压电发电悬臂梁的非线性动力学建模及响应分析

摘要

The electromechanical coupling model of cantilevered piezoelectric harvester was developed by consid-ering the nonlinearities of piezoelectric material,based on Hamilton theory,Rayleigh-Ritz method,Euler-Ber-noulli beam theory and constant electrical field across the piezoelectric element.The response characteristics of the system were investigated numerically,and the influences of piezoelectric material nonlinear coefficient on the system response were analyzed.By exploring the nonlinear characteristics of the piezoelectric vibrator near the resonant frequency,the nature of the multi -solutions and jump phenomena in the resonance region was re-vealed.The results were verified experimentally.which provides a theoretical basis for the study of nonlinear mechanism of piezoelectric power generation system.%以单晶悬臂梁压电发电装置为研究对象，在考虑压电材料非线性的情况下，利用广义Hamilton原理、Rayleigh-Ritz法、Euler-Bernoulli梁理论及压电元件恒定电场假设建立了悬臂梁压电发电装置的分布式机电耦合模型，通过数值计算分析谐振频率附近解的特性与系统参数及初始条件的关系，揭示了压电材料非线性、外激励参数对系统响应的影响规律，并通过实验验证了解析解的正确性。结果表明，压电材料的非线性特性会导致近似解的共振峰向左偏移，呈现软特性的非线性特征；当激励频率变化时，系统响应存在多解、跳跃等现象，主共振解的真正实现与初始条件的选取有关。