Dynamical Response of Hyper-Elastic Cylindrical Shells Under Periodic Load
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摘要: 研究了不可压超弹性圆柱壳在内表面周期载荷及突加常值载荷作用下的运动与破坏等动力响应问题．通过对所得描述圆柱壳内表面运动的非线性常微分方程解的数值计算和动力学定性分析，发现存在一个临界载荷；当突加常值载荷或周期载荷的平均载荷值小于这一临界值时，圆柱壳的运动随时间的演化是周期性的或拟周期性的非线性振动，而当其大于这一临界值时，圆柱壳将被破坏．另外，准静态问题的解可作为突加常值载荷作用下系统动力响应解的不动点，且不动点的性质与动力响应解及圆柱壳运动的性质有关．讨论了圆柱壳的厚度和载荷等参数对临界载荷值和圆柱壳运动特性的影响．Abstract: The dynamical response such as the motion and destruction of hyper-elastic cylindrical shells subjected to periodic or a suddenly applied constant load on the inner surface are studied within the framework of finite elasto-dynamics.It was proved that there exists a certain critical value for the internal load through the numerical computing and dynamic qualitative analysis of the nonlinear differential equation that describes the motion of the inner surface of the shell.The motion of the shell is nonlinear periodic or quas-i periodic oscillation when the mean load of the periodic load or the constant load is less than its critical value.But the shell will be destroyed when the load exceeds the critical value.The solution of the static equilibrium problem is the fixed point for the dynamical response of the corresponding system under a suddenly applied constant load.The property of the fixed point is related to the property of the dynamical solution and the motion of the shell.The effects of the thickness and the load parameters on the critical value and the oscillation of the shell were discussed.
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