, triboelectric, electrostatic, electrostrictive, thermoelectric, pyroelectric, magnetostrictive, and dielectric devices. This is one of the most comprehensive reviews conducted to date, focusing on the entire energy harvesting research scene and providing a guide to seeking deeper and more specific research references and resources from every corner of the scientific community. The entire energy harvesting research field has arrived at the era of harvesting multiple energy sources with hybrid structures and/or multifunctional materials. The development history from single source to multisource harvesters is reviewed. Research directions are suggested for the next generation of harvesters which must be capable of dealing with real ambient environments as opposed to stable or idealized laboratory conditions.
The characteristics and performances of four distinct vortex-induced vibrations (VIVs) piezoelectricenergy harvesters are experimentally investigated and compared. The difference between these VIV energy harvesters is the installation of the cylindrical bluff body at the tip of cantilever beam with different orientations (bottom, top, horizontal, and vertical). Experiments show that the synchronization regions of the bottom, top, and horizontal configurations are almost the same at low wind speeds (around 1.5 m/s). The vertical configuration has the highest wind speed for synchronization (around 3.5 m/s) with the largest harvested power, which is explained by its highest natural frequency and the smallest coupled damping. The results lead to the conclusion that to design efficient VIV energy harvesters, the bluff body should be aligned with the beam for low wind speeds (<2 m/s) and perpendicular to the beam at high wind speeds (>2 m/s).
Energy harvesting is the process by which light, thermal, solar, and kinetic energy can be converted to a usable form of energy with the ultimate objective of developing self-powered sensors, actuators, and other electronic devices. Each of these sources of energy can be used to power remote sensors, however, many researchers have emphasized on vibration-based energy harvesting. Converting ambient and aeroelastic vibrations can be achieved using either electromagnetic, electrostatic or piezoelectric transduction mechanisms. The piezoelectric option has attracted significant interest because it can be used to harvest energy over a wide range of frequencies and the ease of its application. Many researchers have used the piezoelectric transducer to develop simple and efficient energy harvesting devices from vibrations. In this paper, we review recent literature in the field of energy harvesting from aeroelastic vibrations during the last few years. Various types of aeroelastic vibration mechanisms and representative mathematical models are also reviewed. Qualitative and quantitative comparisons between different existing flow-induced vibrations energy harvesters are discussed. Limitations and future recommendations are also presented.
This special issue is a result of discussions performed during a workshop (with the same name) held in Lublin, February 2014. This meeting served as the seed to invite several experts in the field to present contributions for this Special Topics issue which reflect the present state of the art for research and development of smart materials and their possible applications for energy control and energy harvesting.
A long-standing encumbrance in the design of low-frequency energy harvesters has been the need of substantial beam length and/or large tip mass values to reach the low resonance frequencies where significant energy can be harvested from the ambient vibration sources. This need of large length and tip mass may result in a device that is too large to be practical. The zigzag (meandering) beam structure has emerged as a solution to this problem. In this letter, we provide comparative analysis between the classical one-dimensional cantilever bimorph and the two-dimensional zigzag unimorph piezoelectric energy harvesters. The results demonstrate that depending upon the excitation frequency, the zigzag harvester is significantly better in terms of magnitude of natural frequency, harvested power, and power density, compared to the cantilever configuration. The dimensions were chosen for each design such that the zigzag structure would have 25.4×25.4 mm
In this paper, a new energy harvesting system based on wind energy is investigated. To this end, the characteristics and mechanisms of various aerodynamic instability phenomena are first examined and the most appropriate one (i.e. wake galloping) is selected. Then, a wind tunnel test is carried out in order to understand the occurrence conditions of the wake galloping phenomenon more clearly. Based on the test results, a prototype electromagnetic energy harvesting device is designed and manufactured. The effectiveness of the proposed energy harvesting system is extensively examined via a series of wind tunnel tests with the prototype device. Test results show that electricity of about 370 mW can be generated under a wind speed of 4.5 m s - 1 by the proposed energy harvesting device. The generated power can easily be increased by simply increasing the number of electromagnetic parts in a vibrating structure. Also, the possibility of civil engineering applications is discussed. It is concluded from the test results and discussion that the proposed device is an efficient, economic and reliable energy harvesting system and could be applied to civil engineering structures.
