压电磁耦合振动能量俘获系统的非线性模型研究

Nonlinear Model for Piezoelectric Energy Harvester with Magnetic Coupling

为了建立压电磁耦合振动能量俘获系统的动力学模型,提出了一种非线性多项式拟合系统的非线性回复力的建模方法。使用微型测力仪直接测得悬臂梁处于不同位置时的非线性回复力,并用多项式进行参数拟合以获得非线性回复力的表达式。根据哈密顿原理、欧拉-伯努利梁理论和压电理论等,建立了考虑非线性回复力的系统模型,由龙格-库塔数值算法仿真后得到系统的非线性输出特性。研究结果表明,该模型具有参数求解简单、计算量小、无需直接求解磁场力等优点,能够描述非线性宽频能量系统的跳跃频率、最大电压和有效频带等关键设计参数,为压电磁耦合振动能量俘获系统的机理研究奠定了理论基础。

coupling descripti being in . To establish the dynamical model of piezoelectric energy harvester with magnetic , the modeling approach for the harvester is proposed based on nonlinear polynomial on of nonlinear restoring force. The nonlinear restoring force of the cantilever beam different positions is measured directly by a small electronic dynamometer and the polynomial parameters of the force are estimated. Then the nonlinear restoring force is taken into account to establish the nonlinear model following Hamilton principle, Euler-Bernoulli beam theory and piezoelectric theory. Runge-Kutta method is introduced to simulate the nonlinear output characteristics of the harvester. The results show that the proposed model enables to simply solve the parameters, reduce calculation task and avoid the direct calculation of magnetic force. And the model can describe the important designing parameters in terms of the jump frequency, maximum voltage and effective bandwidth for the mechanism analysis of magnetic coupled piezoelectric energy harvester.