Nonlinear dynamics and performance analysis of modified snap-through vibration energy harvester with time-varying potential function

Vibration energy harvesting has emerged as a promising method to harvest energy for small-scale applications.Enhancing the performance of a vibration energy harvester(VEH)incorporating nonlinear techniques,for example,the snap-through VEH with geometric non-linearity,has gained attention in recent years.A conventional snap-through VEH is a bi-stable system with a time-invariant potential function,which was investigated extensively in the past.In this work,a modified snap-through VEH with a time-varying potential function subject to harmonic and random base excitations is investigated.Modified snap-through VEHs,such as the one considered in this study,are used in wave energy harvesters.However,the studies on their dynamics and energy harvesting under harmonic and random excitations are limited.The dynamics of the modified snap-through VEH is represented by a system of differential algebraic equations(DAEs),and the numerical schemes are proposed for its solutions.Under a harmonic excitation,the system exhibits periodic and chaotic motions,and the energy harvesting is superior compared with the conventional counterpart.The dynamics under a random excitation is investigated by the moment differential method and the numerical scheme based on the modified Euler-Maruyama method.The Fokker-Planck equation representing the dynamics is derived,and the marginal and joint probability density functions(PDFs)are obtained by the Monte Carlo simulation.The study shows that the modified snap-through oscillator based VEH performs better under both harmonic and random excitations.The dynamics of the system under stochastic resonance(SR)is investigated,and performance enhancement is observed.The results from this study will help in the development of adaptive VEH techniques in the future.

Performance of beam-type piezoelectric vibration energy harvester based on ZnO film fabrication and improved energy harvesting circuit

We demonstrate a piezoelectric vibration energy harvester with the ZnO piezoelectric film and an improved synchronous electric charge extraction energy harvesting circuit on the basis of the beam-type mechanical structure,especially investigate its output performance in vibration harvesting and ability to generate charges.By establishing the theoretical model for each of vibration and circuit,the numerical results of voltage and power output are obtained.By fabricating the prototype of this harvester,the quality of the sputtered film is explored.Theoretical and experimental analyses are conducted in open-circuit and closed-circuit conditions,where the open-circuit mode refers to the voltage output in relation to the ZnO film and external excitation,and the power output of the closed-circuit mode is relevant to resistance.Experimental findings show good agreement with the theoretical ones,in the output tendency.It is observed that the properties of ZnO film achieve regularly direct proportion to output performance under different excitations.Furthermore,a maximum experimental power output of 4.5 mW in a resistance range of 3 kΩ-8 kΩis achieved by using an improved synchronous electric charge extraction circuit.The result is not only more than three times the power output of classic circuit,but also can broaden the resistance to a large range of 5 kΩunder an identical maximum value of power output.In this study we demonstrate the fundamental mechanism of piezoelectric materials under multiple conditions and take an example to show the methods of fabricating and testing the ZnO film.Furthermore,it may contribute to a novel energy harvesting circuit with high output performance.

Analysis on Output Power for Multi-direction Piezoelectric Vibration Energy Harvester

To predict the performance of multi-direction piezoelectric vibration energy harvester,an equation for calculating its output power is obtained based on elastic mechanics theory and piezoelectricity theory.Experiments are performed to verify theoretical analysis.When the excitation direction is along Y direction,a maximal output power about 0.139 mW can be harvested at a resistive load of 65kΩ and an excitation frequency of 136 Hz.Theoretical analysis agrees well with experimental results.Furthermore,the performance of multi-direction vibration energy harvester is experimentally tested.The results show that the multi-direction vibration energy harvester can harvest perfect energy as the excitation direction changes in XY plane,YZ plane,XZ plane and body diagonal plane of the harvester.

