摘要
对受轴压理想弹性圆柱壳,利用环向工程应变和环向对数应变分别建立了线性和非线性的横向轴对称运动的支配方程。利用线性的运动方程对轴压圆柱壳稳定性进行了定性分析。依动力学参数取值范围的不同,方程的解有稳定平衡、中性平衡和不稳定平衡三种情况,并给出了动力学参数与载荷参数之间的依赖关系。对于非线性运动方程,引入了外加强迫力和阻尼对系统的摄动,借助Galerkin方法从非线性偏微分方程得到了含二次非线性的常微分方程。定性分析表明:对于前屈曲和后屈曲两种情况,系统的相图具有相同的同宿轨道,只是位置在相平面上沿横轴发生了一个简单的平移。进而,利用Melnikov方法给出了可能发生Smale马蹄型混沌的临界条件,两种情况下给出的临界条件相同。
Using engineering and logarithmic circumferential strain definitions, a linear and nonlinear partial differential equations governing transverse axisymmetrical motion of a elastic cylindrical shell in axial compression are derived respectively. The dynamic stability of the shell under axial compression is analyzed qualitatively by the linear equation of motion. There are three kinds of equilibrium state with different value dynamic parameter. They are stable, neutral and unstable equilibrium respectively. Next for a simply supported shell the relation between dynamic parameter and load parameter is given. Damping and external forcing are introduced into the nonlinear equation of mo- tion. By using Galerkin＇s method the partial differential equation is reduced ordinary differential equation with quadratic nonlinearity. The results of qualitative analysis indicate that the system has homoclinic orbit. Further, the threshold condition of the existence of Smale horseshoe-type chaos is obtained by Melnikov method. In the two cases of pre-buckling and post-buckling, the critical conditions are same.
出处
《科学技术与工程》
2009年第19期5631-5636,5642,共7页
Science Technology and Engineering
基金
国家自然科学基金项目(10772129)资助
