On a two–small–parameter dynamic stability of a lightly damped spherical shell pressurized by a harmonic excitation

Abstract

This paper is concerned with asymptotic solution, using multi-timing technique, of a nonlinear coupled elastic system in a dynamical setting where the structure investigated is a discretized imperfect spherical shell .The normal displacement at a point on the shell surface is assumed to be partly in the form of a symmetric pre-buckling mode, and partly in the form of buckling modes that have both axisymmetric and non-axisymmetric components. The geometric imperfection is assumed to be in the shape of the buckling modes. The explicitly time-dependent load function is assumed harmonic (or periodic) and the dynamic buckling load is obtained nontrivially with specializations of the results made. The results show, among other things, that (i) the only condition under which the effects of any coupling is felt is if none of the imperfections in the shapes of the modes coupling is neglected and (ii) neglecting an imperfection automatically nullifies the effects of the nonlinearity that is in the shape of the neglected imperfection. JONAMP Vol. 11 2007: pp. 333-362