热超弹性圆柱壳的振动与破坏

FINITE OSCILLATION AND DESTRUCTION OF THERMO-HYPERELASTIC CYLINDRICAL SHELLS

研究了热超弹性圆柱壳在内表面突加载荷及不同温度场作用下的运动与破坏问题。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动力学定性分析和数值计算,发现当突加内压小于某一确定的临界值时,圆柱壳的运动随时间的演化是周期性的非线性振动,而当突加内压大于这个临界值时,圆柱壳将被破坏。通过对振动的振幅、相图和周期的计算,讨论了均匀或非均匀温度场及圆柱壳的厚度等参数对临界载荷和圆柱壳振动的影响。

The finite oscillation and destruction of thermo-hyperelastic cylindrical shells subjected to a suddenly applied dead-load on the inner surface under different temperature fields were studied.A nonlinear differential equation describing the motion of the inner surface of the shell was proposed.It is proved that there exists a certain critical value for the internal load through dynamics qualitative analysis and numerical computing.The motion of the shell is nonlinear periodic oscillation when the load is less than the critical value,and the shell will be destroyed when the load exceeds the critical value.The effects of the non-uniform or uniform temperature fields and other parameters of the shell on the critical value and the oscillation of the shell were discussed through examining the vibration amplitude,phase diagram and period.