Probabilistic dynamic stability of a damped spherical shell pressurized by a random load

Abstract

This investigation examines the dynamic stability of a damped imperfect spherical shell within the precinct of a random dynamic load applied just after the initial time. The statistical characterizations of the random load ,such as the mean and the autocorrelation , are assumed given and non-vanishing .In particular, the autocorrelation of the random dynamic load is a stationary noise that is correlated as an exponentially decaying harmonic function of time . Such stochastic and random characterizations of the dynamic load function confer some element of randomness on the normal displacement whose statistical mean we shall first seek for the determination of the dynamic buckling load . Lastly, the dynamic buckling load is determined via a suitable maximization and certain useful deductions are made . Assuming that the variance of the random load is and using the mean normal displacement as a relevant statistical characterization of the response, it is observed that the dynamic buckling load is of order R 0 -1 , that is O( 1 R 0 ), of the load variance R 0 JONAMP Vol. 11 2007: pp. 311-322