压电夹层梁的分岔、混沌及主动控制

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 Karman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,chaos and active control of piezoelectric sandwich beams

The paper investigated the bifurcation, chaotic dynamics and active control of simply supported piezoelectric sandwich beams with axial loading. Based on the piezoelectric materials constitutive relations and von Karman type geometrically nonlinear strain-displacement relations, considering a proportional and derivative potential feedback laws coupling the direct and inverse piezoelectric coefficients, the nonlinear partial differential equation of motion of the beams is derived by Hamilton’s principle and then discretize it using Galerkin approach. Numerical simulation is carried out to investigate the dynamic bifurcation of the beams. The results show that the oscillation of the piezoelectric sandwich beams can be controlled with the gain proportional and derivative potentials of the considered feedback control.