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Extending the dynamic range of an energy harvester using nonlinear damping

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... Additional nonlinear damping has shown many advantages in vibration suppression and exploitation [1][2][3][4][5]. For example, Magneto-rheological (MR) nonlinear damping has been widely applied in vibration isolations for engineering structures such as buildings [1] and vehicles [2]. ...
... For example, Magneto-rheological (MR) nonlinear damping has been widely applied in vibration isolations for engineering structures such as buildings [1] and vehicles [2]. Recently, nonlinear damping has also been proven to be beneficial for vibrational energy harvesting [3,5]. These have shown that nonlinear damping can play important roles and have great potential in solving different engineering problems. ...
... Yan et al. [12] indicate that antisymmetric nonlinear damping suspension can benefit high-speed rotor systems achieving a desired isolation performance with more stable response than the linear damping. Recently, researchers have also explored the application of antisymmetric nonlinear damping in energy harvesting systems [3][4][5], demonstrating that, under certain conditions, an antisymmetric nonlinear dampingbased energy harvester can harvest more energy than a linear energy harvester system. Hendijanizadeh et al. [5] developed an energy harvesting device for small boats and yachts where the dynamic range of the energy harvester was expanded using variable load resistance mechanism that can produce nonlinear damping characters. ...
Article
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Beneficial effects of nonlinear damping on energy harvesting and vibration isolation under harmonic inputs have been investigated showing that the introduction of nonlinear damping can increase the harvested energy and reduce the vibration over both the resonant and higher frequency ranges. However, the scenario becomes more complicated when the loading inputs are of more general form such as multi-tone and random inputs, which can produce system responses that are induced by an interaction of system input components of different frequencies. In the present study, by introducing the concept of power transmissibility, the study of the beneficial effects of nonlinear damping is extended to the systems subject to general inputs including both multi-tone and random inputs. A rigorous analysis is conducted based on single degree of freedom systems subject to general inputs. The analysis reveals the conditions under which the antisymmetric nonlinear damping is beneficial for improving energy harvester performance and reducing of the power of system output in vibration isolation. Moreover, the beneficial effects are demonstrated by two case studies.
... Although the VEH operational bandwidth limitation has received considerable attention in literature, its operational dynamic range limitation has not been given much attention until recently [11][12][13][14][15]. It was proposed in [11] that the dynamic range of a VEH could be extended with the use of nonlinear cubic damping. ...
... Although the VEH operational bandwidth limitation has received considerable attention in literature, its operational dynamic range limitation has not been given much attention until recently [11][12][13][14][15]. It was proposed in [11] that the dynamic range of a VEH could be extended with the use of nonlinear cubic damping. This analytical study was done using the Harmonic Balance Method (HBM) to examine the effects of the two damping systems on the amount of power harvested. ...
... Based on the findings in [11], an analysis, design and optimisation of a nonlinear VEH system was performed in [14,15]. An optimum cubic damping parameter was estimated in these studies for a desired harvester energy, using the OFRF method recently proposed in [16,17]. ...
... The nonlinear characteristics have been explored to improve the energy harvesting performance in the low frequency range [6][7][8][9][10][11][12][13][14][15][16][17]. The snap-through energy harvesting system composed of two incline linear springs is designed to achieve good harvesting performance of low frequency. ...
... In Fig. 13, the harvesting power of the proposed system is compared with a recently reported nonlinear damping system in Ref. [16]. The parameters of the nonlinear damping system in Ref. [16] are taken as linear damping ratio ζ 1 = 0.04, nonlinear damping ratio ζ 3 = 0.02 and the base excitation Y = 0.006, where the damping ratio of proposed harvesting system is taken of ξ = 0.04. ...
... In Fig. 13, the harvesting power of the proposed system is compared with a recently reported nonlinear damping system in Ref. [16]. The parameters of the nonlinear damping system in Ref. [16] are taken as linear damping ratio ζ 1 = 0.04, nonlinear damping ratio ζ 3 = 0.02 and the base excitation Y = 0.006, where the damping ratio of proposed harvesting system is taken of ξ = 0.04. The mechanical-electrical conversion coefficient is taken as 0.5 for both the harvesting systems in the calculation of Fig. 13. ...
Article
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A novel nonlinear structure with adjustable stiffness, damping and inertia is proposed and studied for vibration energy harvesting. The system consists of an adjustable-inertia system and X-shaped supporting structures. The novelty of the adjustable-inertia design is to enhance the mode coupling property between two orthogonal motion directions, i.e., the translational and rotational directions, which is very helpful for the improvement of the vibration energy harvesting performance. Weakly nonlinear stiffness and damping characteristics can be introduced by the X-shaped supporting structures. Combining the mode coupling effect above and the nonlinear stiffness and damping characteristics of the X-shaped structures, the vibration energy harvesting performance can be significantly enhanced, in both the low frequency range and broadband spectrum. The proposed 2-DOF nonlinear vibration energy harvesting structure can outperform the corresponding 2-DOF linear system and the existing nonlinear harvesting systems. The results in this study provide a novel and effective method for passive structure design of vibration energy harvesting systems to improve efficiency in the low frequency range.
... The application of a nonlinear softening spring proposed in [9] was employed to effect the adjustment of the resonant frequency as it was also shown that this improved the energy harvester bandwidth over which power can be harvested. Contrary to increasing the energy-harvester operational bandwidth to improve the range over which energy can be harvested, it has been recently revealed in [10] that the dynamic range of an energy-harvester can be improved by employing an energy harvester with nonlinear damping. The performance of an energy harvester with a nonlinear cubic damping coefficient was compared with that of an equivalent linear damper with same mass displacement response at resonance. ...
... However, when excited below the maximum acceptable excitation level, the nonlinear harvester performed better compared to the linear version hence harvested more power. An analytical study was done in [10,11] using the Harmonic Balance Method (HBM) to see the effects of the two damping systems on the amount of power harvested while additionally investigating the effect of coil resistance in [11] for each case. However, in the current study, an analysis and design of a nonlinear harvester will be explored using the Output Frequency Response Function (OFRF) whereby an optimum cubic damping parameter will be evaluated to achieve the maximum power attainable for the harvester. ...
... The set of monomials required to obtain the OFRF representation is obtained using the algorithm stated in (9)(10)(11) which is applied to the model (3) ...
... Several methods have been developed for enlarging the effective energy harvesting bandwidth, including multi-generator methods [7][8][9][10][11][12] and nonlinear methods [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. In the multi-generator methods, the effective power harvesting bandwidth can be increased through using generator arrays [7,8] or multi-resonance modes [9][10][11]. ...
... Some nonlinear damping and stiffness techniques have been increasingly utilized to improve the vibration energy harvesting performance [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The harvesting performance around the resonant frequency can be much improved by a cubic nonlinear damper [14]. ...
... Some nonlinear damping and stiffness techniques have been increasingly utilized to improve the vibration energy harvesting performance [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. The harvesting performance around the resonant frequency can be much improved by a cubic nonlinear damper [14]. Nonlinear stiffness-based nonlinear oscillators or bi-stable generators are studied to harvest vibration energy with more than one stable equilibrium [15][16][17][18][19][20][21][22][23][24][25]. ...
Article
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In the paper, beneficial nonlinearities incurred by an X-shape structure are explored for advantageous vibration energy harvesting performance. To this aim, a nonlinear structure beneficial for vibration energy harvesting is proposed, which is composed by X-shape supporting structures and a rigid body. By designing structure nonlinearities, which are determined by several key structure parameters, the power output peak of the harvesting system can be much improved and the effective frequency bandwidth for energy harvesting can be obviously increased, especially at the low frequency range. A coupling effect can be created among nonlinear stiffness and damping characteristics by constructing a 2-DOF vibration system, which has great influence on the energy harvesting performance. The proposed nonlinear energy harvesting systems can obviously outperform the corresponding linear systems in the whole frequency range and also demonstrate advantages compared with some other existing nonlinear energy harvesting systems in the literature. The results in this study provide a novel and practical method for the design of effective and efficient energy harvesting systems (especially in the low frequency range).
... However, excitations below the maximum value reduces the energy harvested. A recent study in [8] revealed that a nonlinear cubic electrical damping extends the harvestable power of a VEH. It was shown that by integrating a cubic nonlinear damper to a VEH system, it outperformed an equivalent linear VEH. ...
... It was shown that by integrating a cubic nonlinear damper to a VEH system, it outperformed an equivalent linear VEH. The results obtained in [8] indicated that at maximum excitation, the same relative displacement of the VEH and hence average power, are provided by both nonlinear and equivalent linear VEHs. Nevertheless, at excitations below the maximum level, the nonlinear VEH provided more energy compared to its linear equivalent. ...
... In this study, a base-excited single degree-of-freedom (SDOF) VEH is considered, as illustrated in Figure 1. The SDOF system is seen to have an oscillating mass, m , basedisplacement ( ) y t , spring stiffness 1 k , the relative displacement between the oscillating mass and the support-base of the harvester ( ) The dynamic equation [8] is given as ...
Chapter
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One of two major limitations of a vibration energy harvester (VEH), concerns its limited performance due to its confined physical enclosure. The maximum span realizable is attained at a specific excitation level. This excitation level provides the maximum energy harvested by the VEH device. Due to span constraints, VEHs are designed to operate at the maximum span achievable at the maximum excitation level existing within the region of interest. In this study, a constrained optimisation problem (for the VEH) is formulated and investigated. This paper focuses on the analysis, design and optimisation of a nonlinear VEH device.
