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Dynamic vibration control devices provided with inertance, such as Tuned Inerter Dampers, Tuned Mass Damper Inerters or Tuned Liquid Column Damper Inerters, have been shown in numerous numerical studies to have superior vibration mitigation performance compared to conventional devices, such as Tuned Mass Dampers. One possible way to produce this in...
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... Prototype design Fig. 2 shows the experimental setup for the small-scale prototype of a fluid inerter developed at the Unit of Applied Mechanics, University of Innsbruck. The prototype consists of a cylinder barrel in which a piston, connected to a piston rod, moves back and forth. The barrel is closed at one end by the cylinder bottom and rigidly connected ...
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... mentioned in Section 3, increasing the amplitude of the input voltage signal for the complete configuration does not result in a significant change in the receptance for a given preload level. For a prestress of 0.05 V and input voltage ranges 0.40-0.60 V and 0.50-0.70 V, respectively, this is shown in Fig. 20 by the solid black and dashed red lines. This behavior is accurately reproduced by the derived mechanical model, as shown by the corresponding lines with markers in Fig. 20. Note that although the receptances are practically unaffected by the change in input voltage amplitudes, the displacement amplitudes in terms of the PSD increase ...
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... significant change in the receptance for a given preload level. For a prestress of 0.05 V and input voltage ranges 0.40-0.60 V and 0.50-0.70 V, respectively, this is shown in Fig. 20 by the solid black and dashed red lines. This behavior is accurately reproduced by the derived mechanical model, as shown by the corresponding lines with markers in Fig. 20. Note that although the receptances are practically unaffected by the change in input voltage amplitudes, the displacement amplitudes in terms of the PSD increase clearly as the input voltage level increases. This comparison shows that the distinct amplitude dependence that occurs in the dry configuration due to the non-linearity ...
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... Prototype design Fig. 2 shows the experimental setup for the small-scale prototype of a fluid inerter developed at the Unit of Applied Mechanics, University of Innsbruck. The prototype consists of a cylinder barrel in which a piston, connected to a piston rod, moves back and forth. The barrel is closed at one end by the cylinder bottom and rigidly connected ...
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... mentioned in Section 3, increasing the amplitude of the input voltage signal for the complete configuration does not result in a significant change in the receptance for a given preload level. For a prestress of 0.05 V and input voltage ranges 0.40-0.60 V and 0.50-0.70 V, respectively, this is shown in Fig. 20 by the solid black and dashed red lines. This behavior is accurately reproduced by the derived mechanical model, as shown by the corresponding lines with markers in Fig. 20. Note that although the receptances are practically unaffected by the change in input voltage amplitudes, the displacement amplitudes in terms of the PSD increase ...
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... significant change in the receptance for a given preload level. For a prestress of 0.05 V and input voltage ranges 0.40-0.60 V and 0.50-0.70 V, respectively, this is shown in Fig. 20 by the solid black and dashed red lines. This behavior is accurately reproduced by the derived mechanical model, as shown by the corresponding lines with markers in Fig. 20. Note that although the receptances are practically unaffected by the change in input voltage amplitudes, the displacement amplitudes in terms of the PSD increase clearly as the input voltage level increases. This comparison shows that the distinct amplitude dependence that occurs in the dry configuration due to the non-linearity ...
Citations
... However, while for the mass the governing law (Newton's second law) is assumed to be exact, the inerter is a technical device that must be manufactured [31][32][33]. This means that the linear mass amplification effect of the inerter only exists approximately due to deviations from linear behavior such as backlash [34], nonlinear compliance [35], friction [36], fluid compressibility [37], nonlaminar flow [38], cavitation [39], etc. As shown in previous studies [40], for efficient dynamic simulations using a linearization procedure, a linear mathematical model can be found that preserves the intrinsic characteristic of a real (nonlinear) inerter prototype. ...
... To extend and consolidate the findings of previous studies [39,40], this paper presents a new experimental campaign with the fluid inerter prototype. Specifically, the inerter is applied to a cross-laminated timber (CLT) panel in order to evaluate its effectiveness in reducing excessive displacements due to vertical excitation, while, for the first time, experimentally validating the numerical outcomes related to the connection conditions. ...
... Previous studies [39] have shown that it is both necessary and efficient to consider the electro-mechanical shaker as part of the analyzed system, so that the same excitation voltage signal used during the test can be used in the numerical analyses. This is achieved by modeling the shaker an electromechanical system with 2 DOFs, with M. Chillemi et al. the shaker displacement 1 ( ) (assumed to be equal to that of corner (1)) and the electrical current ( ) as DOFs [63]. ...
