A fast algorithm for periodic structures in vibration

Abstract

Periodic structures are popular in engineering applications for economical and architectural reasons. A fast method for calculating the natural vibration of periodic structures having identical constituents (substructures) with general boundary conditions is introduced. The number of arithmetic counts is proportional to PlogP, instead of P² in the conventional method with band solver, where P is the number of substructures involved. Because of the fact that the general boundary conditions have been considered, a periodic structure can be represented by its condensed matrices associated with the boundary stations to form a superstructure which can be connected to other structures. Four illustrative examples are given.