A model for an extensional mode resonator used as a frequency-adjustable vibration energy harvester

In an effort to identify techniques for harvesting energy from ambient vibrations, a prototype device that utilizes stretching piezoelectric film to support a proof mass, with an adjustable support that allows the resonant frequency of the device to be easily altered, has been developed. This extensional mode resonator (XMR) device is described by a model developed in this paper that predicts the power that is harvested as a function of the frequency and amplitude of the external vibration, the elastic and piezoelectric materials properties, and the device geometry. The model provides design guidelines for the effects of device geometry and applied tension through an adjustable support that suggest a strong dependence on mechanical damping and a weak dependence on frequency, as opposed to a bending cantilever device. The model predictions are compared to experimental measures from a prototype device for frequencies between 120 and 180 Hz, and at accelerations between 0.1 and 10 m/s². Up to 9 mW is generated from a device with a mass of ∼82 g, and over the range of frequencies tested the power harvested at 4 m/s² is between 3 and 4 mW.     

Electric power generation using vibration of a polyurea piezoelectric thin film

An energy harvesting system is proposed, in which mechanical energy is converted to electrical energy through the piezoelectric effect of a polymer polyurea film on the device. Electrical energy harvesting methods that use piezoelectric elements have been reported by several groups, and lead zirconate titanate (PZT) is predominantly employed as the piezoelectric material. An energy harvesting device with a polyurea thin film formed through vapor deposition polymerization with 4,4′-diphenylmethane diisocyanete (MDI) and 4,4′-diamino diphenyl ether (ODA). The conversion efficiency from mechanical to electrical energy was calculated using finite elemental analysis (FEA) of the cantilever configuration. Higher conversion efficiency was obtained using a thinner and shorter cantilever configuration with increased resonance frequency of the device. Experiments were conducted using an electric power generation device with a 3 μm thick polyurea thin film attached to a 0.1-mm-thick, 18-mm-long beryllium copper cantilever. Vibration in the vertical direction, which induces the bending vibration on the cantilever, was applied to the device and the output voltage was measured by connecting load resistances. The output power was measured with a change in the load resistance from 10 kΩ to 10 MΩ, and an optimum output was obtained at 1 MΩ, which corresponds to the value calculated using FEA. The conversion efficiency was improved by changing the cantilever length and an efficiency of 0.233% was obtained with a 4-mm-long cantilever.     

Study of broad bandwidth vibrational energy harvesting system with optimum thickness of PET substrate

In this paper, we present the development of a flexible PET-based (polyethylene terephthalate; PET) vibrational energy harvesting system with broad bandwidth. This broad bandwidth harvesting system comprises of four units of individual ZnO (zinc oxide) piezoelectric harvester in the form of a cantilever structure connected in parallel, and rectifying circuit with storage module. This system has ability to convert mechanical energy into electrical energy from the varying ambient vibration. The design and simulation of a piezoelectric cantilever plate was described by using commercial software ANSYS FEA (Finite Element Analysis) to determine the optimum thickness of PET substrate, internal stress distribution, operation frequency and electric potential. With the optimum thickness predicted by developed accurate analytical formula analysis, the one-way mechanical strain that is efficient to enhance the induced electric potential can be controlled within the piezoelectric ZnO layer. In addition, the relationship among the model solution of piezoelectric cantilever plate equation, vibration-induced electric potential and electric power was realized. An individual piezoelectric harvester consists of flexible PET substrate, piezoelectric ZnO thin film with (002) c-axis preferred orientation, and selectively deposited UV-curable resin lump structure which is used to change the resonant frequency of the harvester. In combination with multi-harvesters and rectifying with storage module together, an energy harvesting system with broad bandwidth can be fabricated. One individual harvester achieves a maximum OCV (open-circuit voltage) up to 4 V with power density of 1.247 μW/cm³. So far, we succeeded in accomplishing a broad bandwidth system with operating frequency range within 100 Hz-450 Hz to enhance powering efficiency. When the DC voltage (direct current voltage) across a storage module is charged up to 1.55 V after rectification, a flash LED (light emitting diode) is driven.     

