Transient Response of Structural Dynamic Systems with Parametric Uncertainty

Abstract

The time-domain response of a randomly parameterized structural dynamic system is investigated with a polynomial chaos expansion approach and a stochastic Krylov subspace projection, which has been proposed here. The latter uses time-adaptive stochastic spectral functions as weighting functions of the deterministic orthogonal basis onto which the solution is projected. The spectral functions are rational functions of the input random variables and depend on the spectral properties of the unperturbed system. The stochastic system response can be accurately resolved even when using low-order spectral functions, which are computationally advantageous. The time integration required for the resolution of the transient stochastic response has been performed with the unconditionally stable single-step implicit Newmark scheme using a stochastic integration operator. A semistatistical hybrid analytical and simulation-based computational approach has been utilized to obtain the moments and probability density functions of the solution. The simulations have been performed for different degrees of variability of the input randomness and different dimensions of the input stochastic space and compared with the direct Monte-Carlo simulations for accuracy and computational efficiency.