... Nonlinear control can be achieved by introducing nonlinearities in the damping force or stiffness force, to enhance the performance of the system through vibration isolation [1] or energy harvesting [2]. Nonlinear damping has been observed in a significant number of engineering systems such as automotive shock absorbers [3,4], orifices [5], loudspeakers [6], nanoelectromechanical systems such as graphenes [7] and aircraft wings [8]. ...
... Nonlinear damping has also been investigated for the problem of energy harvesting by Ghandchi Tehrani et al [2] to extend the dynamic performance range of the harvester. The system with nonlinear damper can harvest more energy at resonance when driven below its maximum amplitude compared to the system with linear damper. ...
Article
Full-text available
This paper presents the inverse design method for the nonlinearity in an energy harvester in order to achieve an optimum damping. A single degree-of-freedom electromechanical oscillator is considered as an energy harvester, which is subjected to a harmonic base excitation. The harvester has a limited throw due to the physical constraint of the device, which means that the amplitude of the relative displacement between the mass of the harvester and the base cannot exceed a threshold when the device is driven at resonance and beyond a particular amplitude. This physical constraint requires the damping of the harvester to be adjusted for different excitation amplitudes, such that the relative displacement is controlled and maintained below the limit. For example, the damping can be increased to reduce the amplitude of the relative displacement. For high excitation amplitudes, the optimum damping is, therefore, dependent on the amplitude of the base excitation, and can be synthesised by a nonlinear function. In this paper, a nonlinear function in the form of a bilinear is considered to represent the damping model of the device. A numerical optimisation using Matlab is carried out to fit a curve to the amplitude-dependent damping in order to determine the optimum bilinear model. The nonlinear damping is then used in the time-domain simulations and the relative displacement and the average harvested power are obtained. It is demonstrated that the proposed nonlinear damping can maintain the relative displacement of the harvester at its maximum level for a wide range of excitation, therefore providing the optimum condition for power harvesting.
... To overcome the limitation of linear harvesters possessing narrow effective frequency range [7] [8], several nonlinear oscillators have been considered and the corresponding nonlinear power generators are proposed to broaden the effective frequency range such as monostable [9], bistable [10] [11], tristable [12], and multistable energy harvesters [13][14][15][16][17]. The dynamics and energy capture performance of these nonlinear harvesters have been thoroughly investigated via analytical [18] [19], numerical [20] and experimental methods [21] under abundant simulation and environmental excitations such as harmonic [22], stochastic [23][24][25], and compound excitations [26] [27]. These researches reveal that the large-orbit well escaping phenomenon can be activated in a large range of frequency [2], making the nonlinear energy harvesters beneficial in realistic environments. ...
... in which, (20) into (17), the decaying amplitude of the second-piece snap-through vibration is ...
Article
Bistable vibration energy harvesters are sensitive to impulsive excitations widely existed in environments, and the favorable large-orbit snap-through oscillation possesses high energy conversion efficiency and output voltage. The enhanced averaging method (EA) with Jacobian elliptic functions provides an analytical, efficient tool of guiding the structural design and parameters optimization of bistable harvesters excited in impulsive environments. However, the EA method still suffers some limitations: the predicted transient dynamics undergo undesired sudden jump at the end moment of the snap-through regime; and phase error occurs during the intrawell regime when large initial velocity is applied. To address these limitations, an improved EA method is proposed in this paper. The transient dynamics in the snap-through and intrawell regimes are separately approximated via two-piecewise expressions, leading to high-fidelity estimation of the vibration amplitude and critical moment dividing the snap-through from intrawell dynamics which occur later in the time. A novel, more accurate estimation of the vibration phase is derived. The prediction performance of the improved EA method is validated via numerous comparisons with the EA method and numerical simulations. It shows that the improved EA method effectively eliminates the aforementioned limitations induced by EA method, providing high-fidelity reconstruction of the transient dynamics of the bistable harvesters excited in impulsive environments.
... To enhance the power generation capabilities of micro systems, the ideas of tunable resonant frequency [17], multi-modal vibratory excitation [18], multi-DoF oscillators [19,20] and adjusting the mass [21] and damping [22] were employed in piezoelectric energy harvesters. The advent of these proposals, increased the efficiency of the energy harvesters, while complicating the corresponded mathematical models. ...
... and = / . Substituting the electrical field as 3 = − /ℎ in (22) and simplifying the outcome of (23), one can get ...
Article
The construction of self-powered micro-electro-mechanical units by converting the mechanical energy of the systems into electrical power has attracted much attention in recent years. While power harvesting from deterministic external excitations is state of the art, it has been much more difficult to derive mathematical models for scavenging electrical energy from ambient random vibrations, due to the stochastic nature of the excitations. The current research concerns analytical modeling of micro-bridge energy harvesters based on random vibration theory. Since classical elasticity fails to accurately predict the mechanical behavior of micro-structures, strain gradient theory is employed as a powerful tool to increase the accuracy of the random vibration modeling of the micro-harvester. Equations of motion of the system in the time domain are derived using the Lagrange approach. These are then utilized to determine the frequency and impulse responses of the structure. Assuming the energy harvester to be subjected to a combination of broadband and limited-band random support motion and transverse loading, closed-form expressions for mean, mean square, correlation and spectral density of the output power are derived. The suggested formulation is further exploited to investigate the effect of the different design parameters, including the geometric properties of the structure as well as the properties of the electrical circuit on the resulting power. Furthermore, the effect of length scale parameters on the harvested energy is investigated in detail. It is observed that the predictions of classical and even simple size-dependent theories (such as couple stress) appreciably differ from the findings of strain gradient theory on the basis of random vibration. This study presents a first-time modeling of micro-scale harvesters under stochastic excitations using a size-dependent approach and can be considered as a reliable foundation for future research in the field of micro/nano harvesters subjected to non-deterministic loads.
... An interesting idea to reduce the displacement and therefore size of a harvester whilst maintaining strong performance is to introduce nonlinear damping [83]. An upper bound on electrical power dissipation for a system with nonlinear damping similar to those of Eqs. ...
... (2.10) and (2.15) can be derived provided the electrical resistance is linear, but only for a prescribed rather than a general damping nonlinearity. As such, the method will be described below for a linear plus cubic damping nonlinearity as in [83], although it would need modifying accordingly for a different damping profile. ...
Thesis
With the rapid development of electronic technology, the power consumption of electronic devices has decreased significantly. Consequently, there is substantial interest in harvesting energy from ambient sources, such as vibration, in order to power small-scale wireless devices. To design optimal vibration harvesting systems it is important to determine the maximum power obtainable from a given vibration source. Initially, white noise base excitation of a general nonlinear energy harvester model is considered. The power input from white noise is known to be proportional both to the total oscillating mass of the system and the magnitude of the noise spectral density, regardless of the internal mechanics of the system. This power is split between undesirable mechanical damping and useful electrical dissipation, where the form of the stiffness profile and device parameters determine the relative proportion of energy dissipated by each mechanism. An upper bound on the electrical power is derived and used to guide towards optimal harvesting devices, revealing that low stiffness systems exhibit maximum performance. Many engineering applications will exhibit more complicated spectra than the flat spectrum of white noise. Expanding upon the white noise analysis, a method to investigate the power dissipation of nonlinear oscillators under non-white excitation is developed by extending the Wiener series. The relatively simple first term of the series, together with the excitation spectrum, is found to completely define the power dissipated. An important property of this first term, namely that the integral over its frequency domain representation is proportional to the oscillating mass, is derived and validated both numerically and experimentally, using a base excited cantilever beam with a nonlinear restoring force produced by magnets. Another form of excitation prevalent in many mechanical systems is a combination of deterministic and broadband random vibration. Lastly, the Duffing oscillator is used to illustrate the behaviour of a nonlinear system under this form of excitation, where the response is observed to spread around the attractor that would be seen if purely deterministic excitation was present. The ability of global weighted residual methods to produce the complex responses typical of nonlinear oscillators is assessed and found to be accurate for systems with weak nonlinearity.
... Some other different methods for employing nonlinear damping and stiffness characteristics to improve the vibration energy harvesting performance have also been reported in the literature [67][68][69][70][71][72][73][74]. The harvesting performance around the resonant frequency can be improved by a cubic nonlinear damper [71]. ...
... Some other different methods for employing nonlinear damping and stiffness characteristics to improve the vibration energy harvesting performance have also been reported in the literature [67][68][69][70][71][72][73][74]. The harvesting performance around the resonant frequency can be improved by a cubic nonlinear damper [71]. As mentioned above, larger effective harvesting bandwidth can be obtained through the design of nonlinear oscillation compared with linear ones. ...
... Apart from increasing the deformation of piezoelectric materials to obtain more energy, the energy recovery bandwidth can be improved. This includes changing the structure to adjust its resonant frequency [17][18][19][20] or employing a structure with two degrees of freedom [21][22][23]. The nonlinear structure in article [17] was optimized to improve the energy recovery bandwidth. ...
