Circular Shallow Spherical Shells with Central Circular Hole Under Simultaneous Actions of Arbitrary Unsteady Temperature Field and Arbitrary Dynamic Normal Load

In this paper,under assumption that tempeature is linearly distributed along the thickness of theshell,we deal with problems as indicated in the title and obtain general solutions of them which areexpressed in analytic form.In the first part,we investigate free vibration of circular shallow spherical shells with circularholes at the center under usual arbitrary boundary conditions.As an example,we calculate fundamen-tal natural frequency of a circular shallow spherical shell whose edge is fixed(m=0).Results we get areexpressed in analytic form and check well with E.Reissner’s[1].Method for calculating frequencyequation is recently suggested by Chien Wei-zang and is to be introduced in appendix3.In the second part,we investigate forced vibration of shells as indicated in the title under arbitr-ary harmonic temperature field and arbitrary harmonic dynamic normal load.In the third part,we investigate forced vibration of the above mentioned shells with initialconditions under arbitrary unsteady temperature