High-density stacked microcoils integrated microminiaturized electromagnetic vibration energy harvester for self-powered acceleration sensing

With the rapid development of microelectronics and flexible electronics technology,self-powered sensors have significant application prospects in human-machine interface systems and Internet of Things.However,piezoelectric-and triboelectricbased sensors have low current output and are easily affected,while electromagnetic-based sensors are difficult to miniaturize.This work proposes a high-density stacked microcoil integrated microminiaturized electromagnetic vibration energy harvester(EVEH).The double-layer high-density microcoil is fabricated on both sides of the flexible polyimide substrate interconnected via the central through-hole.Owing to reduced single coil line width,line spacing,and stacked structure,the number of turns can be substantially enhanced.Moreover,the relative position of the coils and magnet has a considerable influence on the performances;due to the huge change rate in magnetic flux when the coil is placed in the radial direction of the magnet than in the axial direction,the open-circuit voltage in the radial direction is 10 times greater.The microcoil can maintain good performance at high,low temperatures and under bending conditions.When the distance between the ends of the coil changes from 2 to 20 mm in 2 mm steps,the bending angle of the coil changes from 45°to 270°in 45°steps;furthermore,when the coil is exposed to-40and 60℃conditions,the coil resistance is maintained at approximately 447Ω.The peak open-circuit voltage of three-piece microcoils reaches 0.41 V at 4 Hz under 2g,and the output voltage and current increase with an increasing number of stacked layers.These excellent properties indicate that EVEH can be used for self-powered acceleration sensing.The sensitivity is measured to be 0.016 V/(m/s^(2))with a correlation coefficient of 0.979 over the acceleration range of 1–18 m/s^(2).Thus,the developed microminiaturized EVEH has enormous potential for self-powered sensing applications in confined spaces and harsh environments.

Bayesian system identification and chaotic prediction from data for stochastic Mathieu-van der Pol-Duffing energy harvester

In this paper,the approximate Bayesian computation combines the particle swarm optimization and se-quential Monte Carlo methods,which identify the parameters of the Mathieu-van der Pol-Duffing chaotic energy harvester system.Then the proposed method is applied to estimate the coefficients of the chaotic model and the response output paths of the identified coefficients compared with the observed,which verifies the effectiveness of the proposed method.Finally,a partial response sample of the regular and chaotic responses,determined by the maximum Lyapunov exponent,is applied to detect whether chaotic motion occurs in them by a 0-1 test.This paper can provide a reference for data-based parameter iden-tification and chaotic prediction of chaotic vibration energy harvester systems.

Resin-bonded NdFeB micromagnets for integration into electromagnetic vibration energy harvesters

A micromachining technique is presented for the fabrication of resin-bonded permanent magnets in the microscale.Magnetic paste is prepared from NdFeB powder and an epoxy resin,filled into lithographically defined photoresist molds or metal molds,and formed into resin-bonded magnets after curing at room temperature.A coercivity of 772.4 kA/m,a remanence of 0.27 T,and a maximum energy product of 22.6 kJ/m3 have been achieved in an NdFeB disk micromagnet with dimensions of Ф200 μm×70 μm.Based on the developed micro-patterning of resin-bonded magnets,a fully integrated electromagnetic vibration energy harvester has been designed and fabricated.The dimensions of the energy harvester are only 4.5 mm×4.5 mm×1.0 mm,and those of the micromagnet are 1.5 mm×1.5 mm×0.2 mm.This microfabrication technique can be used for producing permanent magnets tens or hundreds of micrometers in size for use in various magnetic devices.

A magnetoelectric-based broadband vibration energy harvester for powering wireless sensors

Scavenging vibration energy directly from environments is an attractive technique for potentially powering small and/or wireless electronic devices in a smart structure and system.In this paper,a novel broadband vibration energy harvester is designed and analyzed,which consists of three cantilever beams,two magnetoelectric(ME) transducers and a magnetic circuit.A theoretical model is developed to analyze the effects of the structure parameters on the frequency response and the electrical output for achieving the optimal vibration energy harvesting performances.A prototype is fabricated and tested.The experimental results show that the harvester has a bandwidth of 7.2 Hz and an average power of 0.21 mW at an acceleration of 0.2 g(with g=9.8 ms-2).

