不可压缩超弹性材料中预存微孔的周期振动

对于由横观各向同性不可压缩的修正Varga材料组成的含有微孔的球体,研究了球体在外表面突加的拉伸恒定载荷作用下的径向运动问题,得到了描述微孔运动的二阶非线性常微分方程.通过对方程的解的定性性质的分析,证明了当方程有唯一平衡点时,它是方程的中心;当方程有三个平衡点时,其中一个是方程的鞍点,另两个是方程的中心.进而证明了在给定的拉伸载荷作用下,球体内部微孔随时间的演化是非线性周期振动.讨论了材料关于径向各向异性的参数对微孔振动的影响,并给出了相应的数值算例.

Periodic Oscillation of a Pre-existing Microvoid in Incompressible Hyperelastic Materials

The radial motion of a sphere,which has a pre-existing microvoid at its center, and is composed of the transversely isotropic incompressible modified Varga material was studied when the sphere was subjected to a suddenly applied tensile constant load on its outer-surface.A second-order nonlinear ordinary differential equation that describes the motion of the microvoid is obtained.Analysis of the qualitative properties of the solution of the equation proves that the only existing equilibrium point of the equation is a center,and that when there are three equilibrium points,one is a saddle point and the other two are centers.Furthermore,it can be concluded that,under the prescribed tensile constant load,the motion of the microvoid in the interior of the sphere presents a nonlinear periodic oscillation with the increasing time.The effect of parameter,on the periodic oscillation of the microvoid is also discussed and the corresponding numerical examples are presented.