... The nonlinear structure in article [17] was optimized to improve the energy recovery bandwidth. The energy-recovery bandwidth was increased in another study [18] using nonlinear damping. In reference [20], the natural frequency of a nonlinear vibration-energy recovery device can be adjusted, to harvest power near the resonance frequency. ...
Article
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Because the power consumption of a controlled suspension is huge, the power harvest potential of a nonlinear controlled suspension is analyzed. Instead of simplifying the suspension to a linear model or adopting some control strategies to solve the problem, this paper investigates the effect of the nonlinear characteristics on the power harvesting potential. A mathematic model is introduced to calculate the nonlinear vibration, and the amount of harvested power was obtained using the multi-scale method. A numerical validation is carried out at the end of this study. The results show that the investigated mechanical parameters affect both the vibration amplitude and the induced current, while the electric parameters only affect the induced current. The power harvesting potential of the nonlinear suspension is generally greater than the linear suspension because the frequency band of the actual pavement also contains bandwidth surrounding the body resonance point. The only exception occurs if the vehicle travels on a road with a particular profile, e.g. a sine curve. To optimize harvested power, it is better to consider the nonlinear characteristics rather than simplifying the suspension to a linear model.
... In spite of the inherent complexity related to the description of the peculiar properties of each specific device, the simplest elasto-viscous constitutive laws are reproduced by the Kelvin-Voigt (KV) or Maxwell (Ma) model, fully described by two parameters, a stiffness and a viscous damping coefficient, whose assessment may play an important role in the preliminary design stage [8]. Nonlinear damping has been considered for the problem of energy harvesting and it has been demonstrated that it can extend the dynamic performance range of the harvester [9]. Quasi-linear models have been used to describe the dynamic response of the system with nonlinear damping. ...
... . Substituting the two time responses and their derivatives into Eqs. (9) and (10), and ignoring higher order harmonics leads to, ...
Article
Full-text available
In this paper, a dynamical system, which consists of two linear mechanical oscillators, coupled with a nonlinear damping device is considered. First, the dynamic equations are derived, then, an analytical method such as harmonic balance method, is applied to obtain the response to a harmonic base excitation. The response of the system depends on the excitation characteristics. A parametric study is carried out based on different base excitation amplitudes, frequencies, and different nonlinear damping values and the response of the system is fully described. For validation, time domain simulations are carried out to obtain the nonlinear response of the coupled system.
... In spite of the inherent complexity related to the description of the peculiar properties of each specific device, the simplest elasto-viscous constitutive laws are reproduced by the Kelvin-Voigt (KV) or Maxwell (Ma) model, fully described by two parameters, a stiffness and a viscous damping coefficient, whose assessment may play an important role in the preliminary design stage [8]. Nonlinear damping has been considered for the problem of energy harvesting and it has been demonstrated that it can extend the dynamic performance range of the harvester [9]. Quasi-linear models have been used to describe the dynamic response of the system with nonlinear damping. ...
... . Substituting the two time responses and their derivatives into Eqs. (9) and (10), and ignoring higher order harmonics leads to, ...
Conference Paper
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In this paper, a dynamical system, which consists of two linear mechanical oscillators, coupled with a nonlinear damping device is considered. First, the dynamic equations are derived, then, an analytical method such as harmonic balance method, is applied to obtain the response to a harmonic base excitation. The response of the system depends on the excitation characteristics. A parametric study is carried out based on different base excitation amplitudes, frequencies, and different nonlinear damping values and the response of the system is fully described. For validation, time domain simulations are carried out to obtain the nonlinear response of the coupled system. 1. Introduction Structural control deals with methodologies to design control systems for structural vibration attenuation even in the presence of strong external loadings such as the ones induced by seismic motion. Structural control methodologies can be grouped in three categories: active, semi-active and passive control [1]. The design solutions offered in the recent available literature aim to balance the opposite needs of synthesis and representativeness for either the damping system or the damped structure. A pair of simple oscillators or a pair of equivalent one-dimensional beams, coupled with a variety of damping devices, have often been employed as a synthetic but representative model to describe a wide class of structural realizations – for instance, adjacent tall buildings – or quasi-independent subsystems that compose a single complex structure. Several studies have been carried out for the optimization and design of the structures. For example, different strategies have been proposed for the optimal placement of viscous-type coupling devices into seismic joints to dissipate energy and to avoid hammering phenomena [2, 3]. A series of studies has also been devoted to dissipative interconnections realized through hysteretic dampers [4, 5], friction dampers [6] or semi-active devices [7]. In spite of the inherent complexity related to the description of the peculiar properties of each specific device, the simplest elasto-viscous constitutive laws are reproduced by the Kelvin–Voigt (KV) or Maxwell (Ma) model, fully described by two parameters, a stiffness and a viscous damping coefficient, whose assessment may play an important role in the preliminary design stage [8]. Nonlinear damping has been considered for the problem of energy harvesting and it has been demonstrated that it can extend the dynamic performance range of the harvester [9]. Quasi-linear models have been used to describe the dynamic response of the system with nonlinear damping. The quasi-linear model can provide a good representation since the response of the system with nonlinear damping does not include jump phenomena or bifurcation in contrast to that with nonlinear stiffness [10]. In this paper, a simple dynamic system composed of two linear oscillators is employed to analyze the control performance that can be achieved through a nonlinear damper connecting the two oscillators.
... Nonlinear control can be achieved by introducing nonlinearities in the damping force or stiffness force, to enhance the performance of the system through vibration isolation [1] or energy harvesting [2]. Nonlinear damping has been observed in a significant number of engineering systems such as automotive shock absorbers [3,4], orifices [5], loudspeakers [6], nanoelectromechanical systems such as graphenes [7] and aircraft wings [8]. ...
... Nonlinear damping has also been investigated for the problem of energy harvesting by Ghandchi Tehrani et al [2] to extend the dynamic performance range of the harvester. The system with nonlinear damper can harvest more energy at resonance when driven below its maximum amplitude compared to the system with linear damper. ...
Conference Paper
Full-text available
This paper presents the inverse design method for the nonlinearity in an energy harvester in order to achieve an optimum damping. A single degree-of-freedom electro-mechanical oscillator is considered as an energy harvester, which is subjected to a harmonic base excitation. The harvester has a limited throw due to the physical constraint of the device, which means that the amplitude of the relative displacement between the mass of the harvester and the base cannot exceed a threshold when the device is driven at resonance and beyond a particular amplitude. This physical constraint requires the damping of the harvester to be adjusted for different excitation amplitudes, such that the relative displacement is controlled and maintained below the limit. For example, the damping can be increased to reduce the amplitude of the relative displacement. For high excitation amplitudes, the optimum damping is, therefore, dependent on the amplitude of the base excitation, and can be synthesised by a nonlinear function. In this paper, a nonlinear function in the form of a bilinear is considered to represent the damping model of the device. A numerical optimisation using Matlab is carried out to fit a curve to the amplitude-dependent damping in order to determine the optimum bilinear model. The nonlinear damping is then used in the time-domain simulations and the relative displacement and the average harvested power are obtained. It is demonstrated that the proposed nonlinear damping can maintain the relative displacement of the harvester at its maximum level for a wide range of excitation, therefore providing the optimum condition for power harvesting. 1. Introduction Nonlinear control can be achieved by introducing nonlinearities in the damping force or stiffness force, to enhance the performance of the system through vibration isolation [1] or energy harvesting [2]. Nonlinear damping has been observed in a significant number of engineering systems such as automotive shock absorbers [3,4], orifices [5], loudspeakers [6], nanoelectromechanical systems such as graphenes [7] and aircraft wings [8]. It has been demonstrated that quasi-linear models can provide a very good approximations to obtain the dynamic response of such systems [9], since nonlinear damping in contrast to nonlinear stiffness does not introduce jump or bifurcation phenomena to the system's response.
... Thus, traditional linear energy harvesters are usually limited to very narrow frequency ranges. In order to broaden the frequency bandwidth for effective energy harvesting, different techniques such as nonlinear energy harvesting [2,[18][19][20][21][22][23][24][25][26][27], array-harvester systems [28,29], and frequencytunable systems [30] have been developed so the harvester can accommodate a broader frequency range. Each technique has its own advantages and disadvantages. ...
... For instance, the array-harvester design can harvest the vibration energy over resonant frequencies of each linear system; however, the system set-up and the corresponding electronic configuration are complex, which makes the utilization very challenging [5]. Nonlinear energy harvesters [2,[18][19][20][21][22][23][24][25][26][27], which are commonly used in piezoelectric and electromagnetic generators, can broaden the effective frequency bandwidth by exploiting geometric and material nonlinearities; however, these nonlinear techniques are not as efficient as linear energy harvesters at resonance. ...
Article
Vibration energy is becoming a significant alternative solution for energy generation. Recently, a great deal of research has been conducted on how to harvest energy from vibration sources ranging from ocean waves to human motion to microsystems. In this paper, a theoretical model of a piecewise-linear (PWL) nonlinear vibration harvester that has potential applications in variety of fields is proposed and numerically investigated. This new technique enables automatic frequency tunability in the energy harvester by controlling the gap size in the PWL oscillator so that it is able to adapt to changes in excitations. To optimize the performance of the proposed system, a control method combining the response prediction, signal measurement and gap adjustment mechanism is proposed in this paper. This new energy harvester not only overcomes the limitation of traditional linear energy harvesters that can only provide the maximum power generation efficiency over a narrow frequency range but also improves the performance of current nonlinear energy harvesters that are not as efficient as linear energy harvesters at resonance. The proposed system is demonstrated in several case studies to illustrate its effectiveness for a number of different excitations.
