压电悬臂梁机电耦合系统的建模及动力学特性分析

Model and Dynamic Analysis of the Electro-mechanical Coupling System of Piezoelectric Vibration Energy Harvesters

基于压电能量采集器中最为经典的压电悬臂梁模型展开研究。考虑悬臂梁的阵型信息和轴向应变分布,这导致与梁耦合的压电片的电边界条件复杂。分别基于均匀电场分布和均匀电位移分布的两种不同电边界条件,深入探讨压电悬臂梁的机电耦合原理和耦合特性,并建立机电耦合系统的数学模型;在传统一阶能量采集电路的基础上,在电路中加入电感,建立二阶电路,并改进数学模型;对于加入电感后的模型,2阶电路可以与其耦合的n自由度机械系统共同构成一个n+1自由度系统,从而可对耦合系统进行系统整体的仿真分析,同时深入研究不同电路元件对系统采集效率的影响,发现电感的加入可极大提高系统能量采集效率。

Cantilever beams with piezoelectric ceramic layers have been frequently used as piezoelectric vibrationenergy harvesters.The most classical piezoelectric cantilever model d31of the piezoelectric energy harvesters(PEH)isstudied in this paper.The exact analytical solution of the cantilever PEH is presented based on Euler-Bernoulli beamassumption.The influence of dynamic mode shape and strain distribution of the cantilever PEH is considered.Themathematical model of the cantilever PEH is established and the electro-mechanical coupling principle and characteristicsare deeply analyzed with the two boundary conditions of uniformly distributed electric field and uniformly distributedelectric displacement respectively.Based on the traditional PEH of order one,an inductance is added to the circuit toestablish a second order circuit and improve the mathematical model.In the improved model,a new system with n+1DOFs is obtained by combining the second order circuit with the n-DOF oscillatory system so that the global simulation ofthe coupled system can be realized.In addition,the influence of different elements of the circuit is analyzed.It is found thatthe added inductance can greatly increase the energy-harvesting efficiency of the PEH.