Electromechanical modeling and experimental analysis of a compression-based piezoelectric vibration energy harvester

Over the past few decades,wireless sensor networks have been widely used in the field of structure health monitoring of civil,mechanical,and aerospace systems.Currently,most wireless sensor networks are battery-powered and it is costly and unsustainable for maintenance because of the requirement for frequent battery replacements.As an attempt to address such issue,this article theoretically and experimentally studies a compression-based piezoelectric energy harvester using a multilayer stack configuration,which is suitable for civil infrastructure system applications where large compressive loads occur,such as heavily vehicular loading acting on pavements.In this article,we firstly present analytical and numerical modeling of the piezoelectric multilayer stack under axial compressive loading,which is based on the linear theory of piezoelectricity.A two-degree-of-freedom electromechanical model,considering both the mechanical and electrical aspects of the proposed harvester,was developed to characterize the harvested electrical power under the external electrical load.Exact closed-form expressions of the electromechanical models have been derived to analyze the mechanical and electrical properties of the proposed harvester.The theoretical analyses are validated through several experiments for a test prototype under harmonic excitations.The test results exhibit very good agreement with the analytical analyses and numerical simulations for a range of resistive loads and input excitation levels.

A comprehensive review of miniatured wind energy harvesters

Following the current rapid development of the Internet of Things(IoT)and wireless condition monitoring systems,energy harvesters which use ambient energy have become a key part of achieving an energy-autonomous system.Miniature wind energy harvesters have attracted widespread attention because of their great potential of power density as well as the rich availability of wind energy in many possible areas of application.This article provides readers with a glimpse into the state-of-the-art of miniature wind energy harvesters.The crucial factors for them to achieve high working efficiency under lower operational wind speed excitation are analyzed.Various potential energy coupling mechanisms are discussed in detail.Design approaches for broadening operational wind-speed-range given a variety of energy coupling mechanisms are also presented,as observed in the literature.Performance enhancement mechanisms including hydrodynamic configuration optimization,and non-linear vibration pick-up structure are reviewed.Conclusions are drawn and the outlook for each coupling mechanisms is presented.

Highly adaptive and broadband triboelectric energy harvester with stretching silicone rubber strip for variable harmonic frequency vibration

An enormous number of wireless sensing nodes(WSNs)are of great significance for the Internet of Things(IoT).It is tremendously prospective to realize the in-situ power supply of WSNs by harvesting unutilized mechanical vibration energy.A harmonic silicone rubber triboelectric nanogenerator(HSR-TENG)is developed focusing on ubiquitous constant working frequency machinery.The unique design of the strip serving as a flexible resonator realizes both soft contact and high and broadband output.The significant factors influencing the 1^(st)-order vibration mode of the strip are developed for realizing the harmonic frequency adaptation to external vibration.The surface treatment of the strip improves the output performance of HSR-TENG by 49.1%as well as eliminates the adhesion effect.The HSR-TENG is able to achieve a voltage output bandwidth of 19 Hz under a vibration strength of 3.0,showing its broadband capability.The peak power density of 153.9 W/m^(3)is achieved and 12×0.5 W light-emitting diodes(LEDs)are successfully illuminated by the HSR-TENG.It can continuously power a temperature sensor by harvesting the actual compressor vibration energy.In brief,the HSR-TENG provides a promising way for constant frequency vibration energy harvesting,so as to achieve in-situ power supply for the WSNs in the vicinity.

Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting

A bimorph piezoelectric beam with periodically variable cross-sections is used for the vibration energy harvesting. The effects of two geometrical parameters on the first band gap of this periodic beam are investigated by the generalized differential quadrature rule （GDQR） method. The GDQR method is also used to calculate the forced vibration response of the beam and voltage of each piezoelectric layer when the beam is subject to a sinusoidal base excitation. Results obtained from the analytical method are compared with those obtained from the finite element simulation with ANSYS, and good agreement is found. The voltage output of this periodic beam over its first band gap is calculated and compared with the voltage output of the uniform piezoelectric beam. It is concluded that this periodic beam has three advantages over the uniform piezoelectric beam, i.e., generating more voltage outputs over a wide frequency range, absorbing vibration, and being less weight.