The so-called inerter is an attracting device that offers a solution to the goal of realizing or improving structural control devices with high mass ratios while avoiding the undesirable increase in dead load. The research presented here focuses on evaluating the performance of a fluid inerter in mitigating vertical vibrations of structures that exhibit multi-modal behavior, such as plates. First, a numerical study based on previous experimental data investigates the properties of the connection between the inerter and the structure to be controlled. Considering that a flexible connection has been shown to introduce a linearization effect, while a rigid connection of the inerter to the controlled structure can achieve significant displacement reductions, the influence of these two connection types over different inertance ratios is analyzed. To evaluate the practical suitability of the flexible connection to reduce the inherent nonlinear effects associated with the device, a novel application of the fluid inerter for vibration control in multi-modal structures is presented, exemplified by a cross-laminated timber panel, and compares its control performance with that of a conventional Tuned Mass Damper (TMD). This provides insight into the effectiveness of the inerter in controlling vertical vibrations. In addition, optimization procedures are employed to determine connection parameters that enhance the effectiveness of both the TMD and the inerter in mitigating vertical vibrations.
... • Nonlinear damping [33] • Durable sealing necessary [34] • Friction [35] = radius of the rack pinion, 0 = rack pinion and gear mass, 0 = rack pinion and gear radius of gyration, = flywheel and pinion mass, = flywheel and pinion radius of gyration, = gearing ratio, = pitch of the screw, = density of the working fluid, = length of the external pipe, 1 = cross-sectional area of the main cylinder minus the rod, 2 = cross-sectional area of the external pipe. mechanical elements, theoretically allow the realization of more effective alternatives to these devices due to the application of a lower mass to reduce accelerations in vibrations-prone structures. ...
... In a previous study [35], a fluid inerter prototype was experimentally tested and its parameter numerically identified. In this case, the model was developed with only one design parameter setting. ...
... Second, the inerter without the presence of the working fluid, referred to as the dry inerter device (DID), is examined ( Fig. 2 -DID). This type of test was deemed necessary in previous studies [35] because hydraulic systems such as hydraulic cylinders require accurate consideration of friction in the model employed [38]. It is obvious that its understanding is facilitated when other effects related to the presence of the working fluid are not present. ...
In the study presented here, the dynamic properties of a fluid inerter, including nonlinear effects, are characterized and the degree of its effectiveness in structural control is assessed. A fluid inerter is a mechanical device that models an element with unit of mass whose mass property (called inertance) greatly exceeds its physical mass. To this end, a small-scale prototype is realized and experimentally investigated. Linear and nonlinear parameters are identified to obtain a mechanical model suitable for more accurate parametric studies. Numerical simulations based on a finite element model are performed to evaluate the effects of the air unavoidably trapped in the system. In order to apply the device to engineering problems in more general configurations, a linearization procedure is performed for the nonlinear system elements and a comparison is made between the real and the linearized system.
... Some natural phenomena can be modeled by linear and non-linear systems of integral and differential equations, which are commonly used in fields such as biology, chemistry, and physics [1][2][3][4][5][6][7][8][9][10][11]. Many numerical methods, such as collocation boundary value methods, discontinuous Galerkin approximations, Euler matrix method, spectral element method, Chebyshev wavelets approach, and Radial basis Functions, have been provided to solve linear and nonlinear Volterra integral equations [12][13][14][15][16][17]. ...
This article proposes a new approach for solving linear Volterra integral equations with variable coefficients using the Reproducing Kernel Method (RKM). This method eliminates the need for the Gram-Schmidt process. However, the accuracy of RKM is influenced by various factors, including the selection of points, bases, space, and implementation method. The main objective of this article is to introduce a generalized method based on the Reproducing Kernel, which is successful in solving a special type of singular weakly nonlinear boundary value problems (BVPs). The easy implementation, elimination of the Gram-Schmidt process, fewer calculations, and high accuracy of the present method are interesting. The conformity of numerical results, including tables and figures, with theorems related to error analysis and convergence order, confirms the practicality of the present method.
... The systems of BVPs have recently been applied for modeling various phenomena in nature, such as those used in mechanical sciences, finance, biology, and so on [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Various computational methods are used to solve systems of BVPs, including a gradient descent method, a new piecewise reproducing kernel function algorithm, an RBF collocation approach, an explicit integration method, a convolutional iterative solver, a Legendre wavelet collocation method, analytical accurate solutions, and a novel Petrov-Galerkin method. ...
... In Sect. 4, three examples are solved using the present method and their numerical results are presented in the form of tables and figures. Finally, we conclude in the last section. ...