A generic double-curvature piezoelectric shell energy harvester: Linear/nonlinear theory and applications

Converting vibration energy to useful electric energy has attracted much attention in recent years. Based on the electromechanical coupling of piezoelectricity, distributed piezoelectric zero-curvature type (e.g., beams and plates) energy harvesters have been proposed and evaluated. The objective of this study is to develop a generic linear and nonlinear piezoelectric shell energy harvesting theory based on a double-curvature shell. The generic piezoelectric shell energy harvester consists of an elastic double-curvature shell and piezoelectric patches laminated on its surface(s). With a current model in the closed-circuit condition, output voltages and energies across a resistive load are evaluated when the shell is subjected to harmonic excitations. Steady-state voltage and power outputs across the resistive load are calculated at resonance for each shell mode. The piezoelectric shell energy harvesting mechanism can be simplified to shell (e.g., cylindrical, conical, spherical, paraboloidal, etc.) and non-shell (beam, plate, ring, arch, etc.) distributed harvesters using two Lamé parameters and two curvature radii of the selected harvester geometry. To demonstrate the utility and simplification procedures, the generic linear/nonlinear shell energy harvester mechanism is simplified to three specific structures, i.e., a cantilever beam case, a circular ring case and a conical shell case. Results show the versatility of the generic linear/nonlinear shell energy harvesting mechanism and the validity of the simplification procedures.     

采用Helmholtz共鸣器与悬臂梁压电换能器的声能采集器研究

针对环境中广泛存在的声能,提出了一种采用Helmholtz共鸣器和悬臂梁压电换能器的声能采集器。Helmholtz共鸣器对入射声压进行放大,放大后的声压引起共鸣器弹性薄壁振动,薄壁的振动传递到压电换能器产生电能输出。建立了带弹性壁的立方形共鸣器的等效集中参数理论模型,并与压电换能器的机电特性结合,分析了声能采集器的声-机-电转换原理,研究了声压、声波频率和负载阻抗对输出功率的影响,研究结果为此类声能采集器的优化设计及工程应用提供了一种可行的方法。实验中,声源通过声波导管输出声能,当共鸣器管口处的声压级为94 dB时,系统实测最大输出功率达240μW。该采集器不仅可作为声能自供能采集器,还可在较远距离为低能耗电子装置进行有源声供能。      

共晶键合与减薄技术的压电能量采集器（英）

采用微硅 锆钛酸铅（Si-PZT）悬臂梁结构并在悬臂梁末端附加镍质量块,构成可以工作于低频环境（小于1 000 Hz）的微压电能量采集器,一种利用压电效应将环境振动能转换为电能的器件。利用金薄膜作为中间层的共晶键合技术和PZT研磨减薄技术制备了微压电悬臂梁结构,PZT减薄实验最好结果为减薄至8 m。镍质量块（2 mm2 mm0.6 mm）采用微电铸工艺制备。通过对硅片与块材PZT的共晶键合工艺与PZT减薄技术的研究,制备出总厚度约为71 m的Si-PZT悬臂梁结构,其中硅梁厚约为47 m,PZT梁厚约为24 m。制备的微压电振动能量采集器样品的测试结果表明:在谐振频率为950 Hz,1.0g加速度激励条件下,其交流输出峰值电压可达958 mV。     

Theoretical investigations of energy harvesting efficiency from structural vibrations using piezoelectric and electromagnetic oscillators

Conversion of ambient vibrational energy into electric power has been the impetus of much modern research. The traditional analysis has focused on absolute electrical power output from the harvesting devices and efficiency defined as the convertibility of an infinite resource of vibration excitation into power. This perspective has limited extensibility when applying resonant harvesters to host resonant structures when the inertial influence of the harvester is more significant. Instead, this work pursues a fundamental understanding of the coupled dynamics of a main mass-spring-damper system to which an electromagnetic or piezoelectric mass-spring-damper is attached. The governing equations are derived, a metric of efficiency is presented, and analysis is undertaken. It is found that electromagnetic energy harvesting efficiency and maximum power output is limited by the strength of the coupling such that no split system resonances are induced for a given mass ratio. For piezoelectric harvesters, only the coupling strength and certain design requirements dictate maximum power and efficiency achievable. Since the harvesting circuitry must "follow" the split resonances as the piezoelectric harvesters become more massive, the optimum design of piezoelectric harvesters appears to be more involved than for electromagnetic devices.     

Fokker–Planck equation analysis of randomly excited nonlinear energy harvester

The probability structure of the response and energy harvested from a nonlinear oscillator subjected to white noise excitation is investigated by solution of the corresponding Fokker–Planck (FP) equation. The nonlinear oscillator is the classical double well potential Duffing oscillator corresponding to the first mode vibration of a cantilever beam suspended between permanent magnets and with bonded piezoelectric patches for purposes of energy harvesting. The FP equation of the coupled electromechanical system of equations is derived. The finite element method is used to solve the FP equation giving the joint probability density functions of the response as well as the voltage generated from the piezoelectric patches. The FE method is also applied to the nonlinear inductive energy harvester of Daqaq and the results are compared. The mean square response and voltage are obtained for different white noise intensities. The effects of the system parameters on the mean square voltage are studied. It is observed that the energy harvested can be enhanced by suitable choice of the excitation intensity and the parameters. The results of the FP approach agree very well with Monte Carlo Simulation (MCS) results.     

