Random Eigenvibrations of Elastic Structures by the Response Function Method and the Generalized Stochastic Perturbation Technique

This paper addresses the important question in structural analysis how to efficiently model the eigenvibrations of the spatial structures with random physical and/or geometrical parameters. The entire computational methodology is based on the traditional Finite Element Method enriched with the stochastic perturbation technique in its generalized nth order approach, while the computational implementation is performed by the use of the academic FEM software in conjunction with the symbolic algebra computer system MAPLE. Contrary to the previous straightforward solution techniques, now the response function method is applied to compute any order probabilistic moments and coefficients of the structural eigenvalues. The response function is assumed in the polynomial form, the coefficients of which are computed from the several solutions of the deterministic problem around the mean value of the given input random parameter. This method is illustrated with the stochastic eigenvibrations of the simple single degree of freedom system and small steel tower modelled as the 3D truss structure with random mass density and Young modulus. This technique may find its wide application in reliability analysis of the real existing engineering structures using the commercial Finite Element Method packages as well as the other discrete computational techniques like the Finite Difference Method at least.