... The harvester consists of a nonlinear single degree of freedom system (spring-masse-damper) subjected to a base excitation near the primary resonance. This study extends the results obtained in the case without the time delay reported in [1]. ...
... Thanks to its flexibility and adaptability, of particular interest is parametric resonance [12], which refers to time-variations of one or more system parameters, typically either the stiffness coefficient [13] or the damping coefficient [14]. Practical implementations of such energy maximisation principles can be obtained via variable orifice dampers, controllable fluid dampers, or magneto-rheological dampers [15]. ...
Article
Recent years have witnessed an increasing interest in energy harvesting in order to improve the overall power efficiency and making sensors self-sufficient and durable. One major potential source of energy is related to vibrations, ubiquitous in every mechanical system. In order to increase net harvested power and absorption frequency bandwidth, nonlinearities inducing instability may be exploited: this paper considers periodic variations of the damping term of the power takeoff system, which creates conditions for parametric resonance. The stability transition curves of the system are studied according to the Floquet theory, computed by harmonic balance. Numerical simulations are performed in order to study the performance of active and passive parametric control, as well as constant-coefficient passive control. Active control requires a more complex power takeoff system able to feed energy into the system in order to increase the overall net harvested power. The increase in complexity should be justified by the marginal gain in power extraction performance. A fundamental role is played by the level of internal dissipation of the system, which is found to make the active parametric control strategy best for applications with low internal damping, while less attractive for more dissipative systems.
... A bigger amount of power harvested using the developed nonlinear device compared to the linear one. Nonlinear cubic damping has been investigated by Tehrani et al. [38] to increase the dynamic range of an energy harvester, and it is noticed that the nonlinear damping also leads to nonlinear stiffness properties. ...
... Thereby some work focus on obtaining a broadband energy harvester by using nonlinearities. Mann [7] suggested a bistable system with magnetic interaction, a system with a nonlinear damping was proposed by Tehrani [8], while Litak [9] proposed an inverted beam with a tip mass. ...
Conference Paper
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Smart material has the ability to convert energy between two distinct physical domains. Piezoelectric material are an example of this material, the vibration-based energy harvesting using piezoelectric elements is possible by exploring the direct effect, where the piezoelectric material is able to convert mechanical in to electrical energy. This application can be very useful for applications in powering small electronic devices. The energy harvesting system presented in this work is a magnetoelastic structure that consists of a ferromagnetic cantilevered beam with two permanent magnets, one located in the free end of the beam and the other at a vertical distance d from the beam free end. In order to use this device as a piezelectric power generator, two piezoceramic layers are attached to the root of the cantilever and a bimorph generator is obtained. The piezomagnetoelastic structure is subjected to a combination of harmonic and random excitations. The parameter Noise-to-Signal Ratio (NSR) is used in order to quantify different combinations of the forcing terms. A method to evaluate the harvested energy and the performance of the piezomagnetoelastic structure is proposed. The method is applicable both to deterministic and to non-deterministic signals and is based on the Power Spectral Density (PSD) of the input, dimensionless force, and the output signal, dimen-sionless electrical voltage. Numerical simulations are carried out identifying better combinations of harmonic and random excitations for energy harvesting purposes.
... In the early stage, the resonant-based vibration harvesters have been widely used to generate energy, which could only achieve considerable energy harvesting performance at or near its resonant frequency [5,6]. To remedy this problem, many structural optimization designs [7,8] and technologies including resonance tuning technique [9][10][11][12], monostable technique [13][14][15][16][17], bistable technique [18][19][20][21][22] and tristable technique [23][24][25][26][27] have been proposed. Theoretical analysis and experimental results have shown that the nonlinear harvester could improve the ability to harvest energy under certain circumstances. ...
Article
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In the stage of modelling, measuring, mechanical processing and manufacturing of the nonlinear energy harvesting system, deviations and errors of system parameters are inevitable. Even slight variation of key parameters may have a significant influence on the output voltages, especially for the multi-stable nonlinear case. Therefore, the investigation of dynamic behaviors for the tristable energy harvesting system with uncertain parameters is of important value both for research and application. In this paper, the uncertainty of a tristable piezoelectric vibration energy harvester with a random coefficient ahead of the nonlinear term is studied. By using the Chebyshev polynomial approximation, this tristable energy harvesting system is first reduced into an equivalent deterministic form, the ensemble mean responses of which are derived to exhibit the stochastic behaviors. The periodic and chaotic motions, bifurcations and crises under different conditions are analyzed. The results show that the output voltage is sensitive to the uncertainty of the nonlinear coefficient, which leads to unstable behavior around the bifurcation and crisis points particularly. Exploring the influence pattern of uncertain parameters on the output voltage and avoiding the unstable parameter intervals are essential for optimizing the structure. It can further improve the efficiency of the nonlinear energy harvesting system.
... To overcome this problem, harvesters with adjustable natural frequencies [20] and multiple oscillators [21] have been proposed to improve the performance of the harvesters. Furthermore, the use of damping to allow better extraction over a broad frequency band [22] and the use of nonlinear behavior [23] and magnetic buckling [24] have been exploited to harvest energy efficiently over a wider frequency range. ...
... In order to increase the frequency range and the dynamic range of the excitation amplitude over which the vibration energy harvester operates, various nonlinear arrangements have been suggested, particularly using nonlinear springs [8,9], which have been previously used for vibration isolation [10,11]. Recently, semi-active strategies [12] have been used and nonlinear damping in the form of cubic damping has been introduced to extend the dynamic range of an energy harvester [13]. In the semi-active control paper [12], the damping consisted of a series of harmonics of the excitation frequency. ...
... For instance, the resonance frequency of the cantilever-based PEHs can be tuned to be close to the external vibration frequency so that the energy harvesting efficiency can be improved [1][2][3][4]. The unique nonlinear vibration characteristics can stimulate nonlinear-based PEHs to produce larger deformation [5][6][7][8]. Most of the reported PEHs so far focus on harvesting the energy of alternating vibration, but the collection of instantaneous energy generated in the process of collision or impact has seldom been reported. ...
Article
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In this study, a novel piezoelectric energy harvester (PEH) based on the array composite spherical particle chain was constructed and explored in detail through simulation and experimental verification. The power test of the PEH based on array composite particle chains in the self-powered system was realized. Firstly, the model of PEH based on the composite spherical particle chain was constructed to theoretically realize the collection, transformation, and storage of impact energy, and the advantages of a composite particle chain in the field of piezoelectric energy harvesting were verified. Secondly, an experimental system was established to test the performance of the PEH, including the stability of the system under a continuous impact load, the power adjustment under different resistances, and the influence of the number of particle chains on the energy harvesting efficiency. Finally, a self-powered supply system was established with the PEH composed of three composite particle chains to realize the power supply of the microelectronic components. This paper presents a method of collecting impact energy based on particle chain structure, and lays an experimental foundation for the application of a composite particle chain in the field of piezoelectric energy harvesting.
... In order to improve the performances in the practical environment, the wideband and high energy conversion efficiency at the low frequency are the two main difficulties needing to solve for the energy harvester (Deng et al. 2016;Chen et al. 2015;Bryn and Kean 2015;Mahmoudi et al. 2014). Some methods have been proposed in the literatures, among which the nonlinear energy harvesting method is one of the feasible solutions (Maryam and Stephen 2014;Al-Ashtari et al. 2012;Marzencki et al. 2009). ...
Article
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In this paper, a novel broadband hybrid piezoelectric and electromagnetic energy harvester using in the low frequency vibration environment is proposed, which combines nonlinear magnet force and frequency-up conversion mechanism simultaneously. Performances are studied by theoretical analysis and experimental test. Electromechanical governed equations of harvester are established, and analytical solutions of vibration response, output voltage and power are derived. Then, effects of nonlinear force, spacing between low frequency vibration beam and piezoelectric beam, load resistance and input excitation on harvester performances are investigated by experimental test. It can be concluded that the harvester can be used to work at the low-frequency environment efficiently, and the resonant frequency and harvesting bandwidth can be tuned by the nonlinear force between the magnets and the spacing between beams. Moreover, the larger the nonlinear magnetic force and the smaller the distance between two beams, the lower working frequency and the larger bandwidth. Compared with the corresponding linear apartment, output power and bandwidth of proposed harvester are improved 90% and 125% respectively.
... Zhou et al. and Santon et al. applied HB method to calculate the frequency response curves of tristable [16] and bistable [17] piezoelectric energy harvester, respectively. Tehrani et al. [18] also investigated an electromagnetic vibration energy harvester based on HB method. All these above-mentioned examples only considered fundamental harmonic responses in the calculating process. ...
... In addition to multistable systems based on cantilever beams and magnets, several researchers have proposed alternative designs of nonlinear energy harvesters. Tehrani et al in 2014 [227] showed that using nonlinear Coulomb damping, a higher level of power can be harvested when the system is excited below the resonant frequency. Arrieta et al in 2010 [228] suggested the application of a bistable piezoelectric composite plate for nonlinear energy harvesting. ...
