Non-linear dynamic analysis of shallow spherical shells on elastic foundations

The present study investigates the effect of Winkler-Pasternak elastic foundation parameters on the nonlinear dynamic response of shallow spherical shells. The values of foundation parameters ( and ) have been determined for the minimaximum central response of the shallow shells for both the clamped as well as simply supported immovable edge conditions. Donnell type partial differential equations governing the moderately large amplitude behaviour of shallow spherical shells resting on Winkler-Pasternak elastic foundations under step pressure loading, have been analysed. The space and time-wise integrations of governing equations have been carried out using Chebyshev series and Houbolt techniques, respectively. It is also shown that the present analysis can be extended to study the dynamic buckling of shallow shells resting on elastic foundations.