In this paper, a new implementation based on the reproducing kernel method (RKM) without the Gram–Schmidt orthogonalization for solving linear and nonlinear systems of second-order boundary value problems is presented. In the RKM method, components such as points, space, inner product, bases, and a suitable method have an effect on increasing the accuracy. The easy implementation, elimination of the Gram–Schmidt process, fewer calculations, and high accuracy of the present method are interesting. The compatibility of numerical results and theorems demonstrates that the Present method is effective.
... Kuhnert et al. [50] reviewed the history of inerter's development. This type of inerter, such as ballscrew [51] and fluid [52] inerters, is important for the weight reduction of the vibration isolator. Zhang et al. [53] proposed to use an inerter instead of mass in the NES, and the present paper is also inspired by their work. ...
A two-degree-of-freedom (2DOF) vibration isolation structure with an integrated geometric nonlinear inerter (NI) device is proposed. The device is integrated into an inertial nonlinear energy sink (INES), and its vibration suppression performance is examined by the Runge-Kutta (RK) method and verified by the harmonic balance method (HBM). The new isolator is compared with a traditional vibration isolator. The results show a significant improvement in the vibration suppression performance. To investigate the effects of the excitation amplitude and initial condition on the dynamics of the system, a series of transmissibility-frequency response analyses are performed based on the displacement transmissibility. The energy flow of the system is analyzed, and numerous calculations reveal a series of ideal values for the energy sink in the NI-INES system. This study provides new insights for the design of vibration isolators.
... In order to enhance the control performance with limited physical mass of the DVA, a device called "inerter" [29] has been introduced in the recent decade. Physically realized by different mechanisms, such as the rack and pinion [30], ball-screw [31], hydraulic [32,33] etc.. The inerter device can produce control force in proportion to the relative acceleration between its two ends, which is equivalent to a mass or inertial effect. ...
A novel Lever-type Inerter-based Vibration Absorber (LIVA) is proposed. The proposed LIVA is based on a lever supported on a flexible auxiliary structure, connecting between the primary structure and a paralleled inerter-dashpot system. Based on analytical H∞ and H2 optimization, the formulas of the optimal parameters for the LIVA are derived. The parametric influences on optimal parameters and control performance of the LIVA are systematically investigated. Consequently, the control performance of the LIVA can be enhanced by increasing the auxiliary mass, lever ratio, or the frequency of the auxiliary structure. Considering practical aspect, the influences of damping ratios are discussed to compensate the assumptions adopted in analytical optimization. Thus, a design criterion is proposed to ensure the effectiveness of the LIVA. Finally, the vibration absorption performance of the LIVA is illustrated and compared through time domain analysis subjected to a recent earthquake event. The results have shown that the proposed LIVA exhibits a superior control performance than traditional TMD and another lever-type vibration absorber reported in a literature due to the leverage and inertance effects. Moreover, compared to the existed lever-type vibration absorbers with a fixed fulcrum, the proposed LIVA supported by a flexible auxiliary structure appears more feasible in practice.
... In order to numerically reproduce the experimental results and reveal nonlinear effects, the mechanical model of the FID is developed as shown in Fig. (3). In previous studies [12] it has proven necessary to include the vibration exciter in the simulation model. Hence, the latter results in electro-mechanical system whose input signal is the same voltage signal as in the experimental investigations. ...
... the system of Eqs (2) can be reformulated as a first-order system and solved, for example, in MATLAB by the standard ode45 solver [12]. Finally, the system consists of an electrical DOF q(t), and two mechanical DOFs x 1 (t) and x 2 (t) corresponding to the displacement of the piston and the water mass with respect to the ground, respectively. ...
... In general, for hydraulic systems, such as hydraulic cylinders, a proper model of the tribological interactions is required [15]. In particular, to obtain the correct friction model of the piston rod sliding in the cylinder, a dissipation force element f diss is introduced [12]. Due to a pronounced stick-slip phenomenon detected during testing, velocity-independent models such as Coulomb friction proved to be unsuitable for the system. ...
Vibrations can occur as a result of natural disasters such as earthquakes or strong wind, or simply due to human activity. To protect civil structures subjected to these undesirable conditions, the vibrations mitigation effect of well-known passive control systems can be improved by using a mass amplification device called inerter. This is a mechanical system that can be treated as a two-terminals element capable of producing an apparent mass (inertance), which can be orders of magnitude larger than its physical mass. One way to create the inertance effect is to use a moving fluid, which is known as fluid inerter. In this study, an experimental and numerical investigation is carried out to assess the behavior of such a device and its influence on the response of vibration-prone systems. The prototype consists of a hydraulic cylinder in which the flow of water through an external channel provides the fictitious mass effect. The identified dynamic properties of the device is assigned to an accurate mechanical model. The latter shows a nonlinear behavior due to the fluid viscous, shear friction, pressure drops and other tribological effects, which are verified by comparative studies. The remarkable agreement between numerical and experimental outcomes demonstrates that the found nonlinear mechanical model can be used for further realistic numerical simulations.
