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.

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.

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.

Research on Coupling Transfer Characteristics of Vibration Energy of Free Piston Linear Generator

In order to clarify the mechanism and main influencing factors of the vibration energy coupling transmission with a dual-piston structure,a thermodynamic and dynamic coupling model of the free piston linear generator(FPLG)was established.The system energy conversion,vibration energy coupling transmission,and influencing factors were studied in detail.The coupling transmission paths and the secondary influence mechanism from in-cylinder combustion on vibration energy transmission were obtained.In addition,the influence of the movement characteristics of the dual-piston on the vibration energy transmission was studied,and the typical parameter variation law was obtained,which provides theoretical guidance for the subsequent vibration reduction design of the FPLG.

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.

Vibration energy regeneration of electric vehicle shock absorber

The twin-tube shock absorber was studied and the relevant factors of thermal equilibrium were simulated. The dynamic model of the shock absorber was constructed and simulation curves of force-displacement and force-velocity were output. The experiment of the twin-tube shock absorber was carried out, and the results were compared with the modeling resultss. Further, the vibration energy regeneration model was established, and the bench simulation study was carried out. The re- sults showed that the energy regeneration model not only absorbed shock energy but also converted vibration energy into electricity energy.

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.

High performance wide frequency band triboelectric nanogenerator based on multilayer wave superstructure for harvesting vibration energy

Efficiently converting the random vibration energy widely existed in human activities and natural environments into electricity is significant to the local power supply of sensor nodes in the internet of things.However,the conversion efficiency of energy harvester is relatively low due to the limitation of device’s intrinsic frequency.In this work,a multi-layered,wavy super-structuredtriboelectric nanogenerator(SS-TENG)is designed,whose output performances can be greatly promoted by combining the charge excitation mechanism.The steel sheet acts not only as an electrode but also as a supporter for the overall frame of SSTENG,which effectively improves the space utilization rate and results in a volume charge density up to 129 mC·m^(−3).In addition,the resonant frequency width of the SS-TENG can be widened by changing the parameters of the superstructure.For demonstration,the SS-TENG can sustainably drive two temperature and humidity sensors in parallel by harvesting vibration energy.This work may provide an effective strategy for harvesting vibration energy and broadening frequency response.

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.

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.

Hybrid electromagnetic-triboelectric nanogenerator for harvesting vibration energy

We report a hybrid nanogenerator that includes a triboelectric nanogenerator （TENG） and an electromagnetic generator （EMG） for scavenging mechanical energy. This nanogenerator operates in a hybrid mode using both the triboelectric and electromagnetic induction effects. Under a vibration frequency of 14 Hz, the fabricated TENG can deliver an open-circuit voltage of about 84 V, a short-circuit current of 43 μA, and a maximum power of 1.2 mW （the corresponding power per unit mass and volume are 1.82 mW/g and 3.4 W/m^3, respectively） under a loading resistance of 2 MΩ, whereas the fabricated EMG can produce an opencircuit voltage of about 9.9 V, a short-circuit current of 7 mA, and a maximum power of 17.4 mW （the corresponding power per unit mass and volume are 0.53 mW/g and 3.7 W/m^3, respectively） under a loading resistance of 2 kΩ. Impedance matching between the TENG and EMG can be achieved using a transformer to decrease the impedance of the TENG. Moreover, the energy produced by the hybrid nanogenerator can be stored in a home-made Li-ion battery. This research represents important progress toward practical applications of vibration energy generation for realizing self-charging power cells.

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).

The fabrication of vibration energy harvester arrays based on AlN piezoelectric film

： The fabrication and measurement results of the vibration energy harvester arrays based on the piezoelectric aluminum nitride （AlN） film are presented. The structure design and fabrication process of the device are introduced. The key material, the AIN film with crystal orientation （002）, was deposited by pulsed-DC magnetron sputtering and characterized by X-ray diffraction （XRD）. The resonant frequency, power out, and the open circuit voltage of the device are detected. The optimized load of 80 kΩ and a remarkable maximum power out of 30.4 μW are obtained when the acceleration of 0.9g （g is standard gravity acceleration） is applied. Key words： A1N; crystal orientation; harvester arrays; vibration energy

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.

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.

Improved Calculation of Vibrational Energy Levels in F2 Molecule using the RKR Method

The potential energy curves of the ground state X2∑＋g of the fluorine molecule have been accurately reconstructed employing the Ryderg-Klein-Rees （RKR） method extrapolated by a Hulburt and Hirschfeler potential function for longer internuclear distances. Solving the corresponding radial one-dimensional Schr？dinger equation of nuclear motion yields 22 bound vibrational levels above v=0. The comparison of these theoretical levels with the experimental data yields a mean absolute deviation of about 7.6 cm^-1 over the 23 levels. The highest vibrational level energy obtained using this method is 13308.16 cm？1 and the relative deviation compared with the experimental datum of 13408.49 cm^-1 is only 0.74%. The value from our method is much closer and more accurate than the value obtained by the quantum mechanical ab initio method by Bytautas. The reported agreement of the vibrational levels and dissociation energy with experiment is contingent upon the potential energy curve of the F2 ground state.

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.

Discussion on Establishing a Metrology Standard for Vibration-Driven Energy Harvesting

Energy harvesting is an area of substantial and increasing research attention, and vibration-based devices dominate this research. The primary goal of most researchers is producing maximum electrical output from the harvester systems. However, there have been little metrological considerations for circumstances under which the energy harvester devices are characterized. This makes comparison of different device prototypes very difficult. It is the focus of this paper to highlight the need for metrological considerations to energy harvesting so that a universal metric can be developed. An attempt is also made to discuss the critical parameters that are essential in establishing an international standard on vibration-based energy harvesting. Finally, a simple standard for energy harvesting is proposed.

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.

Intermolecular Vibrational Energy Transfers in Melts and Solutions

Resonant and nonresonant intermolecular vibrational energy transfers in Gdm- SCN/KSCN=1/1, GdmSCN/KS^13CN=1/1 and GdmSCN/KS^13C^15N=1/1 mixed crystals in melts and in aqueous solutions are studied with the two dimensional infrared spectroscopy. The energy transfers in the samples are slower with a larger energy donor/acceptor gap, independent of the Raman spectra. The energy gap dependences of the nonresonant energy transfers cannot be described by the phonon compensation mechanism. Instead, the experi- mental energy gap dependences can be quantitatively described by the dephasing mechanism. Temperature dependences of resonant and nonresonant energy transfer rates in the melts are also consistent with the prediction of the dephasing mechanism. The series of results suggest that the dephasing mechanism can be dominant not only in solutions, but also in melts （pure liquids without solvents）, only if the molecular motions （translations and rotations） are much faster than the nonresonant energy transfer processes.