On a randomly imperfect spherical cap pressurized by a random dynamic load

Abstract

In this paper, we investigate a dynamical system in a random setting of dual randomness in space and time variables in which both the imperfection of the structure and the load function are considered random , each with a statistical zero-mean .The auto- covariance of the load is correlated as an exponentially decaying function of the time variable .For simplicity, the normal displacement at a point on the shell surface is
discretized into a symmetric pre-buckling mode and a buckling mode that has both axisymmetric and non-axisymmetric components. The imperfection is assumed in the shape of the buckling mode with its axisymmetric and non-axisymmetric amplitudes considered random-all with known first and second statistical moments. All these random parameters induce some form of randomness on the normal displacement
whose mean square we shall first seek as a suitable statistical characterization of the random process for determining the dynamic buckling load which is determined asymptotically using perturbation methods.