Recursive Approach of Eigenvalues of Random Structure

Abstract eng:
This paper focuses on solving eigenvalue problem, one basic and classical problem in stochastic dynamics, of structures with random material variability. The random material properties, such as modulus of elasticity, are represented by Karhunen-Loeve expansion or independent random variables. The isolated eigenvalues of random structures are expressed as non-orthogonal polynomials expansions. With the aid of the traditional perturbation technique, a set of deterministic recursive equations is established in terms of non-orthogonal polynomials bases of the same order. After the coefficients of the non-orthogonal polynomials expansion are determined, the explicit expressions of the random eigenvalues can be built up. Hence, it can be easily conducted to determine the statistics of eigenvalues. In numerical example, a beam problem is investigated to demonstrate the effectiveness of the proposed method, and the second order statistics of random eigenvalues from the suggested method are found in good agreement with the results of the Monte Carlo simulation, such as shown in Figure1.

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