Performance of a cantilever piezoelectric energy harvester impacting a bump stop

Piezoelectric cantilever beam energy harvesters are commonly used to convert ambient vibration into electrical energy. In practical applications, energy harvesters are subjected to large shocks which can shorten the service life by causing mechanical failure. In this work, a bump stop is introduced into the design of a piezoelectric cantilever beam energy harvester to limit the maximum displacement of the cantilever and prevent excessively high bending stresses developing as a result of shocks. In addition to limiting the maximum displacement of the beam, it is inevitable that the deflected shape of the beam and the electrical output are modified. A theoretical model for a piezoelectric cantilever beam harvester impacting against a stop is derived, which aims to develop an understanding of the vibration characteristics of the cantilever and quantify how the electrical output of the harvester is affected by the stop. An experiment is set up to measure the dynamics and the electrical output of a bimorph energy harvester and to validate the theoretical model. Numerical simulation results are presented for energy harvesters with different initial gaps and different stop locations, and it is found that the reduction in maximum bending stress is at the expense of the electrical power of the harvester.     

An experimentally validated electromagnetic energy harvester

A relatively simple method for determining the electromechanical parameters of electromagnetic energy harvesters are presented in this paper. The optimal power generated through a load resistor at both off-resonance and resonance is derived analytically. The experimentally measured performance of a rudimentary electromechanical energy harvester using a rare-earth magnet shows good agreement with the results from the model. The parasitic generator coil resistance can have a profound effect on the overall performance of an electromagnetic generator by essentially acting to degrade the effective coupling coefficient. Data from the setup electromagnetic generator shows normalized power densities of 1.7 μW/[(m/s²)² cm³] operating at a resonance frequency of 112.25 Hz. This power density is comparable with other electromagnetic devices of the same volume operating at these frequencies. The power output of the presented electromagnetic generator is comparable to equivalent piezoelectric generators.     

Designing and manufacturing a piezoelectric tile for harvesting energy from footsteps

The objective of this research is to design a piezoelectric tile for harvesting energy from footsteps and to optimize the system for harvesting maximum energy. Because piezoelectric modules easily break when directly subjected to energy generated by human movements, we designed a tile that employs indirect energy transmission using springs and a tip mass. We aimed at matching the mechanical resonance frequency of the tile with that of the piezoelectric modules. The resonance frequency of a piezoelectric module with a 10-g tip mass was almost similar to the vibration frequency of the tile at 22.5 Hz when we dropped an 80-g steel ball from a 1-m height. We performed impedance matching and realized a matching value of 15 kΩ. Under these optimal mechanical and electrical conditions, we harvested 770-μW RMS and 55-mW peak output power.     

Broadband energy harvesting via magnetic coupling between two movable magnets

Harvesting energy from ambient mechanical vibrations by the piezoelectric effect has been proposed for powering microelectromechanical systems and replacing batteries that have a finite life span. A conventional piezoelectric energy harvester （PEH） is usually designed as a linear resonator, and suffers from a narrow operating bandwidth. To achieve broadband energy harvesting, in this paper we introduce a concept and describe the realization of a novel nonlinear PEH. The proposed PEH consists of a primary piezoelectric cantilever beam coupled to an auxiliary piezoelectric cantilever beam through two movable magnets. For predicting the nonlinear response from the proposed PEH, lumped parameter models are established for the two beams. Both simulation and experiment reveal that for the primary beam, the introduction of magnetic coupling can expand the operating bandwidth as well as improve the output voltage. For the auxiliary beam, the magnitude of the output voltage is slightly reduced, but additional output is observed at off-resonance frequencies. Therefore, broadband energy harvesting can be obtained from both the primary beam and the auxiliary beam.     

Experimental model validation for a nonlinear energy harvester incorporating a bump stop

In some practical applications, cantilever beam piezoelectric energy harvesters are subjected to large amplitude base excitations which induce nonlinear behaviour in the harvester that affects their performance. In this paper, a cantilever piezoelectric energy harvester model is developed which takes account of geometric nonlinearity arising through the inextensible beam condition and material nonlinearity arising in the piezoelectric layers of the harvester. The model is validated against experimental measurements for different base accelerations and load resistances, and an investigation into the nonlinear behaviour indicates that nonlinear softening is caused predominantly by material nonlinearity. To reduce the beam amplitude and the resulting bending stress in the cantilever harvester, a bump stop is incorporated into the harvester design and the influence of the bump stop is modelled. Comparisons of theoretical predictions with experimental measurements indicate that taking account of the nonlinear behaviour improves the prediction significantly in some cases. Parameter studies are also conducted to investigate how the stop location and initial gap size between the harvester and stop affect the performance of the nonlinear energy harvester.     

