一类不可压缩超弹性圆柱壳的周期振动  

Periodic Oscillation of a Class of Hyper-Elastic Cylindrical Shell

作　　者：赵艳青[1] 赵旭强[1] 

机构地区：[1]烟台大学数学与信息科学系,山东烟台264005

出　　处：《烟台大学学报（自然科学与工程版）》2006年第4期235-241,共7页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(10272069);烟台大学博士基金资助项目(SX04B24)

摘　　要：研究了均匀各向同性不可压缩neo-Hookean材料组成的圆柱壳在内、外表面分别受到不同的突加死载荷作用的径向对称运动问题.得到了描述圆柱壳内表面径向运动的二阶非线性常微分方程.通过对方程解的动力学性质分析,讨论了各个参数对方程解的定性性质影响.特别地,证明了当内压与外压之差小于某临界值时,圆柱壳内表面随时间的演化是非线性周期振动;当内压与外压之差大于临界值时,圆柱壳内表面随时间的演化将无限增大.最后给出了相应的数值模拟.The problem of radial symmetric motion of a cylindrical shell composed of the homogeneous isotropic incompressible neo-Hookean material, subjected to different sudden applied deadloads at the inner-surface and outer-surface respectively, .is examined. The second-order nonlinear ordinary differential equation that describes the motion about the radial direction of the inner-surface of the shell is obtained. The effect of each parameter on existence of the periodic solution is discussed by analyzing the dynamical properties of the solutions of the equation. In particular, it is proved that the motion of the inner-surface of the shell with respect to time will present a nonlinear periodic oscillation as the difference between the inner-press and the outer-press is smaller than a certain critical value; however, as the difference exceeds the critical value, the value of the inner-surface will increase infinitely with respect to time. Finally, the corresponding numerical simulations are carried out.

关 键 词：不可压缩超弹性圆柱壳 非线性常微分方程 动力学性质 非线性周期振动 

分 类 号：O175[理学—数学] O343[理学—基础数学]