在任意不定常温度场和任意法向动载荷联合作用下中心开孔圆底扁球壳的动力问题

本文得出了在任意不定常温度场和任意法向动载荷联合作用下中心开孔圆底扁球壳的动力问题的解析解.我们假设温度沿壳体厚度直线分布.在第一部分.我们研究了常用边界条件下的中心开孔圆底扁球壳的自由振动.作为例子,我们计算了一边缘夹紧的扁球壳的自然基频(m=0),所得结果与E.Reissner[1]的结果作了比较.频率方程的解法是钱伟长[2]提出来的.这将在附录3中介绍.在第二部分,我们研究了在任意谐温度场和任意谐法向动载荷联合作用下的中心开孔圆底扁球壳的强迫振动.在第三部分,我们研究了在任意不定常温度场和任意法向动载荷联合作用下的具有初始条件的上述壳体的强迫振动.在附录1和2中,我们讨论了如何用应力函数来表示位移边界条件和m=1情形的边界条件.

Circular Shallow Spherical Shells with Circular Holes at the Center under Simultaneous Actions of Arbitrary Unsteady Temperature Field and Arbitrary Dynamic Normal Load

In this paper,under assumption that temperature is linearly distributed along the thickness of the shell.we deal with problems as indicated in the title and obtain general solutions of them which are expressed in analytic form.In the first part,we investigate free vibration of circular shallo w spherical shells with circular holes at the center under usual arbitrary boundary conditions.As an example,we calculate fundamental natural frequency of a circular shallow spherical shell whose edge is fixed(m=0).Results we get are expressed in analytic form and check well with E,Reissner's[1].Method for calculating frequency equation is recently suggested by Chien Wei-zang and is to be introduced in appendix 3.In the second part,we investigate forced vibration of shells as indicated in the title under arbitrary harmonic temperature field and arbitrary harmonic dynamic normal load.In the third part,we investigate forced vibration of the above mentioned shells with initial conditions under arbitrary unsteady temperature field and arbitrary normal load.In appendix 1 and 2,we discuss how to express displacement boundary conditions witli stress function and boundary conditions in the case m=1.