粘弹壁板颤振的非线性动力特性

Nonlinear dynamic analysis of viscoelastic panel flutter

关键词:  壁板颤振  粘弹性  分岔+  迦辽金法+

Key words:  Panel flutter  Viscoelasticity  Bifurcation+  Galerkin method+

摘要:

研究粘弹材料壁板在超声速气流作用下颤振时的分岔及混沌等复杂动力学特性。采用von Karman大变形理论及Kelvin粘弹阻尼模型建立壁板的动力学方程,通过线性活塞理论建立气动力模型。利用迦辽金法将壁板颤振模型转化为常微分方程组,并使用Gear的BDF方法进行数值求解。通过数值模拟研究了该系统在粘弹阻尼作用下的动力学行为以及粘弹阻尼的影响。计算结果表明,粘弹壁板颤振系统表现出丰富的动力学行为,其二次分岔特性很复杂。随着粘弹性阻尼的增大,系统的稳定解区域在减小,而静态屈曲解几乎不受影响,同时发现混沌运动区域也随着粘弹阻尼的增大而减小。

Abstract:

A nonlinear viscoelastic panel flutter model was developed and its bifurcation and chaos behavior was studied.Von Karman’s large deflection theory and Kelvin’s viscoelastic damping model were applied to derive the governing equation,while the first order piston theory was used to simulate the gas pressure applied on the panel.Then,the partial differential governing equation was transformed to ordinary differential equations by use of Galerkin method,and solved with Gear’s BDF method.The study is focused on the bifurcation and chaos characteristics of the flutter model,and the influence of viscoelastic damping.The results demonstrate that the viscoelastic panel flutter system may represent complex dynamic characteristic with variation of bifurcation parameters,and both the stable region and chaotic region decrease as the viscoelastic damping increases.