Article
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Energy harvesting technologies have been explored by researchers for more than two decades as an alternative to conventional power sources (e.g. batteries) for small-sized and low-power electronic devices. The limited life-time and necessity for periodic recharging or replacement of batteries has been a consistent issue in portable, remote, and implantable devices. Ambient energy can usually be found in the form of solar energy, thermal energy, and vibration energy. Amongst these energy sources, vibration energy presents a persistent presence in nature and manmade structures. Various materials and transduction mechanisms have the ability to convert vibratory energy to useful electrical energy, such as piezoelectric, electromagnetic, and electrostatic generators. Piezoelectric transducers, with their inherent electromechanical coupling and high power density compared to electromagnetic and electrostatic transducers, have been widely explored to generate power from vibration energy sources. A topical review of piezoelectric energy harvesting methods was carried out and published in this journal by the authors in 2007. Since 2007, countless researchers have introduced novel materials, transduction mechanisms, electrical circuits, and analytical models to improve various aspects of piezoelectric energy harvesting devices. Additionally, many researchers have also reported novel applications of piezoelectric energy harvesting technology in the past decade. While the body of literature in the field of piezoelectric energy harvesting has grown significantly since 2007, this paper presents an update to the authors' previous review paper by summarizing the notable developments in the field of piezoelectric energy harvesting through the past decade.
... The focus is on a single-degree-offreedom (SDOF) system with nonlinear damping force proportional to even or/and odd orders of velocity. Such systems have been widely used for analysis of rolling ship subjected to beam waves, [21][22][23][24] and they are adopted to investigate potential benefits in vibration control [25][26][27] and energy harvesting, [28][29][30] where iterative algorithm is essentially required in a numerical method. As shall be shown in this paper, the present temporal finite element method (TFEM) stemming from EHP formalism adopts non-iterative algorithm and this method with small size of time step is equivalent to the Runge-Kutta-Fehlberg (RKF45) method with default error criteria. ...
Article
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The paper explores application of the variational formalism called extended framework of Hamilton’s principle to nonlinear damping systems. Single-degree-of-freedom systems with dominant source of nonlinearity from polynomial powers of the velocity are initially considered. Appropriate variational formulation is provided, and then the corresponding weak form is discretized to produce a novel computational method. The resulting low-order temporal finite element method utilizes non-iterative algorithm, and some examples are provided to verify its performance. The present temporal finite element method using small time step is equivalent to the adaptive Runge–Kutta–Fehlberg method with default error tolerances in MATLAB, and additional simulation shows its good convergence characteristics.
... As an example, Challa et al. [8] presented the idea of a tunable resonance frequency using magnetic force which is capable of broadening the resonance frequency by ±20% its untuned value. Tehrani and Elliot [9] utilized a cubic nonlinear ...
Article
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The current research investigates the novel approach of coupling separate energy harvesters in order to scavenge more power from a stochastic point of view. To this end, a multi-body system composed of two cantilever harvesters with two identical piezoelectric patches is considered. The beams are interconnected through a linear spring. Assuming a stochastic band limited white noise excitation of the base, the statistical properties of the mechanical response and those of the generated voltages are derived in closed form. Moreover, analytical models are derived for the expected value of the total harvested energy. In order to maximize the expected generated power, an optimization is performed to determine the optimum physical and geometrical characteristics of the system. It is observed that by properly tuning the harvester parameters, the energy harvesting performance of the structure is remarkably improved. Furthermore, using an optimized energy harvester model, this study shows that the coupling of the beams negatively affects the scavenged power, contrary to the effect previously demonstrated for harvesters under harmonic excitation. The qualitative and quantitative knowledge resulting from this analysis can be effectively employed for the realistic design and modelling of coupled multi-body structures under stochastic excitations.
... They showed that the frequency response of the studied model has advantages over linear oscillators. Ghandchi Tehrani et al. [15] used nonlinear damping instead of nonlinear stiffness to improve energy harvester. The results of their study indicated improved efficiency of the system in the resonance area. ...
Article
In this study, fluid energy harvesting by piezoelectric materials has been investigated. COMSOL Multiphysics software is used for numerical modeling. Fluid flow from the cylinder is shed to wake in the downstream flow. The purpose of this study is to investigate the effect of vortex generator shapes and the effect of including a nonlinear mechanism to obtain the maximum energy in the Reynolds range of 770≲Re≲7700. The obtained results show that geometry of the vortex generator has great effects on the vortex frequency, without significant effects on vortex power. The use of nonlinear mechanisms leads to an increased bandwidth of harvested power, which can be achieved by reducing potential system levels and creating chaotic behaviors. Presenting a strategy to design an energy harvester in a specific interval of fluid velocity and giving a practical approach to the comparison between several harvesters within the similar Reynolds range, are the considerable achievements of this work.
... Different approaches have been utilized to solve this intrinsic limitation. A nonlinear mechanism is one the most interesting and recent proposals that could harvest energy from broad-band excitations since they normally work in chaotic mode [8]. One kind of these nonlinear mechanisms is multi-stable ones, that behave different in dissimilar frequencies because of different equilibrium points which gives an extra freedom to the energy harvesting device. ...
Conference Paper
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Vibration is an available source of energy to supply electrical power demand of the freight wagons as it is one the most important challenges in railway engineering. Here we propose an efficient bistable mechanism with linear power take-off and nonlinear stiffness for energy harvesting of freight wagon vibrations. Design parameters of the bitable systems is optimized by genetic algorithm (GA) and simulated annealing (SA) to extract maximum power. It is shown that remarkable enhancement can be achieved in comparison with conventional linear energy harvesters. The reason for this enhancement is harmonic oscillation between stable equilibrium points of the system which is very well matched with the nature of random excitation exerted by the rail irregularities.
Thesis
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Many alternative energy sources have been investigated in the last decades, energy harvesting from the environment is of these possibilities and have been explored recently by using piezoelectric material. This vibration-based energy harvesting using piezoelectric elements is possible by exploring the direct effect, where the piezoelectric material is able convert mechanical in to electrical energy. This application can be very useful for applications in powering small electronic devices. The energy harvesting system presented in this work is a magnetoelastic structure that consists of a ferromagnetic cantilevered beam with two permanent magnets, one located in the free end of the beam and the other at a vertical distance d from the beam free end. In order to use this device as a piezelectric power generator, two piezoceramic layers are attached to the root of the cantilever and a bimorph generator is obtained. The piezomagnetoelastic structure is subjected to harmonic excitation, random excitation and harmonic combined with random excitation. The parameter is proposed in order to verify different combination between random excitation to the harmonic excitation. The goal of the proposed analysis in this work is to evaluate the energy harvested and the performance of the piezomagnetoelastic. The numerical analysis presents a comparison between the Power Spectral Density (PSD) of the input, dimensionless force, and output signal, dimensionless electrical voltage, setting a parameter that evaluates the ratio of PSD of the input and output signal. The results are classified according the periodicity of the response, and can be observed that the energy harvested are better in cases that the response amplitude are bigger.
Chapter
In this chapter, a novel concept known as the GALEs (Generalized Associated Linear Equations) is proposed that can accurately evaluate the system Volterra series representation. By using the GALEs, the solution to the NDE model or the NARX model of nonlinear systems can be obtained by simply dealing with a series of linear differential or difference equations, which can facilitate a wide range of nonlinear system analyses and associated practical applications. The application of the GALEs for the evaluation of the time domain output response of a nonlinear system, the determination of the NOFRFs using the GALEs for nonlinear system frequency analyses, and the use of the GALEs in the identification of the NDE model of a nonlinear system are discussed to demonstrate the effectiveness of the GALEs method.
Article
Most of the dynamic systems are inherently nonlinear either with stiffness nonlinearity or with damping nonlinearity. Presence of nonlinearity often leads to characteristic behaviours in response such as jump phenomenon, limit cycle and super-harmonic resonances. Such behviours can be accurately predicted only if the nonlinearity structure and related parameters are properly known. A majority of identification works is based on a-priori knowledge of nonlinearity structure and most of them consider only stiffness nonlinearities. Not much work has been reported on identification and parameter estimation in the area of damping nonlinearities. This paper presents a systematic classification of asymmetric damping nonlinearity and develops a parameter estimation algorithm using harmonic excitation and response amplitudes in terms of higher order Frequency Response Functions. The asymmetry in damping nonlinearity is modeled as a polynomial function containing square and cubic nonlinear terms and then Volterra series is employed to derive the response amplitude formulation for different harmonics using synthesied higher order Frequency Response Functions. Detailed numerical study is carried out with different combinations of square and cubic nonlinearity parameters to investigate appropriate excitation level and frequency so as to get measurable signal strength of second and third harmonics and at the same time keeping the Volterra series approximation error low. The estimation algorithm is first presented for nonlinear parameters and then it is extended for estimation of linear parameters including damping ratio. It is demonstrated through numerical simulation that nonlinear damping parameters can be accurately estimated with proper selection of excitation level and frequency.