Enhanced vibration energy harvesting using dual-mass systems

A type of dual-mass vibration energy harvester, where two masses are connected in series with the energy transducer and spring, is proposed and analyzed in this paper. The dual-mass vibration energy harvester is proved to be able to harvest more energy than the traditional single degree-of-freedom (dof) one when subjected to harmonic force or base displacement excitations. The optimal parameters for maximizing the power output in both the traditional and the new configurations are discussed in analytical form while taking the parasitic mechanical damping of the system into account. Consistent of the previous literature, we find that the optimal condition for maximum power output of the single dof vibration energy harvester is when the excitation frequency equals to the natural frequency of the mechanical system and the electrical damping due to the energy harvesting circuit is the same as the mechanical damping. However, the optimal conditions are quite different for the dual-mass vibration energy harvester. It is found that two local optimums exist, where the optimal excitation frequency and electrical damping are analytically obtained. The local maximum power of the dual-mass vibration energy harvester is larger than the global maximum power of single dof one. Moreover, at certain frequency range between the two natural frequencies of the dual-mass system, the harvesting power always increases with the electrical damping ratio. This suggests that we can obtain higher energy harvesting rate using dual-mass harvester. The sensitivity of the power to parameters, such as mass ratio and tuning ratio, is also investigated.     

Mechanics of flexible and stretchable piezoelectrics for energy harvesting

As rapid development in wearable/implantable electronic devices benefit human life in daily health monitoring and disease treatment medically, all kinds of flexible and/or stretchable electronic devices are booming, together with which is the demanding of energy supply with similar mechanical property. Due to its ability in converting mechanical energy lying in human body into electric energy, energy harvesters based on piezoelectric materials are promising for applications in wearable/implantable device's energy supply in a renewable, clean and life-long way. Here the mechanics of traditional piezoelectrics in energy harvesting is reviewed, including why piezoelectricity is the choice for minor energy harvesting to power the implantable/wearable electronics and how. Different kinds of up to date flexible piezoelectric devices for energy harvesting are introduced, such as nanogenerators based on Zn O and thin and conformal energy harvester based on PZT. A detailed theoretical model of the flexible thin film energy harvester based on PZT nanoribbons is summarized, together with the in vivo demonstration of energy harvesting by integrating it with swine heart. Then the initial researches on stretchable energy harvesters based on piezoelectric material in wavy or serpentine configuration are introduced as well.     

Physical bounds of metallic nanofingers obtained by mechano-chemical atomic force microscope nanolithography

To obtain metallic nanofingers applicable in surface acoustic wave (SAW) sensors, a mechano-chemical atomic force microscope (AFM) nanolithography on a metallic thin film (50 nm in thickness)/piezoelectric substrate covered by a spin-coated polymeric mask layer (50-60 nm in thickness) was implemented. The effective shape of cross-section of the before and after etching grooves have been determined by using the AFM tip deconvolution surface analysis, structure factor, and power spectral density analyses. The wet-etching process improved the shape and aspect ratio (height/width) of the grooves and also smoothed the surface within them. We have shown that the relaxed surface tension of the polymeric mask layer resulted in a down limitation in width and length of the lithographed nanofingers. The surface tension of the mask layer can be changed by altering the initial concentration of the polymer in the deposition process. As the surface tension reduced, the down limitation decreased. In fact, an extrapolation of the analyzed statistical data has indicated that by decreasing the surface tension from 39 to 10 nN/nm, the minimum obtainable width and length of the metallic nanofingers was changed from about 55 nm and 2 μm to 15 nm and 0.44 μm, respectively. Using the extrapolation’s results, we have shown that the future SAW sensors buildable by this nanolithography method possess a practical bound in their synchronous frequency (∼58 GHz), mass sensitivity (∼6125 MHz-mm²/ng), and the limit of mass resolution (∼4.88 × 10⁻¹⁰ ng/mm²).     

