Computation of the Eigenvalues of Wave Propagation in Periodic Substructural Systems

[+] Author and Article Information
F. W. Williams, P. N. Bennett

Div. of Struct. Eng., School of Eng., Univ. of Wales, College of Cardiff, U.K.

Zhong Wanxie

Research Inst. of Engineering Mech., Dalian Univ. of Tech., Dalian 116024, P.R.C.

J. Vib. Acoust 115(4), 422-426 (Oct 01, 1993) (5 pages) doi:10.1115/1.2930367 History: Received September 01, 1992; Online June 17, 2008


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.

Copyright © 1993 by The American Society of Mechanical Engineers
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