Chapter
Piezoelectric vibration energy harvesting has been extensively investigated in recent years and the majority of results focus on using the cantilever beam model under base driven motion. The main focus of this paper is to perform a parametric analysis of multi degrees of freedom piezo-elastic energy harvester to optimize the capability curve exploiting crossing/veering between modes. The structure under test consists of a combination of slender beams with one or more orthogonal beam segments placed on it. The resulting combined structure exhibits bending vibration modes in orthogonal planes. The cross and veering phenomena are studied in deep, attempting to improve the resulting mechanical-electrical energy conversion of the combined structure. A numerical model of the system under investigation is developed considering also non-classical damping. A parametric analysis of the system’ s performance due to geometrical and electrical properties variations are investigated to design a broadband harvester. An experimental analysis is performed on a test rig specially built to investigate the crossing and veering phenomena effects on the resulting output voltage from the energy harvester. Numerically simulated and experimental data are compared to provide information for updating the model as well as to address the efficiency of the harvester in terms of voltage generation.
Conference Paper
To overcome the easy fracture of cantilever-based harvesters under large amplitude vibration, this paper presents a magnetoelectric vibration energy harvester based on rotary pendulum-type structures. The harvester is made up of a rotary pendulum embedded with six magnets and a magnetoelectric transducer. The dynamic equation of the rotary pendulum-type structures is established. An analytical model is developed to analyze the nonlinear vibration and electrical-output performances of the harvester. A prototype is fabricated and tested. The analytical and experimental results show that the harvester has frequency-doubling characteristics and can produce high power at low frequency vibration. The prototype produces a power of 980µW for an acceleration of 0.4g (1g=9.8ms−2) at resonant frequency of 14.1Hz.
Article
The rising technologies of wearable electronics resulted in urgent demand for developing eco-friendly power sources that can utilize free energies around us including ambient vibrations. Magnetic springs are amongst the most common techniques used to build vibration energy harvesting systems that convert vibrational energy into useful electric power. Here, we present an experimental and theoretical platform for design guidelines and analysis of magnetic springs encountered in vibration energy harvesting systems. An energy harvester prototype consisting of an oscillating solid magnet levitated between two stationary ring magnets is constructed and used for experimental evaluation. Results show excellent agreement between model and experiment. The use of the analytical force model to represent magnetic force nonlinearities is essential at high accelerations. While the magnetic damping coefficient varies during dynamic operation and is dependent on the position of the levitated magnet, it is shown that approximating this coefficient as a constant provides accurate prediction of the dynamic behavior of the system. Approximate analytical expressions for linear and nonlinear stiffness coefficients are obtained. Results suggest that linear and nonlinear stiffness coefficients are coupled. The outer diameter of the stationary ring magnet can be used to tune the nonlinearity of the energy harvesting system to obtain linear, hardening nonlinear, or softening nonlinear response. This work serves as a tool for designers to understand the behavior of magnetic spring based harvesting systems and evaluate their performance in light of their design parameters. This work also can serve other energy systems that utilize magnetic springs including energy sinks.
Article
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This paper presents the design and the manufacturing of an electromagnetic- transducer energy harvester. The design considers the coupling between the mechanical vibrating behaviour, generated by a base excitation, and the electromagnetic conversion of energy, which is aimed to produce the voltage across a load resistance. The design is based on some constraints, which are related to the characteristics of the shaker and aimed to obtain the best performance of the device. Current tests show the presence friction at low input levels, which is associated with the gearbox. The output voltage and the harvested power of the device are studied experimentally for different values of load. By increasing the value of the load from zero (short circuit) to high values (open circuit) the swing angle increases, while the harvested power presents a peak associated with the electrical damping. Also, harmonic tests are run at resonance for different levels of excitation to demonstrate the effect of the nonlinearity on the voltage and the harvested power. A nonlinear load resistance, is then introduced as part of future work. The aim is to try to increase the harvested power with respect to the linear load, at low level of excitation.
Article
In this paper, we perform the nonlinear frequency response function (FRF) estimation for a class of nonlinear systems. Two non-parametric estimation techniques are considered: radial basis function neural network (RBF-NN)-based estimation and support vector machine (SVM)-based estimation. Based on the system's available observations, the proposed estimation models are used to predict its frequency response. Simulation results are provided to demonstrate the model implementation. Finally, a comparative study is carried out to evaluate the effectiveness of the RBF-NN and SVM schemes, which has demonstrated that the SVM outperformed RBF-NN in the FRF estimation.
Article
Damping is often assumed to viscous and linear in modeling a dynamic system. However, damping is inherently nonlinear and often is in non-polynomial forms such as Coulomb damping, bilinear, or quadratic damping. Recently, non-polynomial forms of damping have found wide applications in vibration isolators and absorbers. However, not much study is available for the identification of these non-polynomial forms of damping. The present work attempts to develop an identification and parameter estimation procedure for two non-polynomial damping forms, i.e., bilinear damping and quadratic damping. First, response harmonic amplitudes are formulating using Volterra series and equivalent linearised damping; and then they are compared with representative polynomial forms, i.e., square damping and cubic damping. Bilinear damping was identified employing a method of harmonic probing and studying first and second harmonic amplitude characteristics. Similar way, quadratic damping is identifying using first and third harmonic characteristics. Finally, a parameter estimation procedure is developed as a step-by-step algorithm and demonstrated through numerical simulation and error analysis. It is shown that reasonable accuracy can be obtained in estimation of the nonlinear parameters with proper selection of excitation frequencies and excitation levels.
Article
In this paper we present a novel concept to efficiently harvest vibrational energy at low frequencies and very small displacement. We describe and evaluate an electromagnetic energy harvester which generates power from a magnetic circuit with motion induced variations of an air gap. External vibrations induce oscillations of the gap length around an equilibrium point, due to a linear spring counteracting the magnetic force. The relative position of the spring can be adjusted to optimize the harvester output for excitation amplitude and frequency. A simulation model is built in COMSOL and verified by comparison with lab measurements. The simulation model is used to determine the potential performance of the proposed concept under both harmonic and non-harmonic excitation. Under harmonic excitation, we achieve a simulated RMS load power of 26.5 μW at 22 Hz and 0.028 g acceleration amplitude. From a set of comparable EH we achieve the highest theoretical power metric of 1712.2 µW/cm³/g² while maintaining the largest relative bandwidth of 81.8%. Using measured non-harmonic vibration data, with a mean acceleration of 0.039 g, resulted in a mean power of 52 μW. Moreover, the simplicity and robustness of our design makes it a competitive alternative for use in practical situations.
Article
This work explores an enhanced magnetic spring based energy harvester design that uses a dual-mass and a geometrically nonlinear mechanical planar spring as a route to significantly improve power metrics of traditional magnetic spring based energy harvesters. Prototypes of the enhanced harvester are constructed and characterized experimentally. Nonlinear dynamical models of the harvester are developed and validated against experimental data. Additionally, prototypes of the commonly studied magnetic spring based energy harvesters are constructed, characterized, and modeled. Results show excellent agreement between model simulations and experimental data. Results show that the enhanced harvester significantly outperforms the commonly studied magnetic spring based vibration energy harvesters, especially at low acceleration levels. The enhanced harvester generates 1.97 [mW/cm³ g²] at 0.4 g [m/s²] which is approximately 400% the amount of power generated by the traditional magnetic spring based harvester, i.e. 0.5 [mW/cm³ g²]. Additionally, the half-power frequency bandwidth of the enhanced harvester is 90% wider compared to the traditional harvester. At lower acceleration, i.e. 0.1 g [m/s²], the enhanced harvester exhibits 4000% increase in power metrics compared to the traditional harvester. This makes the presented enhanced harvester design exceptionally suitable for applications where low acceleration oscillations are abundant including harvesting vibrations from highway bridges and human body motion.
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For the designed nonlinear hybrid piezoelectric (PE)–electromagnetic (EM) energy harvester, electromechanical coupling state equations are established at stochastic excitation, and vibration response, output mean power, voltage and current are derived by statistical linearization method. Then, effects of nonlinear strength, load resistance and excitation spectral density on vibration response and electric output of nonlinear hybrid energy harvester are studied by theoretical analysis, simulation and experimental test. It is obtained that mean power of nonlinear hybrid energy harvester increases linearly with acceleration spectral density; the bigger nonlinear strength, the bigger output power of energy harvester and the lower resonant frequency are; besides, mean amplitude of nonlinear hybrid energy harvester reaches the minimum at PE optimal load, but it increases with EM load increasing. Compared with linear hybrid energy harvester, the resonant frequency of nonlinear energy harvester can be decreased by 57%, while output power can be increased by 72%.
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In some energy harvesters, the maximum throw of the seismic mass is limited due to the physical constraints of the device. The shunt load resistance of such a harvester is generally selected based on the allowable throw of the mass when the device is subjected to the maximum level of excitation. However, the energy harvester with this value of shunt resistance does not perform well at lower levels of excitation. In this article, a variable load resistance, scheduled on the excitation level, is introduced to extend the dynamic range of an energy harvester in applications where excitation level varies. This method is applied to the design of an energy harvester, which comprises a sprung mass coupled to an electric motor through a lead screw. The dynamic equation and parameters of the system are introduced and the device is experimentally characterized, by conducting random vibration tests. The harvested power and the relative displacement are then obtained for different sinusoidal base excitation amplitudes when the system is excited at a frequency close to its natural frequency. It is demonstrated that the use of a variable load resistance mechanism can significantly improve the dynamic range and output power of the energy harvester.
