具有初挠度夹层圆板非线性振动与解的稳定性

基于均布载荷作用下夹层圆板大幅度振动的基本方程和四种边界条件,利用空间模态假设和变分法,将初挠度设成空间函数的形式,动挠度设为时间和空间函数的分离形式,并将其代入各非线性振动方程,得出应力和转角用设定的挠度函数表示的形式,再将假定模态函数代入本问题的非线性振动方程,利用伽辽金法推导出时间模态的控制方程,并在相平面上讨论了解的稳定性。

Nonlinear Vibration and Solution Stability of Circular Sandwich Plate With Initial Deflection

Based on the fundamental equation and four kinds of boundary conditions,large amplitude vibration of circular sandwich plate under uniform load, is investigated.Under the supposition of space modes and taking advantage of the variational method the initial deflection is assumed in space function form the dynamical deflection is expressed as the multiplication of time and space functions, and then the stress and rotation angle are formulated in the form of deflection functions. Substituting the supposed mode functions into the nonlinear vibration equation, the control equation of time mode is obtained by Galerkin method.The stability of solution is discussed.