等效刚度对非线性压电俘能系统性能影响研究

基于Hamilton原理，考虑几何非线性和梁的不可伸长条件，建立了五层压电双晶片叠合梁俘能器在直接和参数激励作用下的运动微分方程。利用Galerkin法和谐波平衡法获得了俘能器的位移、输出电压和输出功率的解析解。引入随时间变化的扰动，提出了非线性方程解的稳定性条件。为了对压电俘能器的结构-性能关系进行综合分析，研究了被动层的配置形式、被动层与主动层的厚度比和弹性模量对压电俘能系统性能的影响。结果表明，在叠合梁厚度不变的情况下，采用五层的压电双晶片叠合结构，选择合理的被动层与主动层厚度比、被动层弹性模量、被动层厚度比和负载电阻，可以有效提高能量俘获的效率。

Study of the influence of equivalent stiffness on the performance of nonlinear piezoelectric energy harvesting system

Based on Hamilton''s principle,considering the geometric nonlinearity and the inextensible condition of the beam,the differential equations of motion of an energy harvester in the form of a five-layer piezoelectric bimorph laminated beam under direct and parametric excitations are established.Analytical solutions of the displacement,the output voltage and the output power of the harvester are obtained by the Galerkin approach and Harmonic balance method.Introducing a time-dependent perturbation,the stability condition of the solution of the nonlinear equation is presented.In order to comprehensively analyze the structural performance relationship of the piezoelectric harvester,the effects of the layered form of passive layer (substrate layer),the thickness ratio of the passive layer to the active layer and the modulus of elasticity on the performance of piezoelectric energy harvesting system are studied.The results show that when the thickness of the composite beam is constant,using five-layer piezoelectric bimorph composite structure,selecting a reasonable elastic modulus of passive layer,the thickness ratio of the passive layer to the active layer,the thickness ratio of the passive layers and the load resistance,the efficiency of the piezoelectric energy harvester can be effectively improved.