曲梁压电俘能器强迫振动的格林函数解

CLOSED-FORM SOLUTIONS FOR FORCED VIBRATIONS OF CURVED PIEZOELECTRIC ENERGY HARVESTERS BY MEANS OF GREEN’S FUNCTIONS

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?;(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.

This article investigates the forced vibrations of curved piezoelectric energy harvesters by means of Green’s functions. The differential method is used to analyze the in-plane forces of the cantilevered piezoelectric energy harvester.According to the governing equations of motion, the electromechanical coupled Prescott models are derived based on the piezoelectric constitutive relations, which the circumferential forcing and the circumferential inertia term can be negligible, and a damping effect, radial damping, is taken into account. Utilizing the Laplace transform, the explicit expressions of the Green’s functions of the coupled vibration equations can be acquired. On the basis of the superposition principle and the physical interpretation of Green’s functions, the coupled system is decoupled and the expression of the output voltage can be obtained analytically. The present model for the curved beam can be readily reduced to straight beam. In the numerical sections, the present solutions are verified by the results in some published references. By comparing with the result of traditional straight piezoelectric energy harvesters model, the high energy harvesting efficiency of the curved piezoelectric energy harvesters model in the thesis is demonstrated. It is apparent that the present model has a wider range of application than the existing ones. The influence of radial damping, Young’s modules of two materials and some other essential physical parameters on the evaluation functions for output voltage and resonant frequency are discussed.This research suggests that to make the electric power reach the maximum value, the optimal resistive load is 1 M?;the elasticity modulus for both piezoelectric material and structure material have a profound effect on the resonant frequency.By replacing the base materials with lower modulus of elasticity, the phenomenon of high frequency resonance can be improved to make the curved piezoelectric energy harvesters adapt to more complex working environment. However, the energy harvesting efficiency of the structure will be decline.