A piezoelectric energy harvester based on internal resonance

A vibration-based energy harvester is essentially a resonator working in a limited frequency range.To increase the working frequency range is a challenging problem.This paper reveals a novel possibility for enhancing energy harvesting via internal resonance.An internal resonance energy harvester is proposed.The excitation is successively assumed as the Gaussian white noise,the colored noise defined by a second-order filter,the narrow-band noise,and exponentially correlated noise.The corresponding averaged root-meansquare output voltages are computed.Numerical results demonstrate that the internal resonance increases the operating bandwidth and the output voltage.

Design and dynamic analysis of integrated architecture for vibration energy harvesting including piezoelectric frame and mechanical amplifier

Vibration energy harvesters(VEHs) can transform ambient vibration energy to electricity and have been widely investigated as promising self-powered devices for wireless sensor networks, wearable sensors, and applications of a micro-electro-mechanical system(MEMS). However, the ambient vibration is always too weak to hinder the high energy conversion efficiency. In this paper, the integrated frame composed of piezoelectric beams and mechanical amplifiers is proposed to improve the energy conversion efficiency of a VEH. First, the initial structures of a piezoelectric frame(PF) and an amplification frame(AF) are designed. The dynamic model is then established to analyze the influence of key structural parameters on the mechanical amplification factor. Finite element simulation is conducted to study the energy harvesting performance, where the stiffness characteristics and power output in the cases of series and parallel load resistance are discussed in detail. Furthermore, piezoelectric beams with variable cross-sections are introduced to optimize and improve the energy harvesting efficiency. Advantages of the PF with the AF are illustrated by comparison with conventional piezoelectric cantilever beams. The results show that the proposed integrated VEH has a good mechanical amplification capability and is more suitable for low-frequency vibration conditions.

Dynamic responses of an energy harvesting system based on piezoelectric and electromagnetic mechanisms under colored noise

Because of the increasing demand for electrical energy,vibration energy harvesters(VEHs)that convert vibratory energy into electrical energy are a promising technology.In order to improve the efficiency of harvesting energy from environmental vibration,here we investigate a hybrid VEH.Unlike previous studies,this article analyzes the stochastic responses of the hybrid piezoelectric and electromagnetic energy harvesting system with viscoelastic material under narrow-band(colored)noise.Firstly,a mass-spring-damping system model coupled with piezoelectric and electromagnetic circuits under fundamental acceleration excitation is established,and analytical solutions to the dimensionless equations are derived.Then,the formula of the amplitude-frequency responses in the deterministic case and the first-order and secondorder steady-state moments of the amplitude in the stochastic case are obtained by using the multi-scales method.The amplitude-frequency analytical solutions are in good agreement with the numerical solutions obtained by the Monte Carlo method.Furthermore,the stochastic bifurcation diagram is plotted for the first-order steady-state moment of the amplitude with respect to the detuning frequency and viscoelastic parameter.Eventually,the influence of system parameters on mean-square electric voltage,mean-square electric current and mean output power is discussed.Results show that the electromechanical coupling coefficients,random excitation and viscoelastic parameter have a positive effect on the output power of the system.

Typical dampers and energy harvesters based on characteristics of ferrofluids

Ferrofluids are a type of nanometer-scale functional material with fluidity and superparamagnetism.They are composed of ferromagnetic particles,surfactants,and base liquids.The main characteristics of ferrofluids include magnetization,the magnetoviscous effect,and levitation characteristics.There are many mature commercial ferrofluid damping applications based on these characteristics that are widely used in numerous fields.Furthermore,some ferrofluid damping studies such as those related to vibration energy harvesters and biomedical devices are still in the laboratory stage.This review paper summarizes typical ferrofluid dampers and energy harvesting systems from the 1960s to the present,including ferrofluid viscous dampers,ferrofluid inertia dampers,tuned magnetic fluid dampers(TMFDs),and vibration energy harvesters.In particular,it focuses on TMFDs and vibration energy harvesters because they have been the hottest research topics in the ferrofluid damping field in recent years.This review also proposes a novel magnetic fluid damper that achieves energy conversion and improves the efficiency of vibration attenuation.Finally,we discuss the potential challenges and development of ferrofluid damping in future research.

