Bistable Energy Harvester Research Articles

Buckled MEMS Beams for Energy Harvesting from Low Frequency Vibrations.

Vibration energy harvesters based on the resonance of the beam structure work effectively only when the operating frequency window of the beam resonance matches with the available vibration source. None of the resonating MEMS structures can operate with low frequency, low amplitude, and unpredictable ambient vibrations since the resonant frequency goes up very high as the structure gets smaller. Bistable buckled beam energy harvester is therefore developed for lowering the operating frequency window below 100Hz for the first time at the MEMS scale. This design does not rely on the resonance of the MEMS structure but operates with the large snapping motion of the beam at very low frequencies when input energy overcomes an energy threshold. A fully functional piezoelectric MEMS energy harvester is designed, monolithically fabricated, and tested. An electromechanical lumped parameter model is developed to analyze the nonlinear dynamics and to guide the design of the nonlinear oscillator based energy harvester. Multilayer beam structure with residual stress induced buckling is achieved through the progressive residual stress control of the deposition processes along the fabrication steps. Surface profile of the released device shows bistable buckling of 200μm which matches well with the amount of buckling designed. Dynamic testing demonstrates the energy harvester operates with 50% bandwidth under 70Hz at 0.5g input, operating conditions that have not been demonstrated by MEMS vibration energy harvesters before.

Transient Dynamics and Electric Power Estimation of Bistable Energy Harvesters Under Impulsive Excitations

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.

An Arc-shaped Piezoelectric Bistable Vibration Energy Harvester: Modeling and Experiments.

In order to improve vibration energy harvesting, this paper designs an arc-shaped piezoelectric bistable vibration energy harvester (ABEH). The bistable configuration is achieved by using magnetic coupling, and the nonlinear magnetic force is calculated. Based on Lagrangian equation, piezoelectric theory, Kirchhoff’s law, etc., a complete theoretical model of the presented ABEH is built. The influence of the nonlinear stiffness terms, the electromechanical coupling coefficient, the damping, the distance between magnets, and the load resistance on the dynamic response and the energy harvesting performance of the ABEH is numerically explored. More importantly, experiments are designed to verify the energy harvesting enhancement of the ABEH. Compared with the non-magnet energy harvester, the ABEH has much better energy harvesting performance.

Nonlinear energy harvesting based on a modified snap-through mechanism

A modified snap-through mechanism is used in an electromagnetic energy harvester to improve its effectiveness. It mainly comprises three springs that are configured so that the potential energy of the system has two stable equilibrium points. In particular, the small vibration behavior of the harvester around one of the equilibriums is of interest. A multi-scale method (MSM) is used to analyze the frequency response curve. Two snap-through mechanisms are considered. One has both horizontal and vertical springs. The other has only horizontal springs. The frequency response curves of these two classes are compared under the same excitation and electric loading conditions. The latter exhibits more bending of the frequency response curve than the former one. The results are also validated by some numerical work. The averaged power subject to the Gaussian white noise is calculated numerically, and the results demonstrate that bi-stable energy harvesting with only horizontal springs can outperform the mechanism with both horizontal and vertical springs for the same distance between two equilibriums.

Investigation of the lever mechanism for bistable nonlinear energy harvesting under Gaussian-type stochastic excitations

This study presents a new bistable energy harvester utilizing the lever mechanism, and investigates its dynamic behaviors under two Gaussian-type stochastic excitations: white and exponentially correlated Gaussian noises. Fokker–Planck–Kolmogorov equation is used to predict analytical results of the system’s probability distribution function, which are also numerically validated by Euler–Maruyama (E–M) algorithm. For the white noise excitation, the bistable nonlinearity does not affect the average of the harvested power, but the lever mechanism can significantly improve it if the lever parameters transcend an invariant boundary which identifies the performance improvement region. For the exponentially correlated noise, both the bistable nonlinearity and lever parameters affect the average power. The performance improvement region is insensitive to the excitation intensity, but its boundary varies corresponding to different correlation coefficients of the excitation; the smaller correlation coefficient, the broader region. In addition, time history responses of the harvester’s actuation displacement and velocity are numerically obtained to verify the analytical findings. The results reveal that for some small lever parameters, large-amplitude crossing-well response may lead to smaller actuation velocity, which degrades the average of the harvested power. Hence, better energy harvesting requires larger level parameters to enhance the actuation velocity.

