不可压缩Ogden材料组成的球壳的有限振动

Finite Oscillation of Spherical Shell Composed of a Class of Incompressible Ogden Materials

研究了由一类各向同性不可压缩Ogden材料组成的球壳在突加拉伸载荷作用下的有限振动问题。首先利用平衡微分方程、边界条件和初始条件求得了球壳径向对称运动的微分方程,证明了存在一个临界值。当拉伸载荷未达到这个临界值时,随着时间的增加,球壳的内表面将做非线性周期振动;当拉伸载荷超过这个临界值时,球壳最终会破裂。最后给出了相应的数值算例。

The finite oscillation problem is considered for a spherical shell composed of a class of isotropic incompressible Ogden materials under a suddenly applied tensile load. At first, a differential equation describing the radial symmetric motion of the spherical shell has been obtained by using equilibrium differential equation, boundary conditions and initial condition. It is proved that there exists a critical load, if the tensile load is smaller than the critical value, the radial motion of the inner surface is a nonlinear periodic oscillation with increasing time. However, if the tensile load exceeds the critical value, the spherical shell will be destroyed ultimately. Finally, numerical examples are given to further illustrate the properties of the solutions.