静载荷作用下夹层圆板非线性主共振分析

NONLINEAR PRIMARY RESONANCE OF A CIRCULAR SANDWICH PLATE UNDER STATIC LOAD

基于Reissner夹层板理论,利用Hamilton原理建立静载荷作用下夹层圆板的非线性动力学方程。应用Galerkin法得到静载荷作用下夹层圆板的轴对称非线性振动微分方程。运用多尺度法求解并推导出主共振下系统的幅频响应方程,并依据Lyapunov稳定性理论得到系统稳态运动的稳定性判据。通过算例,得到周边简支约束下夹层圆板主共振的幅频响应曲线图,以及振动幅值随静载荷幅值、激励力幅值和夹心厚度的变化曲线图;研究了不同参数对系统共振幅值的影响规律,并对解的稳定性进行了分析。

Based on Reissner’s sandwich plate theory,the nonlinear dynamic equations of the circular sandwich plate under static load are established by using the Hamilton principle.The axisymmetric nonlinear vibration differential equation of the plate under static load is obtained by Galerkin method.The amplitude-frequency response equation of the primary resonance system is solved by means of a method of multiple scales,and the stability criterion of the steady motion of the system is obtained based on the Lyapunov stability theory.Through the numerical example,the amplitude-frequency response curves of primary resonance of the system with simply supported edge are obtained.The curves of the amplitude varying with static load,excitation and thickness of the core layer are plotted,respectively.The effects of different parameters on the resonance amplitude are discussed,and the stability of steady-state motions of the system is analyzed.