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.
A common energy harvesting device uses a piezoelectric patch on a cantilever beam with a tip mass. The usual configuration exploits the linear resonance of the system; this works well for harmonic excitation and when the natural frequency is accurately tuned to the excitation frequency. A new configuration is proposed, consisting of a cantilever beam with a tip mass that is mounted vertically and excited in the transverse direction at its base. This device is highly non-linear with two potential wells for large tip masses, when the beam is buckled. The system dynamics may include multiple solutions and jumps between the potential wells, and these are exploited in the harvesting device. The electromechanical equations of motion for this system are developed, and its response for a range of parameters is investigated using phase portraits and bifurcation diagrams. The model is validated using an experimental device with three different tip masses, representing three interesting cases: a linear system; a low natural frequency, non-buckled beam; and a buckled beam. The most practical configuration seems to be the pre-buckled case, where the proposed system has a low natural frequency, a high level of harvested power and an increased bandwidth over a linear harvester.
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.
This letter considers a nonlinear piezomagnetoelastic energy harvester driven by stationary Gaussian white noise. The increase in the energy generated by this device has been demonstrated for harmonic excitation with slowly varying frequency in simulation and validated by experiment. This paper considers the simulated response of this validated model to random base excitation and shows that the system exhibits a stochastic resonance. If the variance of the excitation were known then the device may be optimized to maximize the power harvested, even under random excitation.
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.
The modeling and performance of a galloping-based electromagnetic energy harvester are investigated. To convert galloping oscillations into electrical energy, an electromagnetic transducer is used. A set of representative coupled equations that account for the transverse displacement of the bluff body and the induced electromagnetic current are constructed. The galloping force is modeled by using the quasi-steady approximation. The effects of the electrical load resistance on the coupled damping and onset speed of galloping are determined through a linear analysis. It is shown that the electrical load resistance strongly affects the coupled damping and hence the onset speed of galloping of the harvester. For high values of the electrical load resistance, it is demonstrated that the load resistance has a negligible impact on the onset speed of galloping. A nonlinear analysis is then performed to investigate the effects of the electrical load resistance and wind speed on the harvester’s outputs. The nonlinear normal form is first derived and validated with numerical predictions in order to characterize the type of instability for various cross-section geometries. The results show that a very good agreement is obtained between the normal form solutions and numerical predictions near Hopf bifurcation. It is also shown that, for well-defined values of wind speeds, both the transverse displacement amplitude and the generated voltage are increasing with the electrical load resistance. On the other hand, there is an optimum value of the electrical load resistance, which varies with the wind speed, at which the levels of the harvested power are maximized.
In this letter, we establish a universal relationship between a dimensionless version of the output power and the flow speed for galloping energy harvesters. This relationship yields a unique curve, which is only sensitive to the aerodynamic properties of the bluff body, but is, otherwise, invariant under any changes in the mechanical and electrical design parameters of the harvester. The curve permits a simple and direct comparative analysis of the energy harvesting performance of different bluff bodies so long that the other design parameters are kept constant. The universal curve is also shown to facilitate the optimization analysis, thereby providing significant insight into the optimal performance conditions.
A nonlinear distributed-parameter model for harvesting energy from vortex-induced vibrations of a piezoelectric cantilever beam with a circular cylinder attached to its end is developed and validated with experimental results. A reduced-order model is derived by using the Euler-Lagrange principle and implementing the Galerkin discretization. A van der Pol wake oscillator is used to model the vortex-induced lift force. A nonlinear analysis is performed to determine the required number of modes in the Galerkin discretization. It is demonstrated that a one-or two-mode approximation in the Galerkin approach is not sufficient to evaluate the performance of the harvester. Based on a five-mode approximation in the Galerkin approach, an identification for the van der Pol wake oscillator coefficients is performed. To design efficient piezoaeroelastic energy harvesters that can generate energy at low freestream velocities, further analysis is performed to investigate the effects of the cylinder's tip mass, length of the piezoelectric sheet, and electrical load resistance on the synchronization region and performance of the harvester. The results show that depending on the operating freestream velocity, the cylinder's tip mass, length of the piezoelectric sheet, and electrical load resistance can be optimized to design enhanced piezoaeroelastic energy harvesters from vortex-induced vibrations.
