Analysis of Random Responses of Structures with Uncertain Parameters.Analysis by Substructure Synthesis Method and Perturbation Method.

Abstract

In this paper, the method to obtain the sensitivities of eigenvalues and eigenvectors, and the random responses of the structure with uncertain parameters is proposed. The proposed method is a combination of the substructure synthesis method and the perturbation method. The concept of the proposed method is that the perturbation equation of each substructure is obtained using the perturbation method, and the perturbation equation of the overall structure is obtained using the substructure synthesis method. Using the proposed method, the reduced order perturbation equation can be obtained without the analysis of the original whole structure. As a numerical example, a simple piping system is considered as a structure. The damping constant and the spring constant of the support are considered as the uncertainty parameters. Then the variations of the eigenvalues and the eigenvectors, the correlation function and the power spectral density function of the responses are calculated using proposed method. As a result, the proposed method is useful to analyze the sensitivities of eigenvalues and eigenvectors. It is also useful to analyze random response in terms of the accuracy and the calculation time.