Computation of the Eigenvalues of Wave Propagation in Periodic Substructural Systems

Abstract

The wave propagation constants of periodic structures are computed using the exact dynamic stiffness matrix of a typical substructure. The approach used is to show that wave propagation and the natural vibration eigenproblem are similar to such an extent that methods used to find the natural frequencies of a structure can be applied to find its wave propagation constants. The Wittrick-Williams algorithm has been incorporated into a finite element program, JIGFEX, in conjunction with exact dynamic member stiffnesses, to ensure that no phase propagation eigenvalues are missed during computation. The accuracy of the present approach is then demonstrated by comparing the results that it gives to analytically determined wave propagation curves for a Timoshenko beam on periodic simple supports. Finally, phase propagation curves are given for a complex Timoshenko beam structure of a type that would be very difficult to analyze analytically.