A component mode synthesis method using retransformed physical coordinates (1st report, Theoretical analysis and error estimation of the dummy mass technique in the unconstrained mode method)

Abstract

A new method is proposed for analyzing complex structures by a substructure synthesis method. In this method, mass and stiffness matrices of components are expressed by unconstrained modes, and can be applied for both theoretical and experimental modal analysis. Several numbers of the modal coordinates of each component are retransformed to the physical coordinates of the connection points by using normal mode shapes. Therefore, each component can be treated as one of the finite elements in FEM analysis, making it possible to connect them to each other or one another directly or to connect them with nonlinear elements obtained by FEM. A new technique is also proposed for correcting the truncation error of higher order modes by using dummy masses at the connection points. The dummy mass technique improves the dynamic characteristics of the total system without using the residual compliance matrix. The effectiveness of the procedures is demonatrated by numerical examples.