We investigate the potential of using a piezoelectric energy harvester to concurrently harness energy from base excitations and vortex-induced vibrations. The harvester consists of a multilayered piezoelectric cantilever beam with a circular cylinder tip mass attached to its free end which is placed in a uniform air flow and subjected to direct harmonic excitations. We model the fluctuating lift coefficient by a van der Pol wake oscillator. The Euler-Lagrange principle and the Galerkin procedure are used to derive a nonlinear distributed-parameter model for a harvester under a combination of vibratory base excitations and vortex-induced vibrations. Linear and nonlinear analyses are performed to investigate the effects of the electrical load resistance, wind speed, and base acceleration on the coupled frequency, electromechanical damping, and performance of the harvester. It is demonstrated that, when the wind speed is in the pre- or post-synchronization regions, its associated electromechanical damping is increased and hence a reduction in the harvested power is obtained. When the wind speed is in the lock-in or synchronization region, the results show that there is a significant improvement in the level of the harvested power which can attain 150 % compared to using two separate harvesters. The results also show that an increase of the base acceleration results in a reduction in the vortex-induced vibrations effects, an increase of the difference between the resonant excitation frequency and the pull-out frequency, and a significant effects associated with the quenching phenomenon.
The concept of harvesting energy from galloping oscillations of a bluff body with different cross-section geometries attached to a cantilever beam is investigated. To convert these oscillations into electrical power, a piezoelectric transducer is attached to the transverse degree of freedom of the prismatic structure. Modal analysis is performed to determine the exact mode shapes of the structure. A coupled nonlinear distributed-parameter model is developed to determine the effects of the cross-section geometry, load resistance, and wind speed on the level of the harvester power. The quasi-steady approximation is used to model the aerodynamic loads. Linear analysis is performed to investigate the effects of the electrical load resistance and the cross-section geometry on the onset speed of galloping. The results show that the electrical load resistance and the cross-section geometry affect significantly the onset speed of galloping. Nonlinear analysis is performed to determine the effects of the electrical load resistance, cross-section geometry, and wind speed on the system's outputs and particularly the level of the harvested power. A comparison of the performance of the different cross sections in terms of displacement and harvested power is presented. The results show that different sections are better for harvesting energy over different regions of the flow speed. The results also show that maximum levels of harvested power are accompanied with minimum transverse displacement amplitudes for all considered (square, D, and triangular) cross-section geometries.
In this paper, we investigate experimentally the concept of energy harvesting from galloping oscillations with a focus on wake and turbulence effects. The harvester is composed of a unimorph piezoelectric cantilever beam with a square cross-section tip mass. In one case, the harvester is placed in the wake of another galloping harvester with the objective of determining the wake effects on the response of the harvester. In the second case, meshes were placed upstream of the harvester with the objective of investigating the effects of upstream turbulence on the response of the harvester. The results show that both wake effects and upstream turbulence significantly affect the response of the harvester. Depending on the spacing between the two squares and the opening size of the mesh, wake and upstream turbulence can positively enhance the level of the harvested power.
The normal form is proposed as a tool to analyze the performance and
reliability of galloping-based piezoaeroelastic energy harvesters. Two
different harvesting systems are considered. The first system consists
of a tip mass prismatic structure (isosceles 30° or square
cross-section geometry) attached to a multilayered cantilever beam. The
only source of nonlinearity in this system is the aerodynamic
nonlinearity. The second system consists of an equilateral triangle
cross-section bar attached to two cantilever beams. This system is
designed to have structural and aerodynamic nonlinearities. The coupled
governing equations for the structure's transverse displacement and the
generated voltage are derived and analyzed for both systems. The effects
of the electrical load resistance and the type of harvester on the onset
speed of galloping are quantified. The results show that the onset speed
of galloping is strongly affected by the load resistance for both types
of harvesters. The normal form of the dynamic system near the onset of
galloping (Hopf bifurcation) is then derived. Based on the nonlinear
normal form, it is demonstrated that smaller levels of generated voltage
or power are obtained for higher absolute values of the effective
nonlinearity. For the first harvesting system, the results show a
supercritical Hopf bifurcation for both isosceles 30° or square
cross-section geometries. The nonlinear normal form shows that the
isosceles triangle section (30°) is more efficient than the square
section. For the second harvesting system, the normal form is used to
identify the values of the nonlinear torsional spring which changes the
harvester's instability. It is demonstrated that this critical value of
the nonlinear torsional spring depends strongly on the load resistance.