Statistical quantification of DC power generated by bistable piezoelectric energy harvesters when driven by random excitations

Vibration energy harvesting provides prominent potential on leveraging the converted energy to realize self-powered electronics. To satisfy the demand of electronics and rechargeable batteries for DC voltages in practical applications, the high-performing, nonlinear bistable energy harvesters are considered to be interfaced with standard rectifying electrical circuits to extract DC power from environment-like, random base accelerations. To lead to an effective and efficient set of design guidelines for system development, this research proposes a theoretical method to characterize the stationary stochastic dynamic responses and the energy harvesting performance under white noise accelerations. Considering that the bistable harvesters possess multiple vibration regimes which induce drastically different energy harvesting performances, a novel state-probability estimation approach is presented based on the theoretically predicted probability density function (PDF) of system energy to statistically classify the stationary probability of the stochastic vibrations being in the snap-through or intrawell states. Via investigating the effects of the base acceleration strength and system parameters on the dynamic responses and harvested DC power, it is revealed that high energy harvesting performance would be achieved via low system damping and suitable system parameters, such as moderate coupling constant and load resistance. The theoretical predictions are compared with numerical simulations and experimental results to validate the effectiveness of the proposed theoretical method.

Multiple solutions of asymmetric potential bistable energy harvesters: numerical simulation and experimental validation

In this paper, we investigate the multiple solutions of nonlinear asymmetric potential bistable energy harvesters (BEHs) under harmonic excitations. Basins of attraction under certain excitations explain the existence of multiple solutions in the asymmetric potential BEHs and indicate that the asymmetric system has a higher probability to oscillate in the deeper potential well under low and moderate excitation levels. Thus, the appearance of asymmetric potentials in BEHs has a negative influence on the output performance. Average output powers under different excitation frequencies and initial conditions illustrate that the asymmetric potential BEHs are more likely to achieve high-energy branch (HEB) with initial conditions in the shallower potential well, and the probability is influenced by the degree of asymmetry of the BEHs. Finally, experiments are carried out, and results under constant and sweep frequency excitations demonstrate that the output performance will be actually improved for the asymmetric potential BEHs if the initial oscillations are from the shallower potential well.

Exploiting the subharmonic parametric resonances of a buckled beam for vibratory energy harvesting

The potential of harvesting vibratory energy via a bistable beam subjected to subharmonic parametric excitations is investigated. The vibrating structure is a buckled beam with two stable equilibria separated by a potential barrier. The beam is subjected to a superposition of a static axial load beyond its buckling load and a harmonic axial excitation whose frequency is around twice the frequency of the buckled beam’s first vibration mode. A macro-fiber composite patch is attached to one side of the beam to convert the strain energy resulting from the beam’s oscillation into electricity. The study considers two regimes of excitations: an amplitude sweep and a frequency sweep. In the first regime, the amplitude of excitation is quasi-statically varied while the excitation frequency is tuned at twice the natural frequency of the first vibration mode. In the second regime, the excitation frequency is swept forward and backward around the subharmonic resonant frequency while the amplitude of excitation is kept constant. A theoretical model which governs the electromechanical coupling of the transverse vibrations of the beam and the output voltage is used to monitor the response as the excitation parameters are changed. An experimental setup is also built and a series of tests is performed to validate the theoretical findings. It is shown that, depending on the amplitude and frequency of excitation, the harvester can perform small-amplitude periodic intra-well motion, intra- and inter-well chaotic motions, as well as periodic inter-well motions. Experimental results also show that, as compared to the classical linear resonance, utilizing the sub-harmonic resonance of a bistable energy harvesters can result in a broadband frequency response.

Design and analysis of switchable magnetic polarity bistable energy harvester

Multistable vibration harvesters that involve repelling magnet force result in improved efficiency over a wider bandwidth in comparison to the conventional resonant devices. However, the dynamic performance of the vibration harvester can be further improved by switching the magnetic force polarity to ensure pull force on the mass as it moves towards the mean position. In the presented work, the design and analysis of a switching polarity bistable harvester has been presented, which changes the magnetic interaction polarity in order to improve power output as well as efficient operational bandwidth. An innovative mechanism has been developed to operate the harvester with switching polarity for higher base acceleration amplitude. The proposed design has integrated switchable polarity magnetic interaction and rotary electric generator which is driven by a compound gear train in the conventional spring-mass harvester. Analytical and numerical simulations have been formulated to illustrate efficient operational characteristics over the operating frequency band and to determine the optimum electrical damping coefficient. Effects of magnetic interaction force, the inertia of the switching mechanism and gears have been considered in the numerical analysis. A prototype delivered the peak power of 1.49 W at the resonance frequency and exhibited 50% increase in power in comparison to fixed polarity design.

