Transient Dynamics of Stochastic Structural Systems using a Reduced Order Spectral Function Approach

Abstract

The transient dynamics of randomly parametrized structural systems have been considered in context of the stochastic finite element methods for handling a class of stochastic partial differential equations and homogeneous Dirichlet boundary conditions. An approach for solving the time domain equations using highly non-linear spectral functions approximating the solution in a reduced subspace has been proposed. The spectral functions of different orders can be expressed in terms of the spectral properties of the deterministic system matrices. It is shown that the solution can be obtained using a truncated finite series comprising of functions of random variables used to model the parametric uncertainty and the eigen-spectrum of the physical system. The solution at each time step has been computed iteratively with Newmark’s method of time integration. A semi-statical hybrid analytical and simulation based computational approach has been utilized to obtain the moments and probability density functions of the solution. The results have been compared with the Polynomial Chaos solution in terms of accuracy and computational efficiency. Direct Monte Carlo simulations, which serve as benchmark solutions, have been performed in the probability space for different degrees of variability to validate the results.