Vibration Analysis of a Structure with Closed Loops by the Transfer Stiffness Coefficient Method

Abstract

The transfer stiffness coefficient method, which was developed in the previous report by introducing the concept of the substructure synthesis method into the computation process of the transfer influence coefficient method, is applied to a structure with closed loops in the system. Such a structure can not be analyzed easily by the transfer influence coefficient method. However, the transfer stiffness coefficient method becomes applicable to such a structure, since the cross-dynamic stiffness coefficient matrix is introduced to represent the relationship between the state variables of substructure. As a typical example of the structure with closed loops, an algorithm based on the transfer stiffness coefficient method is formulated for the free and forced vibration analyses of a framework structure constructed from some uniform beams. In the analysis, both the truss and rahmen structures are treated. The validity of the present algorithm concerning the computation efficiency and the computational accuracy is confirmed by comparing the numerical computational results obtained by the transfer stiffness coefficient method with those obtained by applying the finite element method and the transfer matrix method.