参数激励下粘弹性圆柱壳的混沌行为

基于大挠度薄壳的Donnell-Kármán理论和Kelvin-Voigt粘弹性本构关系,研究了参数激励下粘弹性圆柱壳的混沌行为。导出了关于挠度和应力函数的控制方程,借助Galerkin原理将粘弹性圆柱壳的控制方程转化为二阶三次非线性微分动力系统。当轴压载荷与圆柱壳的材料参数满足a 0时,用Melnikov函数给出了系统发生混沌的临界条件,数值分析了轴压载荷和粘性阻尼系数对混沌运动的影响。用Runge-Kutta法给出分岔图、位移时程曲线、相平面图和Poincaré映射分析了系统运动行为,给出了a 0和a 0情况下系统定常运动和混沌运动的特征。

CHAOTIC BEHAVIOR OF VISCOELASTIC CYLINDRICAL SHELL UNDER AXIAL PERIODIC EXCITATION

Based on Donnell-Kármán theory of a thin shell with a large deflection and Kelvin-Voigt constitutive relation,the chaotic motion of a viscoelastic cylindrical shell under axial pressure and transverse periodic excitation was investigated.The governing equations for the deflection and stress function are derived,in addition,by utilizing the method of Galerkin,the governing equations of the viscoelastic cylindrical shell are transformed into the square-order and a cubic nonlinear differential dynamic system.With the assumption of the material parameter,the critical conditions of horseshoe-type chaos are obtained by using Melnikov function,and the influences of axial pressures and viscous damper coefficients upon chaotic motion of the system are analyzed by numerical calculation.Furthermore,the motion behaviors of the system are described through the bifurcation diagrams,the time-history curve,phase portrait and Poincaré map were given by means of Runge-Kutta method.At the same time,the results indicate the characteristics of steady motion and chaotic motion when and.