悬臂梁挠曲电俘能器的力电耦合模型及性能分析

挠曲电效应指应变梯度在电介质中引起的电极化现象,是一种普遍存在的力电耦合行为。应变梯度与材料的尺寸成反比,因此挠曲电效应有望在纳米尺度主导材料的物理性质,尤其是力电耦合性能。本文建立了悬臂梁挠曲电俘能器的理论模型,基于哈密顿原理得到了悬臂梁挠曲电俘能器的控制方程和相应的边界条件;进一步,得到了悬臂梁挠曲电俘能器的输出电压频率响应和功率密度频率响应随悬臂梁的振动频率、外电路阻抗、挠曲电层厚度以及弹性层模量的变化规律。聚偏氟乙烯和环氧树脂层合挠曲电悬臂梁俘能器模型的数值结果表明输出电压频率响应和功率密度频率响应在共振频率点取得最大值,且随着各阶模态对应的共振频率的增加悬臂梁挠曲电俘能器的输出电压和功率密度均增加。此外,计算结果还表明悬臂梁俘能器存在最佳匹配阻抗,在匹配阻抗附近悬臂梁俘能器的输出功率密度随挠曲电层厚度的减小而增大,表现出明显的尺寸效应。本文工作提供了一种基于挠曲电效应的悬臂梁俘能器的理论模型,为悬臂梁俘能器的设计提供了理论依据。     

Dynamic analysis of piezoelectric energy harvester under combination parametric and internal resonance: a theoretical and experimental study

In this work, theoretical and experimental analysis of a piezoelectric energy harvester with parametric base excitation is presented under combination parametric resonance condition. The harvester consists of a cantilever beam with a piezoelectric patch and an attached mass, which is positioned in such a way that the system exhibits 1:3 internal resonance. The generalized Galerkin’s method up to two modes is used to obtain the temporal form of the nonlinear electromechanical governing equation of motion. The method of multiple scales is used to reduce the equations of motion into a set of first-order differential equations. The fixed-point response and the stability of the system under combination parametric resonance are studied. The multi-branched non-trivial response exhibits bifurcations such as turning point and Hopf bifurcations. Experiments are performed under various resonance conditions. This study on the parametric excitation along with combination and internal resonances will help to harvest energy for a wider frequency range from ambient vibrations.

     

悬臂梁挠曲电俘能器的力电耦合模型及性能分析

挠曲电效应指应变梯度在电介质中引起的电极化现象，是一种普遍存在的力电耦合行为。应变梯度与材料的尺寸成反比，因此挠曲电效应有望在纳米尺度主导材料的物理性质，尤其是力电耦合性能。本文建立了悬臂梁挠曲电俘能器的理论模型，基于哈密顿原理得到了悬臂梁挠曲电俘能器的控制方程和相应的边界条件；进一步，得到了悬臂梁挠曲电俘能器的输出电压频率响应和功率密度频率响应随悬臂梁的振动频率、外电路阻抗、挠曲电层厚度以及弹性层模量的变化规律。聚偏氟乙烯和环氧树脂层合挠曲电悬臂梁俘能器模型的数值结果表明输出电压频率响应和功率密度频率响应在共振频率点取得最大值，且随着各阶模态对应的共振频率的增加悬臂梁挠曲电俘能器的输出电压和功率密度均增加。此外，计算结果还表明悬臂梁俘能器存在最佳匹配阻抗，在匹配阻抗附近悬臂梁俘能器的输出功率密度随挠曲电层厚度的减小而增大，表现出明显的尺寸效应。本文工作提供了一种基于挠曲电效应的悬臂梁俘能器的理论模型，为悬臂梁俘能器的设计提供了理论依据。     

面内压电振动能量采集动力学设计与性能研究

压电振动能量采集将环境中普遍存在的机械能转换为电能，可以实现自供能传感、控制与驱动，具备灵活、节能环保、可持续的优势，具有广阔的应用前景。为了促进压电振动能量采集器件的集成与融合，提出面内压电振动能量采集，将压电振动能量采集器进行扁平化设计，使其在二维平面内采集振动能量，在保证较大功率输出下能够显著减小器件所需三维空间。为了提高输出功率与工作频宽，设计了具有双稳态与力放大机制的面内压电振动能量采集器。考虑弯张小变形，通过能量法建立了面内压电振动能量采集器的机电耦合动力学模型。分析了关键设计参数对面内压电振动能量采集器性能的影响。数值仿真了面内压电振动能量采集器在简谐激励下的俘能性能，结果表明，通过合理的设计，面内压电振动能量采集器可以低频、宽频弱激励下有效俘获能量。面内压电振动能量采集设计方法有利于推动便携式、可穿戴式自供能等方面的应用和产业化。     