Article
Vibration control and energy harvesting have been extensively investigated over the past decades. Recent engineering applications motivate a new requirement where vibrations are required to be distributed in a designated specification. This vibration distribution requirement represents a generic problem where both vibration control and energy harvesting need be brought in a par. This paper presents a systematic investigation to this important problem. Fundamental issues associated with vibration distribution under specifications, constraints handling, as well as dynamics and/or topology feedback designs etc are disseminated. Important results are obtained with extensive remarks providing guidance for applications. The corresponding claims are verified through numerical examples.
Article
Undesired oscillations commonly encountered in engineering practice can be harmful to structures and machinery. Vibration isolation systems are used to attenuate undesired oscillations. Recently, there has been growing interest in nonlinear approaches towards vibration isolation systems design. This work is focused on investigating the effect of nonlinear cubic viscous damping in a vibration isolation system consisting of a magnetic spring with a positive nonlinear stiffness, and a mechanical oblique spring with geometric nonlinear negative stiffness. Dynamic model of the vibration isolation system is obtained and the harmonic balance method (HBM) is used to solve the governing dynamic equation. Additionally, fourth order Runge–Kutta numerical simulation is used to obtain displacement transmissibility of the system under investigation. Results obtained from numerical simulation are in good agreement with those obtained using HBM. Results show that introducing nonlinear damping improves the performance of the vibration isolation system. Nonlinear damping purposefully introduced into the described vibration isolation system appears to eliminate undesired frequency jump phenomena traditionally encountered in quasi-zero-stiffness vibration isolation systems. Compared to its rival linear vibration isolation system, the described nonlinear system transmits less vibrations around resonant peak. At lower frequencies, both nonlinear and linear isolation systems show comparable transmissibility characteristics.
Article
In the natural environment, rectilinear motions normally take the form of low-frequency and broadband vibrations. This poses problems for devices aimed at harvesting energy from these motions, since conventional linear electromagnetic generators are inefficient under such conditions. Here we present a bistable triboelectric linear generator (BTLG) with nonlinear characteristics for low-frequency and broadband energy harvesting. In this device, a nonlinear structure is used to achieve the bistable contact–separation motion to widen the working bandwidth as well as enhance the energy harvesting efficiency in low-frequency range. Piezoelectric components are also used in the device without increasing the complexity of the structure, which can compensate for the defects that the contact-separation mode triboelectric nanogenerator cannot work at a small amplitude. Experiments show that a 10µF capacitor can be charged to 0.12 V in 60 s at an ultralow frequency of 0.1 Hz. The frequency bandwidth of the BTLG is greatly broadened to 441% compared with a linear device. The proposed BTLG is capable of harvesting mechanical energy at low frequency with large working bandwidth, thus providing a effective method for energy harvesting of ambient low-frequency rectilinear motions.
Article
This study investigates the vibration of and power harvested by typical electromagnetic and piezoelectric vibration energy harvesters when applied to vibrating host systems that rotate at constant speed. The governing equations for these electromechanically coupled devices are derived using Newtonian mechanics and Kirchhoff's voltage law. The natural frequency for these devices is speed-dependent due to the centripetal acceleration from their constant rotation. Resonance diagrams are used to identify excitation frequencies and speeds where these energy harvesters have large amplitude vibration and power harvested. Closed-form solutions are derived for the steady-state response and power harvested. These devices have multifrequency dynamic response due to the combined vibration and rotation of the host system. Multiple resonances are possible. The average power harvested over one oscillation cycle is calculated for a wide range of operating conditions. Electromagnetic devices have a local maximum in average harvested power that occurs near a specific excitation frequency and rotation speed. Piezoelectric devices, depending on their mechanical damping, can have two local maxima of average power harvested. Although these maxima are sensitive to small changes in the excitation frequency, they are much less sensitive to small changes in rotation speed.
Article
A vibration isolation system featuring a combination of elastic and magnetic springs and viscous and magnetic damping is presented. A mechanical flat spring houses a permanent magnet that is levitated between two stationary magnets. A prototype of the isolator is manufactured. COMSOL models are developed for the mechanical and magnetic springs. Measured data and model simulations show that the magnets arrangement results in nonlinear magnetic spring with negative linear stiffness. The mechanical spring exhibits linear behavior with positive stiffness. Experiments are performed and a nonlinear dynamic model is developed. The fabricated isolator is characterized at low and high acceleration levels. Results from model show good agreement with measured data at lower acceleration levels. Slight mismatch between model and experiment is evident at higher accelerations. This mismatch is due to the existence of lateral vibrations that are not accounted for in the unidirectional model. Results show that the combination of mechanical flat spring and magnetic spring reduces the resonant frequency of the isolator. In addition, results confirm the ability of the isolator to attenuate vibrations higher than 11.91 Hz when excited at 2.4525 [m s⁻²].
Article
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In a previous study, the authors have proved that in theory the introduction of a cubic non-linear damping can produce ideal vibration isolation such that the system force transmissibility over the resonant frequency region is modified, but the transmissibility over the non-resonant regions remain unaffected. The present study is concerned with both an experimental verification of this theoretical finding and the selection of the cubic damping characteristic parameter required to achieve a desired performance for a single degree of freedom vibration isolation system. These results provide an important basis for the design and practical application of non-linearly damped vibration isolation systems in engineering practice.
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This review presents possible strategies to increase the operational frequency range of vibration-based micro-generators. Most vibration-based micro-generators are spring-mass-damper systems which generate maximum power when the resonant frequency of the generator matches the frequency of the ambient vibration. Any difference between these two frequencies can result in a significant decrease in generated power. This is a fundamental limitation of resonant vibration generators which restricts their capability in real applications. Possible solutions include the periodic tuning of the resonant frequency of the generator so that it matches the frequency of the ambient vibration at all times or widening the bandwidth of the generator. Periodic tuning can be achieved using mechanical or electrical methods. Bandwidth widening can be achieved using a generator array, a mechanical stopper, nonlinear (e.g. magnetic) springs or bi-stable structures. Tuning methods can be classified into intermittent tuning (power is consumed periodically to tune the device) and continuous tuning (the tuning mechanism is continuously powered). This review presents a comprehensive review of the principles and operating strategies for increasing the operating frequency range of vibration-based micro-generators presented in the literature to date. The advantages and disadvantages of each strategy are evaluated and conclusions are drawn regarding the relevant merits of each approach.
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The nonlinear oscillations of nanoelectromechanical resonators have previously been studied both experimentally and analytically. Nanoresonators have achieved superior sensitivity and high quality factors in many applications. However, the linear operating range of nanoresonators is significantly limited because of the small dimensions and thus the linear regime of nanoresonators may be required to expand performance in various conditions. In order to increase the linear operating range, we proposed that proper adjustments of simultaneous application of drive and electrothermal power can be used to optimize the resonance performance, providing a wider linear range as well as to tune the resonance frequency. For a nanoresonator operated by simultaneous drive and electrothermal power, experimental data are theoretically supported using nonlinear damping and spring terms. In the transition between linearity and nonlinearity by proper combinations of ac drive and dc electrothermal power, the experimental data can be better fitted, by theoretical study, with newly derived nonlinear damping terms. We believe that better understanding of these effects with different ac/dc combinations on radio frequency oscillation is crucial for utilizing nanoresonators for various applications such as sensors, oscillators and filters.
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This paper reports on the design and experimental validation of transducers for energy harvesting from large-scale civil structures, for which the power levels can be above 100W, and disturbance frequencies below 1Hz. The transducer consists of a back-driven ballscrew, coupled to a permanent-magnet synchronous machine, and power harvesting is regulated via control of a four-quadrant power electronic drive. Design tradeoffs between the various subsystems (including the controller, electronics, machine, mechanical conversion, and structural system) are illustrated, and an approach to device optimization is presented. Additionally, it is shown that nonlinear dissipative behavior of the electromechanical system must be properly characterized in order to assess the viability of the technology, and also to correctly design the matched impedance to maximize harvested power. An analytical expression for the average power generated across a resistive load is presented, which takes the nonlinear dissipative behavior of the device into account. From this expression the optimal resistance is determined to maximize power for an example in which the transducer is coupled to base excited tuned mass damper (TMD). Finally, the results from the analytical model are compared to an experimental system that uses hybrid testing to simulated the dynamics of the TMD.
Article
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The benefits of using a non-linear stiffness in an energy harvesting device comprising a mass–spring–damper system are investigated. Analysis based on the principle of conservation of energy reveals a fundamental limit of the effectiveness of any non-linear device over a tuned linear device for such an application. Two types of non-linear stiffness are considered. The first system has a non-linear bi-stable snap-through mechanism. This mechanism has the effect of steepening the displacement response of the mass as a function of time, resulting in a higher velocity for a given input excitation. Numerical results show that more power is harvested by the mechanism if the excitation frequency is much less than the natural frequency. The other non-linear system studied has a hardening spring, which has the effect of shifting the resonance frequency. Numerical and analytical studies show that the device with a hardening spring has a larger bandwidth over which the power can be harvested due to the shift in the resonance frequency.
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Ambient energy harvesting has been in recent years the recurring object of a number of research efforts aimed at providing an autonomous solution to the powering of small-scale electronic mobile devices. Among the different solutions, vibration energy harvesting has played a major role due to the almost universal presence of mechanical vibrations. Here we propose a new method based on the exploitation of the dynamical features of stochastic nonlinear oscillators. Such a method is shown to outperform standard linear oscillators and to overcome some of the most severe limitations of present approaches. We demonstrate the superior performances of this method by applying it to piezoelectric energy harvesting from ambient vibration.
