圆柱壳的轴向动力屈曲、参数共振与混沌运动

Axial dynamic buckling,parametric resonance and chaotic motion of a closed cylindrical shell

首先利用线性的动力屈曲方程,对受压的理想圆柱壳稳定性进行了动力分析。接着利用随时间周期变化的轴压载荷,导出Mathieu方程,讨论了轴压柱壳的参数共振。在Donnell-K偄rm偄n大挠度方程中引入惯性力和阻尼力给出圆柱壳的非线性运动方程,借助Bubnov-Galerkin法,将其转化为含有三次非线性的常微分方程。在定性分析的基础上,利用次谐轨道Melnikov函数和同宿轨道的Melnikov函数分别给出了前屈曲和后屈曲情况下发生Smale马蹄型混沌的临界条件。在此基础上,选用适当参数借用MATLAB数学软件,计算运动时程曲线、相图和Poincar啨映射,给出了混沌运动的数字特征。

The chaotic motion of a closed cylindrical shell under oscillating axial load was studied.The nonlinear motion equations of cylindrical shell were obtained by introducing inertial and damping forces into the Donnell-K rm n large deflection equations,and were transformed into an ordinary differential equation containing third-order nonlinear term by means of the Bubnov-Galerkin method.Based on qualitative analysis,the threshold conditions of the existence of horseshoe-type chaos were presented in the two cases of pre-buckling and post-buckling by using sub-harmonic obit and homoclinic orbit Melnikov functions.The time-history curve,phase portrait and Poincar map were calculated by means of MATLAB software.