Uncoupling of Governing Equations for Cyclic Bi-Periodic Structures

Abstract

The U-transformation method, a new analytical method, is very powerful in the static and dynamic analyses of structures with cyclic periodic properties. using the U-transformation method on a cyclic periodic structure is equivalent to projecting the orthogonal mode subspace displacement vector into the unitary space. The advantage of the U-transformation method is to make it possible to uncouple linear simultaneous equations, either algebraic or differential equations, which have cyclic bi-periodic properties. This paper provides a rigorous proof of this significant statement and gives the form of the uncoupled equations. The uncoupling principle for the governing equations for structures with cyclic bi-periodicity, is demonstrated not only in one direction but also in two directions. The result can be easily used in a procedure to obtain the solutions for static and dynamic analyses of bi-periodic structures.