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Several forms of vibration-driven MEMS microgenerator are possible and are reported in the literature, with potential application areas including distributed sensing and ubiquitous computing. This paper sets out an analytical basis for their design and comparison, verified against full time-domain simulations. Most reported microgenerators are classified as either velocity-damped resonant generators (VDRGs) or Coulomb-damped resonant generators (CDRGs) and a unified analytical structure is provided for these generator types. Reported generators are shown to have operated at well below achievable power densities and design guides are given for optimising future devices. The paper also describes a new class-the Coulomb-force parametric generator (CFPG)-which does not operate in a resonant manner. For all three generators, expressions and graphs are provided showing the dependence of output power on key operating parameters. The optimization also considers physical generator constraints such as voltage limitation or maximum or minimum damping ratios. The sensitivity of each generator architecture to the source vibration frequency is analyzed and this shows that the CFPG can be better suited than the resonant generators to applications where the source frequency is likely to vary. It is demonstrated that mechanical resonance is particularly useful when the vibration source amplitude is small compared to the allowable mass-to-frame displacement. The CDRG and the VDRG generate the same power at resonance but give better performance below and above resonance respectively. Both resonant generator types are unable to operate when the allowable mass frame displacement is small compared to the vibration source amplitude, as is likely to be the case in some MEMS applications. The CFPG is, therefore, required for such applications.
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The small scale generator using a catch-and-release strategy that can turn a casual stroll into useful electric energy has been discussed. Researchers at Clarkson University in Potsdam, USA have successfully built prototype wireless sensing devices to monitor bridges and the electricity comes from generators actuated by the vibration of passing traffic. Georgia Institute of Technology in Atlanta is also experimenting with zinc oxide nanowires that can generate electricity to power implants in the human body which is to be placed in boot heel to power the electronic equipment of soldier. The energy harvesters achieve their efficiency by resonantly coupling to their vibrating sources. Veryst Engineering has developed an energy harvesting concept to achieve the speed up-conversion required for efficient power generation. Veryst Engineering has been also investigating the viability of the catch-and-release concept using several proof-of-concept prototypes and numerical modeling.
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Linear energy harvesters can only produce useful amounts of power when excited close to their natural frequency. Due to the uncertain nature of ambient vibrations, it has been hypothesised that such devices will perform poorly in real-world applications. To improve performance, it has been suggested that the introduction of non-linearities into such devices may extend the bandwidth over which they perform effectively. In this study, a magnetic levitation device with non-linearities similar to the Duffing oscillator is considered. The governing equations of the device are formed in which the effects of friction are considered. Analytical solutions are used to explore the effect that friction can have on the system when it is under harmonic excitations. Following this, a numerical model is formed. A differential evolution algorithm is used alongside experimental data to identify the relevant parameters of the device. The model is then validated using experimental data. Monte Carlo simulations are then used to analyse the effect of coulomb damping and Duffing-type non-linearities when the device is subjected to broadband white noise and coloured noise excitations.
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An important issue in resonant vibration energy harvesters is that the best performance of the device is limited to a very narrow bandwidth around the fundamental resonance frequency. If the excitation frequency deviates slightly from the resonance condition, the power out is drastically reduced. In order to overcome this issue of the conventional resonant cantilever configuration, a non-resonant piezomagnetoelastic energy harvester has been introduced by the authors. This paper presents theoretical and experimental investigations of high-energy orbits in the piezomagnetoelastic energy harvester over a range of excitation frequencies. Lumped-parameter nonlinear equations (electromechanical form of the bistable Duffing oscillator with piezoelectric coupling) can successfully describe the large-amplitude broadband voltage response of the piezomagnetoelastic configuration. Following the comparison of the electromechanical trajectories obtained from the theory, it is experimentally verified that the piezomagnetoelastic configuration can generate an order of magnitude larger power compared to the commonly employed piezoelastic counterpart at several frequencies. Chaotic response of the piezomagnetoelastic configuration is also compared against the periodic response of the piezoelastic configuration theoretically and experimentally. Overcoming the bias caused by the gravity in vertical excitation of the piezomagnetoelastic energy harvester is discussed and utilization of high-energy orbits in the bistable structural configuration for electrostatic, electromagnetic and magnetostrictive transduction mechanisms is summarized.
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;Contents: Introduction; Vibration isolation with viscous damping; Vibration isolation with coulomb damping; Vibration isolation with quadratic damping; Vibration isolation with velocity-nth power damping; Vibration isolation with hysteretic damping; Vibration isolation with combined viscous and coulomb damping.
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The present study is concerned with the theoretical analysis of the effects of nonlinear viscous damping on vibration isolation of single degree of freedom (sdof) systems. The concept of the output frequency response function (OFRF) recently proposed by the authors is applied to study how the transmissibility of a sdof vibration isolator depends on the parameter of a cubic viscous damping characteristic. The theoretical analysis reveals that the cubic nonlinear viscous damping can produce an ideal vibration isolation such that only the resonant region is modified by the damping and the non-resonant regions remain unaffected, regardless of the levels of damping applied to the system. Simulation study results demonstrate the validity and engineering significance of the analysis. This research work has significant implications for the analysis and design of viscously damped vibration isolators for a wide range of practical applications.
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Supplying power to remote microsystems that have no physical connection to the outside world is difficult, and using batteries is not always appropriate. A solution is offered by the device proposed in this paper, which generates electricity from mechanical energy when embedded in a vibrating medium. This microgenerator has dimensions of around 5 mm × 5 mm × 1 mm. Analysis predicts that the power produced is proportional to the cube of the frequency of vibration, and that to maximize power generation the mass deflection should be as large as possible. Power generation of 1 μW at 70 Hz and 0.1 mW at 330 Hz are predicted for a typical device, assuming a deflection of 50 μm.
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This paper investigates the design and analysis of a novel energy harvesting device that uses magnetic levitation to produce an oscillator with a tunable resonance. The governing equations for the mechanical and electrical domains are derived to show the designed system reduces to the form of a Duffing oscillator under both static and dynamic loads. Thus, nonlinear analyses are required to investigate the energy harvesting potential of this prototypical nonlinear system. Theoretical investigations are followed by a series of experimental tests that validate the response predictions. The motivating hypothesis for the current work was that nonlinear phenomenon could be exploited to improve the effectiveness of energy harvesting devices.
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Future MEMS devices will harvest energy from their environment. One can envisage an autonomous condition monitoring vibration sensor being powered by that same vibration, and transmitting data over a wireless link; inaccessible or hostile environments are obvious areas of application. The base excitation of an elastically mounted magnetic seismic mass moving past a coil, considered previously by several authors, is analysed in detail. The amplitude of the seismic mass is limited in any practical device and this, together with the magnitude and frequency of the excitation define the maximum power that can be extracted from the environment. The overall damping coefficient (part of which is mechanical) is associated with the harvesting and dissipation of energy and also the transfer of energy from the vibrating base into the system. It is shown that net energy flow from the base through the damper is positive (negative) for , but is zero when ω=ωn. The mechanical part of the damper cannot contribute more power than it dissipates and is neutral, at best, when ω/ωn→∞. Maximum power is delivered to an electrical load when its resistance is equal to the sum of the coil internal resistance and the electrical analogue of the mechanical damping coefficient, which differs from what has been claimed. A highly damped system has the advantage of harvesting energy over a wider band of excitation frequencies on either side of the natural frequency, is smaller, but will harvest marginally less power. One possible strategy for variable amplitude excitation is proposed.
An idealised electromechanical system, which couples the relative motion of the inertial mass to a nonlinear electrical device, D, for which the current is proportional to the cube of the voltage across it
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Fig. 5. An idealised electromechanical system, which couples the relative motion of the inertial mass to a nonlinear electrical device, D, for which the current is proportional to the cube of the voltage across it. M. Ghandchi Tehrani, S.J. Elliott / Journal of Sound and Vibration 333 (2014) 623–629
Using nonlinearity to improve the performance of vibration-based energy harvesting devices
  • B P Mann
  • N Sims
B.P. Mann, N. Sims, Using nonlinearity to improve the performance of vibration-based energy harvesting devices, Proceedings of the 7th European Conference on Structural Dynamics, Southampton July 2008.
Dominant nonlinearities in micro-speakers
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W. Klippel, Dominant nonlinearities in micro-speakers, Proceedings of AIA-DAGA 2013, Conference on Acoustics, Merano, Italy, March 2013.
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S.C. Jun, S. Moon, W. Kim, J.H. Cho, J.Y. Kang, Y. Jung, H. Yoon, J. Shin, I. Song, J. Choi, J.H. Choi, M.J. Bae, I.T. Han, S. Lee, J.M. Kim, Nonlinear characteristics in radio frequency nanoelectromechanical resonators, New Journal of Physics 12 (2010) 043023.
Dominant nonlinearities in micro-speakers, Proceedings of AIA-DAGA 2013
W. Klippel, Dominant nonlinearities in micro-speakers, Proceedings of AIA-DAGA 2013, Conference on Acoustics, Merano, Italy, March 2013.