Hydrostatic pressure dependence of excitonic optical transitions in strained wurtzite GaN/AlN quantum disks

In the framework of the effective mass approximation, the effects of hydrostatic pressure on optical transitions associated with the excitons confined in strained wurtzite (WZ) GaN/AlN quantum disks (QDisks) with the confinement potential of finite depth are investigated by using a variational technique, with considering the influences of the built-in electric field (BEF) and the biaxial strain dependence of material parameters. The Schrödinger equation via the proper choice of the exciton trial wave function is solved. The behaviors of the excitonic optical transition are examined at different pressures for different QDisk sizes. In our calculations, the effective masses of electron and hole, dielectric constants, phonon frequencies, energy gaps, and piezoelectric polarizations are taken into account as functions of biaxial strain and hydrostatic pressure. Numerical results show that the hydrostatic pressure and the QDisk size have a remarkable influence on exciton states. The calculated pressure coefficient of optical transition energy shows a negative value if the QDisk height L > 3.2 nm, in contrast with the positive pressure coefficient of the GaN band gap. The peculiar pressure behavior is related to the pressure-induced increase of the built-in electric field. For a fixed pressure, the optical transition energy has a red-shift if the QDisk height and radius increase and QDisk height has a more obvious influence on E_ph than QDisk radius. Furthermore, the relationship between the radiative decay time and hydrostatic pressure (QDisk height) is also investigated. It is found that the radiative decay time increases with pressure and the increment tendency is more prominent for the large height QDisks. The radiative decay time strongly increases by three orders of magnitude reaching microsecond order if the QDisk height increases from 1 nm to 3 nm.     

非线性磁式压电振动能量采集系统建模与分析

为便于评价、优化磁式压电振动能量采集系统的性能,系统研究了该类系统的建模与分析方法,建立了非线性的分布参数模型用于描述系统的非线性动力学行为,并采用谐波平衡法给出了谐波响应的解析解.随后利用仿真模型分析了磁铁间距、加速度幅值、负载阻抗对输出功率的影响,比较了不同激励频率和加速度幅值下的最优阻抗.结果表明:双稳态特性适用于低强度的振动环境,且愈接近临界区域,输出功率愈高,而单稳态渐硬特性适用于高强度振动环境,其最优间距并不靠近临界区域;阱间大幅运动和阱内小幅运动均存在高低能量态共存的现象,愈接近临界区域,现象愈明显;激振频率是影响最优负载阻抗的决定性因素.     

Theoretical modeling and experimental realization of dynamically magnified thermoacoustic-piezoelectric energy harvesters

Conventional thermoacoustic-piezoelectric (TAP) harvesters convert thermal energy, such as solar or waste heat energy, directly into electrical energy without the need for any moving components. The input thermal energy generates a steep temperature gradient along a porous medium. At a critical threshold of the temperature gradient, self-sustained acoustic waves are developed inside an acoustic resonator. The associated pressure fluctuations impinge on a piezoelectric diaphragm, placed at the end of the resonator. In this study, the TAP harvester is coupled with an auxiliary elastic structure in the form of a simple spring–mass system to amplify the strain experienced by the piezoelectric element. The auxiliary structure is referred to as a dynamic magnifier and has been shown in different areas to significantly amplify the deflection of vibrating structures. A comprehensive model of the dynamically magnified thermoacoustic-piezoelectric (DMTAP) harvester has been developed that includes equations of motions of the system?s mechanical components, the harvested voltage, the mechanical impedance of the coupled structure at the resonator end and the equations necessary to compute the self-excited frequencies of oscillations inside the acoustic resonator. Theoretical results confirmed that significant amplification of the harvested power is feasible if the magnifier?s parameters are properly chosen. The performance characteristics of experimental prototypes of a thermoacoustic-piezoelectric resonator with and without the magnifier are examined. The obtained experimental findings are validated against the theoretical results. Dynamic magnifiers serve as a novel approach to enhance the effectiveness of thermoacoustic energy harvested from waste heat by increasing the efficiency of their harvesting components.     

Experimental passive self-tuning behavior of a beam resonator with sliding proof mass

A passively self-tuning resonator configuration is presented in this study. Three different prototype beam–mass systems were built and tested and all successfully displayed passive self-tuning behavior when driven by vibrations at frequencies ranging from 45 to 140 Hz and accelerations ranging from 0.007 to 2g. All three systems were able to achieve tuning within their operating regime when driven at a single frequency, as well as maintain a tuned condition as frequency was stepped up or down, demonstrating a bandwidth between 6 and 40 Hz. One application of such a passively self-tuning system is in vibration energy harvesting, where it is critical for performance that the harvester device resonance frequency matches the input vibration frequency, yet the input frequency may change over time and is not known a priori. The self-tuning resonator demonstrated in this paper can enable the energy harvesting system to adjust to the varying input frequencies and thereby increase the energy harvested over time.