Numerical and experimental study of bistable piezoelectric energy harvester

Piezoelectric energy harvesting from mechanical vibrations is a reliable technology to charge low power electronic equipment. It has been reported in the literature that low frequency broadband vibrations cannot be harvested effectively using linear piezoelectric energy harvester (PEH). In this paper a bistable nonlinear PEH with two distinct energy wells generated using repulsive magnetic interactions between a cantilever magnetic proof mass and an external magnet is considered. It has been modeled using finite element method and validated with experimental results. Experimental results verify that, for our study, distance between magnetic proof mass and external magnet of 1.32 T flux density should be less than or equal to 8.5 mm for maintaining bistability. This distance also affects to the resonance frequency of harvester. Maximum efficiency of the harvester has been noticed at 8.5mm. Further it has been shown experimentally that the bistable nonlinear piezoelectric energy harvester takes almost half of the time taken by its linear counterpart to charge a 20 mAh battery.

Finite element analysis of Bi-stable plates for piezoelectric energy harvesting

In order to increase the output voltage of piezoelectric energy harvesting, this paper mainly discusses bi-stable plates for piezoelectric energy harvesting, and its property is analyzed with finite element analysis. The device changes kinetic energy into electrical one, whose core part comprises a substrate, a piezoelectric layer, mass block and the electrode. The research focuses on firstly examining the effect of the area of piezoelectric layer, the temperature and the mass block on the natural frequency of the system, and then analyzing the effect of laying type and area of piezoelectric layer on the output voltage of the system. Eventually a new structure of bi-stable piezoelectric energy harvesting is put forward to improve its harvesting efficiency. This conclusion can be used to provide a theoretical basis for application of piezoelectric technology in engineering.

Analysis of broadband characteristics of two degree of freedom bistable piezoelectric energy harvester

In order to broaden the working frequency band of the piezoelectric energy harvester and improve the energy harvesting efficiency, a new two degree of freedom bistable piezoelectric vibration energy harvester is designed in this paper. It consists of a basic cantilever beam, a mass, a piezoelectric cantilever beam and magnets. The equivalent model of the system is established using lumped parameter method, and the two degree of freedom bistable motion equation is established considering the influence of electromechanical coupling. Using Matlab, the motion equation is calculated, and the curve of the system voltage with time and frequency is obtained. The voltage output characteristics of the system under bistable vibration and the influence of the stiffness and the mass of the basic cantilever beam on the output performance of the system are analyzed. Under the excitation of 0.3 g simple harmonics, the two degree of freedom bistable piezoelectric energy harvester is experimented using one-way frequency-increasing sweep. The results show that the maximum output voltage of the two resonance band of the energy harvester is 26 V and 13 V. Compared with the single degree of freedom bistable structure, the frequency band is widened by 10 Hz. In addition, reducing the stiffness of the basic cantilever beam and increasing the mass of mass block are all beneficial to broadening the working band of the harvester.

Vibration energy harvesting from impulsive excitations via a bistable nonlinear attachment—Experimental study

Abstract A bistable nonlinear electromagnetic energy harvester coupled to an impulsively excited primary linear oscillator has been experimentally investigated. The design of the energy harvesting system was guided by a preliminary numerical study, which predicted a favorable dynamic regime for harvesting purposes. The harvesting system consisted of a lightweight permanent magnet, moving within a stationary coil, nonlinearly coupled to a grounded, weakly damped linear oscillator through a prebuckled, bistable slender steel beam which exhibited both cubic nonlinear and negative linear stiffness behaviors in transverse response along its weak axis. This paper provides the results of an experimental investigation, illustrating the capacity of the bistable element to dramatically enhance harvesting efficiency when subjected to broadband, low-amplitude vibration, executing large amplitude oscillations between the two stable equilibrium positions. Single and repeated impulses of varying amplitude applied to the LO are employed as system inputs, and it is shown, both experimentally and through numerical simulations, that robust harvesting efficiency is achieved primarily through periodic cross-well oscillations, particularly at low levels of input energy.