附磁压电悬臂梁流致振动俘能特性分析

流致振动蕴含巨大的能量, 本文基于流致振动理论,设计了一种附加磁力激励的压电悬臂梁流致振动俘能器,并通过理论和实验研究其振动俘能特性.该俘能器由压电悬臂梁、圆柱绕流体和磁铁组成;首先基于Euler-Bernoulli梁理论,推导了流致振动附磁压电俘能器的能量函数,利用Hamilton原理建立了流致振动附磁压电俘能器的机电耦合方程;利用数值方法研究详细分析了流速、圆柱绕流体直径和长度、磁间距、磁极和外接电阻等系统参数对压电俘能器振动特性和输出电压的影响.分析结果表明, 该型压电俘能器的振动幅值在低流速条件下产生涡激振动,并产生最大的输出电压;磁力可以降低压电俘能器的共振频率并能够拓宽压电俘能器频带带宽,因此,附磁压电俘能器具有相比没有附磁的压电俘能器更适用于低速层流环境;实验结果与数值结果吻合较好,验证了附磁压电悬臂梁流致振动俘能器的理论分析的正确性.      

局域共振型声子晶体板缺陷态带隙及其俘能特性研究

设计了一种由圆柱形散射体嵌入环氧树脂基体而组成的周期阵列局域共振型声子晶体板结构, 分析了其平直带区域以及缺陷态的能量集中特性, 并研究了其振动能量采集特性. 首先基于超元胞法结合有限元方法分析了5 $\times$ 5完美声子晶体结构和缺陷态声子晶体结构的能带曲线和能量传输特性; 考虑点缺陷局域共振声子晶体结构的能量集中特性, 利用压电材料代替超元胞中某点的散射体材料引入点缺陷, 分析其振动能量采集特性, 结果表明单个5 $\times$ 5点缺陷超胞结构共振频带较窄; 为提升俘能效率, 提出两种由3个具有不同缺陷态数量和构型的5 $\times$ 5超元胞结构并联而成的5 $\times$ 15声子晶体板结构, 机电耦合特性分析结果表明: 所提出的局域共振型声子晶体板结构克服了单个点缺陷超胞结构缺陷模过少、共振频带过窄的局限性, 拓宽了俘能器的工作频带, 提高了输出电压; 此外, 引入不同的缺陷态数量和构型, 可以进一步拓宽俘能带宽, 实现更好的俘能效果.      

线绳驱动转速提升式低频俘能器的设计与研究

俘获周围环境中丰富的低频机械能对减少废旧电池数量、实现自维持传感器、降低传感器网络的使用和维护成本等具有重要意义, 但传统的振动型俘能器对低频机械能的俘获效果不佳. 为了有效收集周围环境中的低频机械能, 本文提出一种线绳驱动、具备转速提升功能的电磁式俘能器, 首先借助线绳驱动转轴结构将低频振动转换为双向旋转运动, 再通过刚度自动改变的拨片和磁齿轮将双向旋转运动转换为转速更高的单向旋转运动, 从而提高输出功率. 对所提出的俘能器建立了机电耦合动力学模型, 并通过样机制作和实验测试证实了理论模型的正确性. 实验研究表明, 在激励幅值40 mm和激励频率2 Hz的条件下, 通过本文设计制作的2.5倍转速提升功能的磁齿轮, 可将线绳驱动电磁式俘能器的最大输出功率增加至7.82 mW, 比对应的无磁齿轮提升转速的线绳驱动电磁式俘能器的最大输出功率(3.22 mW)高约143%. 在相同的激励条件下, 制作的俘能器的交流电能经过桥式整流器转换为直流后, 可在1.2 s内将220 μF储能电容器的电压从0 V提升至1.5 V. 在低频、不规则的振动激励下, 所制作的俘能器仍可提供0.35 mW的输出功率, 为设计高性能低频俘能器提供一条可行的解决方案.      

