压电夹层梁的分岔、混沌及主动控制

Bifurcation,chaos and active control of a piezoelectric sandwich beam

研究轴向激励作用下简支压电夹层梁的分岔、混沌振动及其主动控制。基于压电材料本构关系、von Kar-man型几何非线性应变位移关系,考虑耦合正、逆压电效应的比例微分控制策略,运用Hamilton原理建立了压电夹层梁的非线性横向运动偏微分方程并利用Galerkin方法对其进行离散化处理。通过采用数值模拟方法,研究了压电夹层梁的动态分岔,结果表明,通过比例控制增益和微分控制增益都可控制压电夹层梁的横向振动,阻止系统发生混沌运动,保持系统的稳定性。

Bifurcation,chaotic dynamics and active control of a simply supported piezoelectric sandwich beam with axial loading were investigated.Based on the constitutive relation of piezoelectric materials and Von Karman type of geometrically nonlinear strain-displacement relation,considering a proportional and differential feedback control strategy with coupling between the direct and inverse piezoelectric coefficients,the nonlinear partial differential equation of motion of the beam was derived with Hamilton＇s principle and then,it was discretized using Galerkin approach.Numerical simulation was conducted to investigate the dynamic bifurcation of the beam.The results showed that the oscillation of the piezoelectric sandwich beam can be controlled with the proportional gain and the differential gain of the considered feedback control.