Shallow Spherical Shells on Pasternak Foundation

Abstract

Static and dynamic analysis of fully clamped shallow spherical shells, subjected to uniform normal pressure on concave side and continuously supported on Pasternak foundation on the convex side, is made using Berger's and modified Berger's techniques. Expressions for large static deflections are obtained and results compared with those of Nash and Modeer. The preceding techniques are employed to get the approximate expressions for natural frequency. Values of nondimensional natural frequency obtained by various methods are compared with results of Reissner, Nowacki, Bucco, and others. While a modified Berger's approach gives very good results for static analysis of fully clamped shells, the original Berger's approach is found to be more suitable for free vibration analysis, as results tally with those obtained by Réissner, using Rayleigh's method, even for higher ratios of