Homotopy-series Solution of Eigenpairs of Random Structures

Abstract

A new computational method is proposed for solving the eigenpairs of the structures with random parameters based on the basic idea of the homotopy analysis method. For this new method, the eigenvalues and eigenvectors of the random structures are expressed as the homotopy-series. Because each term in the homotopy expressions includes an approaching function with auxiliary parameter h, the convergence domain of the homotopy-series is greatly improved, which makes this new method available for the large fluctuation of random parameters. In practice, a dimension-reduction strategy is applied to the series to reduce the computational effort: the single-variable and double-variable homotopy-series are recommended for calculation. Numerical example of a fixed rectangular plate, indicates that the new method provides an excellent approximation of the eigenpairs of a closely spaced eigenvalues system.