动态多稳态压电风能俘能结构设计与实验验证

传统的线性颤振式风能俘能结构在变风速环境下转换效率不高。针对此问题，本文提出了一种动态多稳态颤振式压电俘能结构，可在较宽的风速范围内保持较高的电压输出。该结构由矩形平板、压电悬臂梁与3块永磁体组成，并通过磁吸力实现结构的多稳态。通过在不同风速下开展的能量转换特性实验研究，发现当风速较小时，该结构具有双稳态特性；而当风速较大时，会出现新的稳定位置，结构变为三稳态系统。这样的动态稳定位置，可以保证结构在很宽的风速范围内出现阱间跳跃，进而保持大的电能输出。实验结果表明，这种动态多稳态结构，风速在2.0m/s—7.5m/s区间变化时，能够激发并保持阱间跳跃，甚至相干共振，产生较大的电能输出。     

曲梁压电俘能器强迫振动的格林函数解

本文运用格林函数法求解了曲梁压电俘能器在强迫振动下的解析解.运用微分法分析了压电层合曲梁结构面内各内力,根据曲梁压电 俘能器的动力学方程组,基于压电本构关系,建立了包含径向阻尼但不考虑俘能器曲梁结构部分的轴向力以及轴向惯性项的Prescott力 电耦合模型. 采用Laplace变换法求得了耦合振动方程的格林函数解.根据叠加原理和格林函数的物理意义,对耦合的系统方程解耦进而 求得强迫振动下曲梁压电俘能器的输出电压. 数值计算中,通过与现有文献的解析解进行对比,验证了本文解析解的有效性,并研究了阻 尼、电阻等重要物理参数对压电函数和谐振频率的影响.通过与有关传统直梁压电俘能器研究成果的对比,体现了曲梁压 电俘能器Prescott模型的高效集能特性. 数值分析研究表明:(1)使得曲梁俘能器达到最大输出电压时连接的最优负载电 阻为1 M$\Omega$;(2)通过更换适当的基底材料,降低材料的弹性模量,可以改变曲梁俘能器的高基频现象,以使结构适应 更复杂的工作环境,但这会导致俘能器的工作效率降低.      

Structural and electrical dynamics of a grating-patterned triboelectric energy harvester with stick–slip oscillation and magnetic bistability

The majority of research work on triboelectric energy harvesting is on material science, manufacturing and electric circuit design. There is a lack of in-depth research into structural dynamics which is crucial for power generation in triboelectric energy harvesting. In this paper, a novel triboelectric energy harvester with a compact structure working in sliding mode is developed, which is in the form of a casing and an oscillator inside. Unlike most sliding-mode harvesters using single-unit films, the proposed harvester utilizes grating-patterned films which are much more efficient. A bistable mechanism consisting of two pairs of magnets is employed for broadening the frequency bandwidth. A theoretical model is established for the harvester, which couples the structural dynamics domain and electrical dynamics domain. This paper presents the first study about the nonlinear structural dynamics of a triboelectric energy harvester with grating-patterned films, which is also the first triboelectric energy harvester integrating grating-patterned films with a bistable magnetic system for power performance enhancement. Theoretical studies are carried out from the perspectives of both structural and electrical dynamics. Surface charge density and segment configuration of the films affect whether the electrostatic force influences the structural dynamics, which can be neglected under a low surface charge density. Differences in structural response and electrical output are found between a velocity-dependent model and Coulomb’s model for modelling the friction in the triboelectric energy harvesting system. The bistable mechanism can effectively improve the output voltage under low-frequency excitations. Additionally, the output voltage can also be obviously enhanced through increasing the number of the hollowed-out units of the grating-patterned films, which also results in a slight decrease in the optimal load resistance of the harvester. These findings enable innovative designs for triboelectric energy harvesters and provide fabrication guidelines in practical applications.

     

基于人体运动的压电-电磁混合式振动能量采集研究

将人体运动产生的动能转化为可利用的电能为传感器供电一直是能量采研究中的一个热点。如何有效利用人体运动，增强环境适应能力以及提高能量采集性能仍是俘能研究中需要解决的关键问题。本文基于人体运动特性，设计了一种新型的混合式能量采集器，同时具有压电和电磁转化机制。压电俘能是基于压电梁变形产生电能，电磁发电机采用堆叠磁组构型来切割线圈产生电动势。首先建立了混合式能量采集器的动力学理论模型，用来描述输出电压特性，并与实验进行了对比验证。理论与实验研究均表明，混合式俘能器的输出电压在一定激励频率范围内出现两个波峰。通过调节压电梁长度，可以改变峰值大小以及两个峰值间的频段范围。人体运动实验表明，混合式俘能器中可以在短时间内提供较高的电压输出，比如当跑步速度为5km/h时，3s内就可以输出1.1V直流电压驱动传感器工作；跑步时长为30s时，传感器正常工作时常可以达到77s。本文设计的混合式俘能器不仅可以快速供电，还具有较强的续航能力，这为电池充电或传感器供电提供了潜在的应用价值。     

