An equation solver for eigenvalue problems of cyclic symmetric structures

Abstract

To obtain the natural frequencies of rotationally periodic structures, a simple block solver is developed. Complex arithmetic is used to reduce the analysis region to a repeating substructure; characteristic matrices are considered to be cyclic in nature (S. Michimura et al., Bull. Jap. Soc. Mech. Engrs24,1968-1993, 1981). Most of the decomposition operations involved in the complex stiffness matrix are done only once, also in real mode. Simple examples are included to illustrate this solution scheme. Triangular finite elements are used to form the characteristic matrices of repeating substructures.