三维粘弹壁板颤振分析

Flutter analysis for a three-dimensional viscoelastic panel

基于Kelvin粘弹模型,根据Von Karman大变形应变-位移关系和一阶活塞气动力理论,运用伽辽金方法建立了三维粘弹壁板颤振方程,并采用Rouge-Kutta法进行数值积分,分析粘弹阻尼,面内压力及壁板几何尺寸对粘弹壁板颤振的影响,进而取动压为分叉参数,研究粘弹壁板颤振时的分叉及混沌等特性。结果表明:随着粘弹性阻尼的增大,系统的静态稳定区域先减小后增大,而静态屈曲解儿乎不受影响,同时发现混沌运动区域随着粘弹阻尼的增大而快速减小。当取动压为分叉参数时发现粘弹壁板分叉特性很复杂,系统由屈曲状态进入混沌振动,再经历一系列的分叉进入简谐极限环振动状态;而较大面内压力和较小的长宽比不利于粘弹壁板的稳定。

Based on Kelvin viscoelastic damping model, the flutter differential equations of a three-dimension panel were set up according to Von Karman large deformation strain-displacement relation and the first piston theory of supersonic aerodynamics by using Galerkin approach, and solved with Rouge-Kutta method. The effects of viscoelastic damping, in-plane loads and panel length-to-width ratios on the flutter of the panel were analyzed. Then, using dynamic pressure as the bifurcation parameter, the bifurcation and chaos behaviors of the panel were studied. The results showed that with rise of viscoelastic damping, the stable region of the panel increases firstly and then decreases; and the chaotic region fleetly decreases; but there is almost no effect on the buckle region. The results also demonstrated that with variation of bifurcation parameters, the viscoelastic panel flutter system may reveal complex dynamic characteristics; it changes from the chaotic oscillation to simply harmonic limit cycle oscillations through a series of bifurcations; the larger compression loads in-plane and the smaller length-to-width ratio are no benefit to the stability of the panel.