Stochastic Response of a Random Mass Structure

This paper proposes a polynomial approximation approach for the estimation of the stochastic response of a random mass structure subjected to an evolutionary random excitation. A bounded, monopeak, and symmetrically distributed probability density function, called $\lambda$ -PDF, together with the Gegenbauer polynomial approximation, is introduced to deal with stochastic dynamic response problems of the random mass structures. The $\lambda$ -PDF model is used to describe the random parameters in the engineering random structures. And then the Gegenbauer polynomial approximation method is used to reduce the random structures into its deterministic equivalent one. The numerical example shows the effectiveness of the proposed method to explore dynamic phenomena in random structures.