不可压缩的修正Varga材料组成的矩形密封圈的径向振动

Radial Oscillation of Rectangular Sealing Rings Composed of Incompressible Modified Varga Materials

研究了由一类关于径向横观各向同性不可压缩的修正Varga材料制成的矩形橡胶密封圈在内表面突加的径向载荷作用下的振动与控制问题,得到了描述密封圈径向运动的非线性常微分方程。对于给定的材料参数和结构参数,通过数值算例求得了一个临界载荷。证明了当突加载荷小于临界载荷时,密封圈随时间的运动将是非线性周期振动;超过临界载荷时,密封圈随时间的增长将会无限增大,最终会被破坏。

The oscillation and control problem has been examined for a vulcanized rubber sealing ring composed of a class of transversely isotropic incompressible modified Varga materials about radial direction, where the sealing ring is subjected to a suddenly applied radial load at its inner surface. A nonlinear ordinary differential equation that describes the radial motion of the sealing ring has been developed. For the given material and structure parameters, a critical load has been obtained by numerical examples. It is proved that if the applied load is lower than the critical load, the motion of the rubber ring with time will present a nonlinear periodic oscillation, while if it exceeds the critical load, the motion will increase infinitely with the increasing time and so the rubber ring will be destroyed ultimately.