Uncoupling of dynamic equations for periodic structures

This paper is aimed at providing some explanation of the physical meaning and mathematical formulation of the U-transformation method, which has found many applications in obtaining solutions for structures with periodicity properties. The U-transformation was first derived from the mode method for rotational periodic structures. The dynamic equation for cyclic periodic structures can be uncoupled in the domain of single substructure by U-transformation. It is then extended to the double U-transformation method for structures with cyclic periodicity in two directions. However, it should be noted that the method may also be applied to some one-way or two-way linear periodic structures.