Hysteresis characteristics influence on the super-harmonic vibration of a bi-stable piezoelectric energy harvester

The smart structures with the harmonic nonlinear vibration are used widely to broaden the frequency range of vibrations energy harvesting. However, it is presently considered that the smart materials have some hysteresis properties. These hysteresis properties have much negative influence on the harvested energy not to be supplied more quickly and more accurately to the micro-systems applications. In the paper, the super-harmonic vibration of a piezoelectric energy harvester is discussed with considering the hysteresis phenomenon, and the piezoelectric energy harvester is described by the Bouc–Wen equation. Moreover, it is observed that there is a stronger hysteresis property when the piezoelectric energy harvester is applied with an external excitation at the harmonic frequency. It is analyzed that the hysteresis will bring about a delay of the harmonic vibration frequency of the energy harvester compared with that without considering hysteresis. Furthermore, it is concluded that the hysteresis decreasingly impacts the super-harmonic vibration of the bi-stable piezoelectric energy harvester when the external excitation is gradually increasing.

The Effect of Axial Displacement of Magnets in Piezoelectric Energy Harvester

The utilization of vibration energy harvesters as a substitute to batteries in wireless sensors has shown prominent interest in the literature. Various approaches have been adapted in the energy harvesters to competently harvest vibrational energy over a wider spectrum of frequencies with optimize power output. A typical bistable piezoelectric energy harvester, where the influence of magnetic field is induced into a linear piezoelectric cantilever, is designed and analyzed in this paper. The exploitations of the magnetic force specifically creates nonlinear response and bistability in the energy harvester that extends the operational frequency spectrum for optimize performance. Further analysis on the effects of axial spacing displacement between two repulsive magnets of the harvester, in terms of x-axis (horizontal) and z-axis (vertical) on its natural resonant frequency and performance based on the frequency response curve are investigated for realizing optimal power output. Experimental results show that by selecting the optimal axial spacing displacement, the vibration energy harvester can be designed to produce maximized output power in an improved broadband of frequency spectrum.

Nonlinear dynamics and performance enhancement of asymmetric potential bistable energy harvesters

Bistable system exhibiting complex dynamic behavior has been viewed as an efficient method to overcome the issue of linear energy harvester only performing well near the resonant frequency. Moreover, performance enhancement strategies of bistable energy harvesters have been extensively discussed mainly for systems with perfectly symmetric potentials. Due to the presence of imperfections as a result of non-uniform manufacturing of the harvesters, eccentricity of the buckling or magnetic force and uneven gravity, the dynamic characteristics and performance enhancement of asymmetric potential energy harvesting remain an open issue. Therefore, this paper investigates the influence mechanism and performance enhancement of a cantilever-based bistable energy harvesting system with asymmetric potentials. Bifurcation diagrams of the dimensionless electromechanical equations are employed to discover the effect of asymmetric potentials on the output response. Based on the numerical results, a performance enhancement method is proposed by compensating the asymmetric potentials with an appropriate bias of the system to decrease the negative impact of asymmetric potentials on bistable energy harvesting. The optimum bias angle is derived and numerical simulations under constant and sweep frequency excitations demonstrate that the performance of the asymmetric potential bistable energy harvesters is enhanced in a certain bias angle range around the optimum value. Two bistable energy harvesters with different asymmetric potential energy functions are investigated in the experiments and results verify the effectiveness of the proposed method for improving the energy harvesting performance.

Improving energy harvesting from random excitation by nonlinear flexible bi-stable energy harvester with a variable potential energy function

Abstract In this paper, aim at improving the performance of bi-stable energy harvester (BEH), we proposed a flexible bi-stable energy harvester (FBEH). The FBEH is composed of two elastic beams: one is the piezoelectric cantilever beam with a tip magnet and the other is the clamped-clamped beam with a mid-magnet. The dynamic behavior of FBEH was studied, and the results show that the FBEH owning a variable potential energy function is beneficial for snap-through. The governing equations of FBEH are derived by energy principles. Then its dynamic response under random excitation was studied. The results prove that the FBEH not only has a smaller threshold for snap-through, but also can generate a larger power output for the excitation intensity larger than the critical one. Validation experiments were designed and carried out. The experimental results are in good agreement with the simulation ones.

