Green’s function method for modal analysis of structures with interval parameters

Abstract

This paper presents a Green’s function method for the modal analysis of structures with interval parameters. By introducing first order approximations, the governing equations of modal displacements for interval analysis are decomposed into two sets of governing equations for the midpoints and deviations of modal responses, respectively. Utilizing the similarity between these equations and the governing equations for deterministic static analysis, Green’s functions for the linear static problem are directly used in the modal analysis process. Different from the traditional finite element method which needs the element refinement to improve solution accuracy, the proposed Green’s function method needs just one element for each beam member to achieve accurate results. Numerical examples presented demonstrate the applicability of the proposed method, and reveal some regular patterns of the effects of interval parameters in structural modal analysis.