A Novel Reduced Spectral Function Approach for Finite Element Analysis of Stochastic Dynamical Systems

Abstract

This work provides the theoretical development and simulation results of a novel Galerkin subspace projection scheme for damped dynamic systems with stochastic coefficients and homogeneous Dirichlet boundary conditions. The fundamental idea involved here is to solve the stochastic dynamic system in the frequency domain by projecting the solution into a reduced finite dimensional spatio-random vector basis spanning the stochastic Krylov subspace to approximate the response. Subsequently, Galerkin weighting coefficients have been employed to minimize the error induced due to the use of the reduced basis and a finite order of the spectral functions and hence to explicitly evaluate the stochastic system response. The statistical moments of the solution have been evaluated at all frequencies to illustrate and compare the stochastic system response with the deterministic case. The results have been validated with direct Monte-Carlo simulation for different correlation lengths and variability of randomness.KeywordsSpectral FunctionProper Orthogonal DecompositionDirect Monte Carlo SimulationStochastic Partial Differential EquationGeneralize Eigenvalue ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.