Drastic bandwidth enhancement of bistable energy harvesters: Study of subharmonic behaviors and their stability robustness

In order to provide a serious alternative to chemical batteries for the energy supply of isolated sensors, bistable generators have been enthusiastically highlighted in recent years for their ability to harvest vibration energy over a wider frequency range compared to linear generators. Nevertheless, these bistable harvesters are generally characterized through a frequency sweep which does not reveal all the steady-state behaviors they can reach and therefore their full energy harvesting potential. Among such behaviors, subharmonic motions are hidden by this classical characterization and therefore had not received a lot of attention. This study proposes an original complete analytical analysis of subharmonic orbits for energy harvesting to predict their contribution to the global bandwidth of bistable generators. In addition, a new criterion, referred as stability robustness, is introduced to estimate the sensitivity of those behaviors to disturbances of different levels, allowing to finely and accurately estimate suitable behaviors for energy harvesting purposes in realistic conditions (behaviors easy to reach and maintain in time). Experimental results conducted with a buckled beam based electromagnetic generator confirm the relevance of this criterion showing good agreement with the analytical predictions. Subharmonic behaviors finally appear, both theoretically and experimentally, to be of significant interest, as exploiting them leads to a 180% increase of the global operating frequency range of the considered bistable energy harvester, for which more than 100 µW are generated on a 70 Hz bandwidth at 0.5 g.

A numerical study on flexoelectric bistable energy harvester

A flexoelectric energy harvesting can be a viable solution of energy source for low power devices and sensors due to its higher performance at nano/micro domain size. Numerical study has been performed on energy harvester based on flexoelectric phenomenon of dielectric materials. Cantilever type structure was opted here as it induces the polarization due to the breaking of lattice symmetry upon bending. Host layer of cantilever is made of barium strontium titanate (BST) as it has high flexoelectric coefficient, and electrodes are attached with the host layer to collect the charges. In this study, nonlinearity has been introduced using pair of magnets at the free end of the cantilever. Characteristics of the harvester performance (linear–non-linear) changes by varying the distance between magnets. Results revealed that the bistable energy harvester gives more operating frequency range when excitation is random as compared to the linear energy harvester. For the given dimension of the harvester, when magnets distance d = 6 mm, effective harvesting frequency ranges are 5–17.3 and 17.6–26 Hz as compared to linear harvester. Further, role of load resistance was investigated to understand the impact on the performance. Hysteresis loop between voltage and displacement significantly varies with the resistance. This hysteresis loop confirmed the backward coupling of flexoelectric layer, in which voltage affects the displacement due to actuation. Area under the hysteresis loop is maximum for optimum resistance value (20.4 kΩ) which confirms the maximum extraction of power during vibration.

Design and analysis of a broadband vibratory energy harvester using bi-stable piezoelectric composite laminate

In this paper, a bi-stable piezoelectric energy harvester based on the bi-stable hybrid composite laminate with a new stacking sequence design is proposed. The new stacking sequence enables this bi-stable energy harvester to have some unique features, such as uniform strains of piezoelectric elements and symmetric stable configurations. Meanwhile, the new stacking sequence design enhances the room to adjust its natural frequency such that this proposed harvester allows for adjusting to lower frequency range and increasing the inertia by a tip mass to lower the demand of excitation level in comparison to previous settings. A finite element analysis is developed to investigate the static and dynamic characteristics of this new bi-stable energy harvester. A simple numerical model with a modified version of the Duffing equation is developed based on the unique nonlinear restoring force obtained from finite element analysis to describe the fundamental response characteristics of this nonlinear bi-stable energy harvester. Numerical simulations and experiments are carried out at different harmonic excitation levels ranging from 10 to 40 Hz. The results verify that the proposed model can reasonably capture the dynamic characteristics of this broadband bi-stable energy harvester. The output powers were measured under different vibration patterns. Maximum power of 31.1 mW was generated under large-amplitude and high-energy orbits cross-well vibration pattern at an excitation frequency of 22 Hz and acceleration of 3g (g = 9.8 m/s2).