超声速气流下黏弹性夹层壁板非线性颤振分析

基于Kelvin-Voigt黏弹性本构模型、von-Karmen薄板大变形理论和三阶气动力活塞理论建立了三维黏弹性夹层壁板的气动弹性颤振方程。使用Galerkin截断方法，对超声速气流下，四边简支黏弹性夹层壁板颤振的非线性特性进行了研究。对于非线性一阶截断方程，研究了它的平衡点及稳定性随来流速度的变化情况，得到了系统发生静态分叉时的临界速度；对于非线性二阶截断方程，使用数值仿真分析方法，得到了系统发生Hopf分叉时的临界速度，并利用响应、相图等手段研究得到黏弹性夹层板随来流速度变化的动力学特性。

Nonlinear analysis of viscoelastic sandwich panel's vibration under supersonic airflow

Based on the Kelvin-Voigt constitutive law, the governing equations for the flutter vibration of the viscoelastic sandwich panel are established with consideration of the von-Karmen thin plate large deflection and the nonlinear piston theory. By using the method of the Galerkin trtmcation, the nonlinear dynamical characteristics of the viscoelastic sandwich panel under the supersonic flow and with the simple supports on four sides are analyzed. For the equation of the first-order Galerkin truncation, the equilibrium of the system and its stability are studied, the critical flow of the static bifurcation is obtained; for the equation of the second-order Galerkin truncation, the critical flow of the Hopf bifurcation is obtained by applying the Hopf bifurcation criterion, the dynamical behavior with the varying flow conditions is observed by employing the diagram of the response and phase portrait.