双向激励下非线性压电俘能系统的稳态响应分析

Steady state response analysis of nonlinear piezoelectric energy capture system under bidirectional excitations

基于基础激励的多向性和实际环境中的低频率环境,研究了在固定基础端受到水平和垂直双向激励的附加端部质量块悬臂梁压电俘能系统的非线性稳态响应问题。通过Hamilton原理对一个附加端部质量块悬臂梁双晶片压电俘能系统模型的非线性偏微分方程进行理论推导和计算分析。假设此悬臂梁为轴向不可伸长的Euler-Bernoulli梁,此模型主要包含几何非线性和阻尼非线性。利用Galerkin法将非线性偏微分方程降阶得到双向激励作用下附加端部质量块悬臂式压电俘能系统的机电耦合运动微分方程。采用多尺度法研究压电俘能系统在其主要的一阶共振情况下的响应,获得了俘能系统的垂直位移、输出电压和输出功率的解析表达式。得到其主要一阶垂直位移幅值,输出电压幅值和输出功率幅值。分析了不同激励情况下,激励相位等对压电俘能系统俘能性能的影响。

Here, based on the multi-directionality of foundation excitation and low-frequency circumstances in actual environment, nonlinear steady-state response of a piezoelectric energy capture system of a cantilever beam with an additional end mass block subjected to horizontal and vertical bi-directional excitations at its fixed foundation end was studied. Based on Hamilton principle, nonlinear partial differential dynamic equations of a cantilever beam bimorph piezoelectric energy capture system model with an additional end mass block were theoretically deduced and analyzed through computing. It was assumed that the cantilever beam is an axially inextensible Euler-Bernoulli beam containing geometric nonlinearity and damping nonlinearity. Galerkin method was used to discretize partial differential dynamic equations, and obtain electromechanical coupled ordinary differential dynamic equations of the cantilever beam piezoelectric energy capture system with an additional end mass block under bidirectional excitations. The response of this energy capture system under its main first-order resonance was studied using the multi-scale method to obtain analytical expressions of vertical displacement, output voltage and output power of the energy capture system. Its main first-order vertical displacement amplitude, output voltage amplitude and output power amplitude were calculated. Effects of excitation phase on energy capture performance of the piezoelectric energy capture system under different excitations were analyzed.