Harvesting vibration energy by a triple-cantilever based triboelectric nanogenerator

Triboelectric nanogenerators （TENG）, a unique technology for harvesting ambient mechanical energy based on triboelectric effect, have been proven to be a cost-effective, simple and robust approach for self-powered systems. Here, we demonstrate a rationally designed triple-cantilever based TENG for harvesting vibration energy. With the assistance of nanowire arrays fabricated onto the surfaces of beryllium-copper alloy foils, the newly designed TENG produces an open-circuit voltage up to 101 V and a short-circuit current of 55.7 ~tA with a peak power density of 252.3 mW/m2. The TENG was systematically investigated and demonstrated as a direct power source for instantaneously lighting up 40 commercial light-emitting diodes. For the first time, a TENG device has been designed for harvesting vibration energy, especially at low frequencies, opening its application as a new energy technologv.

Nonlinear characterization and performance optimization for broadband bistable energy harvester

As two crucial indicators of bistable energy harvesting performance,band width and power amplitude are simultaneously investigated for obtaining the synergy effect.Toward this goal,a nonlinear electromechanical-coupled distributed-parameter model of the bistable piezoelectric energy harvester is established.Based on the electromechanical decoupled method,approximate higher-order analytical solutions of the beam displacement,harvested power and effective bandwidth are derived.The cubic-function discriminant of the analytical solution is introduced to determine the nonlinear excitation-frequency boundaries of multiple solutions and power peak.The stability of the multiple solutions is analyzed through Jacobi matrix of the modulation equation.Superharmonic resonance is notified.Upward and downward sweep experiments and numerical solutions of time history curves,phase portraits and power spectra confirm the analytical findings.To realize optimized broadband energy harvesting,the parametric study on the coefficients of the linear and cubic elastic external forces with the corresponding optimal load resistance is performed.For the nonlinear hardening case,more positive linear coefficient is preferred.For the nonlinear softening case,the cubic coefficient slightly larger than its optimal value is recommended at each given linear coefficient.By tuning the load resistance and linear and cubic coefficients of the external force,broadband bistable energy harvesting with optimized power is realized.

Experiment and performance analysis of serpentine-shaped cantilever beam for pipeline vibration-based piezoelectric energy harvester prototype development

Pipelines produce vibrations during fluid or gas transportation.These vibrations are less likely to cause structural failure as they exist with a small magnitude and can be harvested into useful energy.This paper presents a study on the piezoelectric energy-harvesting method converting mechanical energy from pipeline vibration into electrical energy.The performance of the serpentine-shaped piezoelectric cantilever beam was observed to check whether the design can produce the highest output voltage within the allowable vibration region of the pipeline from 10 to 300 Hz through finite element analysis using COMSOL Multiphysics software(Supplementary Material).In addition,this study investigates the energy-harvesting potential of the proposed design under real pipe­line vibration conditions through a lab vibration test.The harvested energy output is evaluated based on various vibration frequen­cies and amplitudes,which gives an idea of the device and its performance under different operating conditions.The experiment result shows that the energy harvester produced an open-circuit voltage of 10.28-15.45 V with 1 g of vibration acceleration.The results of this research will contribute to the development of efficient piezoelectric energy harvesters adapted for pipeline environments.

Research and development of micro electret power generators

As the size of the electronic system continuously reduces, characteristics of small volume, light weight, high energy it is very important to develop micro power generator, which has density and continuous energy supplying. Vibration energy exists widely in daily environment. Micro vibration power generator can harvest and exchange the vibration energy to the electrical energy. Micro electret power generator is one kind of the power generators for harvesting vibration energy and has been paid much attention by researchers. This paper describes the development and status of micro electret power generators, including electret materials and charging methods, vibration energy harvesting structures and conversion efficiency improvement.