Dynamic Buckling Load of an Imperfect Viscously Damped Spherical Cap Stressed by a Step Load

Abstract

This paper determines the dynamic buckling load of a lightly and viscously damped imperfect spherical cap with a step load. The spherical cap is discretized into a pre-buckling symmetric mode and a buckling mode that consists of axisymmetric and non-axisymmetric buckling modes. The imperfection is taken at the shape of the buckling mode. The inherent problem contains a small parameter which necessitated the adoption of regular perturbation procedures, using asymptotic technique. The general result is designed to display the contributions of each of the terms in the governing differential equations. We deduce the results for the respective special cases where the axisymmetric imperfection parameter, namely  and the non-axisymmetric imperfection parameter , are zeros. We also determine the effects of each of the non-linear terms as well as the effects of the coupling term.