A direct solution method for generalized stochastic eigenvalue problems of structures with random parameters

In this paper, a direct solution method is proposed for solving generalized stochastic eigenvalue problems of structures with random uncertainties in structural parameters. Taking random parameters into consideration, predicting the statistical characteristics of the eigenvalues of structures within a probabilistic framework precisely is significant for structural analysis and design. However, the most typical method, the Monte-Carlo Simulation is highly time consuming. And most of the existing methods with high computational efficiency compared to the Monte-Carlo Simulation are approximate methods and may not be applicable for high-precision requirements. Within the proposed method, the solution equations are deduced in terms of the properties of matrix operations step by step based on the Kronecker product and straightening operation, and thus the mean values and variances of the eigenvalues can be obtained directly with high precision. Three numerical examples are employed to illustrate the feasibility and applicability of the proposed method in specific engineering structures. The results indicate that the proposed method yields consistent mean values and variances of the eigenvalues with those obtained by the Monte-Carlo Simulation respectively with significantly less computation time showing its superiority in accuracy and efficiency.