Wing flapping and morphing can be very beneficial to managing the weight of micro air
vehicles through coupling the aerodynamic forces with stability and control. In this letter, harvesting
energy from the wing morphing is studied to power cameras, sensors, or communication devices
of micro air vehicles and to aid in the management of their power. A three-dimensional unsteady
vortex lattice method is used to simulate the aerodynamic loads on flapping wings. Active wing
shape morphing is considered to enhance the performance of the flapping motion. A gradient-based
optimization algorithm is used to identify the optimal kinematics that maximize the propulsive
efficiency. To benefit from the wing deformation, we place piezoelectric layers near the wing roots.
Gauss law is used to estimate the electrical harvested power. We demonstrate that enough power
can be generated to operate a camera. Numerical analysis shows the feasibility of exploiting wing
morphing to harvest energy and of improving the design and performance of micro air vehicles.
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.
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.
Piezoelectric and electromagnetic transduction techniques have peculiar advantages to leverage in the growing field of flow energy harvesting from aeroelastic vibrations. This letter presents the concept of hybrid piezoelectric-inductive power generation with electroaeroelastic modeling and simulations. Dimensionless analysis of the coupled system dynamics is indispensable to proper geometric scaling and optimization of aeroelastic energy harvesters. The governing electroaeroelastic equations are given in dimensionless form, and the effects of aeroelastic and electrical properties are investigated in detail toward understanding the dependence of the cut-in speed (flutter speed) and the maximum power output of the harvester on the system parameters.
This letter presents a comparative study of different tip cross-sections for small scale wind energy harvesting based on galloping phenomenon. A prototype device is fabricated with a piezoelectric cantilever and a tip body with various cross-section profiles (square, rectangle, triangle, and D-shape) and tested in a wind tunnel. Experimental results demonstrate the superiority of the square-sectioned tip for the low cut-in wind speed of 2.5 m/s and the high peak power of 8.4 mW. An analytical model is established and verified by the experimental results. It is recommended that the square section should be used for small wind galloping 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.
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.
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.
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.
An introduction to the analytical tools used to study the vibrations of
structures exposed to a fluid flow is provided. Models used to analyze
vortex-induced vibrations, galloping vibrations and stall flutter,
vibrations induced by an oscillating flow, and vibrations induced by
turbulence are outlined, together with approaches used to investigate
instabilities of tube rows and arrays and sound induced by vortex
shedding. The damping of structures and the motion of a ship in a seaway
are examined. Appendices describe some unsolved problems in the
theoretical analysis of fluid-flow vibration and provide a review of
vibrations of continuous structures.
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).
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
The vast reduction in the size and power consumption of sensors and CMOS circuitry has led to a focused research effort on
the on-board power sources which can replace the batteries. The concern with batteries has been that they must always be charged
before use. Similarly, the sensors and data acquisition components in distributed networks require centralized energy sources
for their operation. In some applications such as sensors for structural health monitoring in remote locations, geographically
inaccessible temperature or humidity sensors, the battery charging or replacement operations can be tedious and expensive.
Logically, the emphasis in such cases has been on developing the on-site generators that can transform any available form
of energy at the location into electrical energy. Piezoelectric energy harvesting has emerged as one of the prime methods
for transforming mechanical energy into electric energy. This review article provides a comprehensive coverage of the recent
developments in the area of piezoelectric energy harvesting using low profile transducers and provides the results for various
energy harvesting prototype devices. A brief discussion is also presented on the selection of the piezoelectric materials
for on and off resonance applications. Analytical models reported in literature to describe the efficiency and power magnitude
of the energy harvesting process are analyzed.
A quasi-steady analysis is made of the transverse galloping of a long prism of square section in a normal steady wind. Experimental
stationary aerodynamic forces are used in the theory, which leads to an ordinary differential equation with small non-linearity
for the displacement. This is solved by the first approximation method of Krylov and Bogoliubov, and it is found that some
characteristics of non-linear oscillators unusual in a mechanical system are predicted, in particular the occurrence of oscillation
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