^{a}, Bin Huang

^{b}and Zhifeng Wu

^{c}

^{a}supzhangheng@163.com

^{b}binhuang@whut.edu.cn

^{c}wuzhifeng_tujian@163.com

A new computational method is proposed for solving the eigenpair of the structure with random parameters based on the basic idea of the homotopy analysis method. For this new method, the eigenvalues and eigenvectors of the random structure 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 and different from the traditional Taylor series. Actually, the Taylor series is just a special case of the homotopy series where the value of h equals to -1. 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, a fixed rectangular plate with random elastic moduli, indicates that the new method provides excellent approximations of the eigenpairs of a closely spaced eigenvalues system.