Vibration energy harvesting for low frequency using auto-tuning parametric rolling pendulum under exogenous multi-frequency excitations

An electromagnetic parametrically excited rolling pendulum energy harvester with self-tuning mechanisms subject to multi-frequency excitation is proposed and investigated in this paper. The system consists of two uncoupled rolling pendulum. The resonance frequency of each the rolling pendulum can be automatically tuned by adjusting its geometric parameters to access parametric resonance. This harvester can be used to harvest the energy at low frequency. A prototype is developed and evaluated. Its mathematical model is derived. A cam with rolling follower mechanism is employed to generate multi-frequency excitation. An experimental study is conducted to validate the proposed concept. The experimental results are confirmed by the numerical results. The harvester is successfully tuned when the angular velocity of the cam is changed from 1.149 to 1.236 Hz.     

Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters

A global nonlinear distributed-parameter model for a piezoelectric energy harvester under parametric excitation is developed. The harvester consists of a unimorph piezoelectric cantilever beam with a tip mass. The derived model accounts for geometric, inertia, piezoelectric, and fluid drag nonlinearities. A reduced-order model is derived by using the Euler–Lagrange principle and Gauss law and implementing a Galerkin discretization. The method of multiple scales is used to obtain analytical expressions for the tip deflection, output voltage, and harvested power near the first principal parametric resonance. The effects of the nonlinear piezoelectric coefficients, the quadratic damping, and the excitation amplitude on the output voltage and harvested electrical power are quantified. The results show that a one-mode approximation in the Galerkin approach is not sufficient to evaluate the performance of the harvester. Furthermore, the nonlinear piezoelectric coefficients have an important influence on the harvester’s behavior in terms of softening or hardening. Depending on the excitation frequency, it is determined that, for small values of the quadratic damping, there is an overhang associated with a subcritical pitchfork bifurcation.     

Energy harvesting from quasi-periodic vibrations using electromagnetic coupling with delay

In this paper, we study quasi-periodic vibrational energy harvesting in a delayed self-excited oscillator with a delayed electromagnetic coupling. The energy harvester system consists in a delayed van der Pol oscillator with delay amplitude modulation coupled to a delayed electromagnetic coupling mechanism. It is assumed that time delay is inherently present in the mechanical subsystem of the harvester, while it is introduced in the electrical circuit to control and optimize the output power of the system. A double-step perturbation method is performed near a delay parametric resonance to approximate the quasi-periodic solutions of the harvester which are used to extract the quasi-periodic vibration-based power. The influence of the time delay introduced in the electromagnetic subsystem on the performance of the quasi-periodic vibration-based energy harvesting is examined. In particular, it is shown that for appropriate values of amplitudes and frequency of time delay the maximum output power of the harvester is not necessarily accompanied by the maximum amplitude of system response.     

磁耦合式双稳态宽频压电俘能器的设计和俘能特性

为了同时提高振动能量俘获系统的效率和实用性, 俘能器主结构的振动特性与环境振动特性的匹配度显得尤为重要. 非线性系统复杂的动力学行为为设计高效的俘能器奠定了基础, 但结构一旦被设计、生成出来, 其工作频率往往是固定的, 无法根据环境中的振动而发生相应的改变. 本文利用可移动铰支座和非线性磁力设计了一种具有双稳态特性的宽频压电俘能器, 通过拓宽压电俘能器的工作频带, 来匹配环境中较宽的振动频率. 为了保证系统低频宽带的俘能效果, 详细分析了结构的长度比、磁间距、负载阻抗、外激励频率和幅值等对系统线性刚度、非线性刚度以及动力学行为的影响, 并进行了实验验证. 首先将系统简化为欧拉-伯努力梁, 利用拉格朗日方程建立系统的非线性动力学方程, 并利用谐波平衡法进行求解. 针对理论分析给出的不同外激励频率下的最优长度比, 搭建了实验平台进行验证. 理论和实验的结果表明: 非线性磁力的引入使系统呈现负刚度特性, 使俘能器能够在单稳态和双稳态之间的变换, 实现低频俘能效果; 通过调节可移动铰支座的位置, 改变系统的长细比, 能够实现从0到16 Hz的宽频俘能效果.      

