Eigenproblem of substructure chain and the expansion solution

In this paper, a new method for dealing with substructure chain is presented. Here, a substructure chain means a structure consisting of a number of identical substructures connected in series. This method is parallel to the expansion method in the structural analysis according to the transverse section. The method of shift invariance and that of initial parameter and transfer matrix, their mutual-relation and combined use, as well as the analysis of the eigenproblem on the transverse section, and the expansion method based on the eigenvectors are described in this paper. Project supported by National Natural Science Foundation of China.