参数和直接激励下非线性压电俘能器性能分析的多尺度法

考虑几何非线性、阻尼非线性和梁的轴向不可伸长条件,利用Hamilton变分原理,建立了参数激励和直接激励下压电俘能器的非线性力电耦合的运动微分方程;利用Galerkin法,将所建立的动力学偏微分方程降阶为力电耦合的Mathieu-Duffing型方程;采用多尺度法获得了梁的位移和输出电压的解析表达式,给出了解的稳定性条件;利用解析表达式研究了单独参数激励以及参数激励和直接激励共同作用下阻尼系数对压电俘能器性能的影响。结果表明,在参数激励情况下,线性阻尼会显著影响超临界分岔点的位置,非线性二次阻尼不会影响超临界分岔点的位置。参数激励和直接激励的结合可以作为提升压电能量俘获器性能的解决方案。

The performance analysis of nonlinear piezoelectric energy harvester under parametric and direct excitation

Considering geometric nonlinearity,damping nonlinearity and axial inextensible beam,the mechanical-electrical coupling nonlinear differential equations of piezoelectric energy harvester under parametric and direct excitation are established by using Hamilton variational principle.By using Galerkin method,the proposed partial differential equation is reduced to the mechanical-electrical coupling Mathieu-Duffing type equation.The analytical expressions of deflection and output voltage of the beam are obtained by using the method of multiple scales,and the stability conditions of the solution are given.Using analytical expression,the influence of damping coefficient on the performance of piezoelectric energy harvester is studied under individual parametric excitation and combination of parametric and direct excitations.The results show that under parametric excitation the position of the supercritical bifurcation point is significantly affected by the linear damping and not affected by the nonlinear quadratic damping.The combination of parametric excitation and direct excitation can be used as a solution to enhance the performance of piezoelectric energy harvesting devices.