Modeling and preliminary analysis of piezoelectric energy harvester based on cylindrical tube conveying fluctuating fluid

In this contribution, a novel type of piezoelectric tubular energy harvester based on fluctuating fluid pressure is investigated. Analytic model of the proposed energy harvester is built under the assumption of axisymmetric radial vibration. Exact solution of the piezoelectric vibrating tube is obtained with its output performances formulated. A series of numerical simulations are conducted to investigate the influences of geometrical parameters, input mechanical load parameters and output electrical load parameters upon the output performances of the proposed piezoelectric tubular energy harvester. The model and simulation results indicate the potential of the proposed piezoelectric tubular energy harvester. It is expected that the energy harvester be useful in powering wireless sensor network for the health monitoring of hydraulic systems, where fluid conveying pipe vibration is omnipresent.     

Nonlinear energy harvesting from vibratory disc-shaped piezoelectric laminates

Implementing resonators with geometrical nonlinearities in vibrational energy harvesting systems leads to considerable enhancement of their operational bandwidths. This advantage of nonlinear devices in comparison to their linear counterparts is much more obvious especially at small-scale where transition to nonlinear regime of vibration occurs at moderately small amplitudes of the base excitation. In this paper the nonlinear behavior of a disc-shaped piezoelectric laminated harvester considering midplane-stretching effect is investigated. Extended Hamilton's principle is exploited to extract electromechanically coupled governing partial differential equations of the system. The equations are firstly order-reduced and then analytically solved implementing perturbation method of multiple scales. A nonlinear finite element method(FEM) simulation of the system is performed additionally for the purpose of verification which shows agreement with the analytical solution to a large extent. The frequency response of the output power at primary resonance of the harvester is calculated to investigate the effect of nonlinearity on the system performance. Effect of various parameters including mechanical quality factor, external load impedance and base excitation amplitude on the behavior of the system are studied. Findings indicate that in the nonlinear regime both output power and operational bandwidth of the harvester will be enhanced by increasing the mechanical quality factor which can be considered as a significant advantage in comparison to linear harvesters in which these two factors vary in opposite ways as quality factor is changed.     

Performance improvement of the stochastic-resonance-based tri-stable energy harvester under random rotational vibration

In this paper, the stochastic-resonance-based tri-stable energy harvester (TEH) is proposed to enhance harvesting performance under random rotational vibration. An electromechanical coupled system interfaced with a standard rectifier circuit driven by colored noise is considered. The stationary probability density function (SPDF) of the harvester is obtained by the improved stochastic averaging. Then, with the adiabatic approximation theory, the analytical expression of signal-to-noise ratio (SNR) for the TEH is deduced to characterize stochastic resonance (SR). To enhance direct current (DC) power delivery from a rotational TEH, the influences of system parameters on SR is discussed. The obtained results suggest that there are damping-induced resonance and noise-intensity-induced SR in the tri-stable system. The TEH has higher harvesting performance under the optimal SR. That is, the optimal parameter combinations can induce optimal SR and maximize harvesting performance. Thus, the stochastic-resonance-based TEH can be optimized to enhance energy harvesting through choosing the optimal parameter.     

Nonlinear energy harvesting with dual resonant zones based on rotating system

An electromagnetic nonlinear energy harvester(NEH)based on a rotating system is proposed,of which the host system rotates at a constant speed and vibrates harmonically in the vertical direction.This kind of device exhibits several resonant phenomena due to the combinations of the rotating and the vibration frequencies of the host system as well as the cubic nonlinearity of the NEH.The governing equation of motion for the NEH is derived,and the dynamic responses and output power are investigated with the multiple scale method under the 1:1 primary and 2:1 superharmonic resonant conditions.The effects of system parameters including the nondimensional external frequency,the rotating speed,and the nonlinear stiffness on the responses of free vibration for the system are studied.The results of the primary resonance show that the responses exhibit not only the resonant characteristics but also the nonlinear dynamic characteristics such as the saddle-node(SN)bifurcation.The coexistence of multiple solutions and the varying trends of responses are verified with the direct numerical simulation.Moreover,the effects of system parameters on the average output power are investigated.The results of the analyses on the two resonant conditions indicate that the large power can be harvested in two resonant frequency bands.The effect of resonance on the output power is dominant for the 2:1 superharmonic resonance.Moreover,the results also show that introducing the nonlinearity can increase the value of the output power in large frequency bands and induce the occurence of new frequency bands to harvest the large power.The efficiency of the harvested power could be improved by the combined effects of the resonance as well as the nonlinearity of the NEH device.Suitable parameter conditions could help optimize the power harvesting in design.     

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.