压电复合材料悬臂板1∶3内共振的非线性动力学分析

本文以飞行器机翼为工程背景,将机翼简化为悬臂板模型,在应用经典板理论和Hamilton原理建立横向和面内激励共同作用下压电复合材料悬臂板的无量纲非线性偏微分方程的基础上,利用Galerkin方法将系统离散为两自由度的非线性常微分方程.然后考虑主参数共振-1∶3内共振,运用多尺度法将两自由度的系统控制方程进行摄动分析,推导出四维平均方程.基于四阶Runge-Kutta法,使用MATLAB软件研究了横向外激励幅值和压电参数项对压电复合材料悬臂板非线性动力学行为的影响.结果表明,系统存在周期和混沌运动,所得结论对实际工程具有指导意义.

Nonlinear dynamic analysis of a composite cantilever piezoelectric plate with one-to-three internal resonance

The wing is simplified as the cantilever plate model based on the engineering background of the aircraft wing. The nonlinear dimensionless partial differential governing equations ol the composite cantilever piezoelectric plate under the combination ol transverse and in-plane excitations are established by using the Hamilton's principle. The Galerkin approach is used to discretize the partial differential equations to the ordinary differential equations with twodegree-of-freedom under the transverse and parametric excitations. Meanwhile, the method ol multiple scales is employed to obtain the four-dimensional averaged equation considering the primary parametric resonance-1:3 internal resonance. Numerical method is utilized to find the nonlinear dynamics responses ol the composite piezoelectric cantilever plate. The numerical results indicate the existence ol the periodic and chaotic responses. The influences ol the transverse excitation and piezoelectric parameter term on the bifurcations and chaotic behaviors ol the composite piezoelectric cantilever plate are investigated. The conclusions are instructive to the practical engineering. © 2018 Journal of Dynamics and Control. All rights reserved.