A New Method for the Eigenvalue Problem of Structures with Uncertain-but-Non-Random Parameters

Abstract

In this paper, the eigenvalue problem that involves uncertain-but-non-random parameters is discussed. The error of dynamical parameters of a system is unavoidable in the course of manufacture and installation. Eigenvalues of the system are hard to obtain by the traditional dynamical theory. A new method based on matrix inequality theory is developed to evaluate the upper and lower bounds of the eigenvalues. In this method, properties of matrix’s spectral radius and norm are used. The illustrative numerical examples are provided to demonstrate the validity of the method. Compared with the other methods, the calculated results show that the proposed method in this paper is effective in evaluating bounds of the eigenvalues of structures with uncertain-but-bounded parameters.