A Spectral Stochastic Finite Element Method for Modal Analysis of structures with uncertain materials properties

摘要

This paper deals with the eigenproblem associated with the free vibrations of structures with uncertain material properties. The elastic modulus of the structure is considered to be uncertain. Given their random description, a new method is presented for the computation of the second order statistics of the eigenproperties of the structure. The proposed technique is based on polynomial chaos decomposition to characterize the eigenvalues and eigenmodes of the stochastic structure. The random parameters of the structure are represented either by random variables or by stochastic processes which are descretized by Karhunen-Loeve decomposition. The eigen-quantities are then developed as a polynomial chaos in these quantities. The performance of the proposed algorithm indicates that the nonlinear systems from the underlying SSFEM formulation can be solved with considerably less effort and computation time than their size suggests. Comparisons with standard algorithms like Monte Carlo Simulation (MCS) illustrate the efficiency of the proposed algorithm. Numerical studies are also performed to validate the theoretical approach.