... This considerably improves mechanical network implementation [3]. As a result of their outstanding mechanical qualities, inerters have been extensively employed in the area of vibration reduction, such as buildings [4][5][6], cables [7,8], robot joints [9,10], automobiles [11][12][13][14], aircrafts [15,16], etc. Inerters come in a variety of configurations, including fluid [17], ball screw [18][19][20], rack and pinion [21], and others. Among them, the friction of the ball screw type inerter is lower, which may lessen the impact of back clearance by employing the nut pre-tightening force, and the inertance of the same mass is higher, resulting in superior overall performance [22]. ...
The planetary flywheel can significantly reduce the weight of the flywheel, allowing the inerter to be lightweight. When a planetary flywheel ball screw inerter-based active actuator is used in a vehicle suspension system, the nonlinear features of the actuator affect vehicle performance. The planetary flywheel inerter actuator’s nonlinear dynamic model is constructed in this study based on the dynamic features of the planetary flywheel ball screw inerter and the electromagnetic torque generating mechanism of the permanent magnet synchronous motor. The impact of ball screw–nut friction, transmission clearance, planetary gear friction, and meshing clearance on the performance of an active tuned inerter damper suspension is then investigated. As a result, the impact and sensitivity of numerous nonlinear parameters on suspension performance are shown, providing a theoretical foundation for the design of planetary flywheel inerter actuators and active inerter suspension.
... As far as the first aspect is concerned, in order to promote lower-mass alternatives of TMDs and TLCDs, their use in combination with a device referred to as inerter, has recently attracted particular attention due to its peculiar feature of amplifying the mass connected to it. Since its first presentation in 2002 [17], the inerter has been extensively studied and tested in many forms such as rack and pinion, ball-scraw, hydraulic and fluid inerter, in various fields, from automotive to civil engineering [18,19]. Regardless of type, the inerter is a two-terminal device whose resisting force is directly proportional to the relative acceleration between its terminals and to a constant of proportionality called inertance, which has the dimension of a mass (kg). ...
In this paper, the concept of a novel passive control device, namely the Nontraditional Tuned Liquid Column Damper Inerter (NT-TLCDI), is investigated in combination with seismic base isolation (BI), to control lateral displacement demands in base-isolated structures during seismic events. The considered NT-TLCDI is a revision of the ordinary configuration of the recently proposed Tuned Liquid Column Damper Inerter (TLCDI). Unlike the traditional TLCDI layout, which involves a secondary liquid mass in a U-shaped tank coupled with a grounded inerter and connected to the isolation system by a spring-dashpot system, in the NT-TLCDI configuration, the damper is in parallel with the inerter rather than the spring. The optimal design, including the determination of the tuning frequency and damping ratios of the NT-TLCDI, is discussed with the purpose to reduce the base displacement variance of the BI system assuming a white noise base excitation. Under the optimal tuning condition, it is found that the proposed NT-TLCDI provides a larger suppression of vibration amplitude of the BI system than the traditional TLCDI in both the frequency domain and time domain. A more interesting aspect is the reduction of the device displacement achieved by the NT-TLCDI, which may be beneficial in practice when the space for housing the device is limited.
... Smith proposed the concept of the inerter [42], which is an inertial component that can provide large inertia with a small mass. This type of inerter, such as ballscrew [43] and fluid [44] inerters, is important for the weight reduction of the vibration isolator. ...
In this paper, a geometrically nonlinear inerter (NI) device consisting of two inerters with a designed configuration is presented. Such a device is integrated in an inertial nonlinear energy sink (INES), and we examine its vibration suppression performance using the Runge-Kutta (RK) method, which is verified by the harmonic balance method (HBM). The new isolator is compared to a traditional vibration isolator, and the results show a significant improvement in vibration suppression performance. To investigate the effects of different excitation amplitudes and initial conditions on the dynamics of the system, a series of transmissibility-frequency response analyses are performed by defining the displacement transmissibility. These analyses are carried out at frequencies near the natural frequency. The energy flow of the system is analyzed, and numerous calculations reveal a series of ideal values for the energy sink in the NI-INES system. This study provides new insights for the design of vibration isolators.
