Determining the response of infinite, one-dimensional, non-uniform periodic structures by substructuring using waveshape coordinates

A method is presented for determining the wavenumbers, waveshapes and point receptances for an infinite, one-dimensional, non-uniform periodic structure with distributed periodic attachments or supports. The approach is based on a general theory of harmonic wave propagation in one-dimensional periodic systems. Ill-conditioning was previously reported as an impediment to applying the theory to problems of practical importance. In this paper ill-conditioning problems are overcome and a method of substructuring using waveshape coordinates is presented that dramatically improves computational efficiency. The accuracy and generality of the new method are tested by comparing computed and measured receptances for a typical TGV railway track with UIC60 rail, rail pad, ballast and concrete sleepers. The computed results are found to correlate well with measured data. (c) 2004 Elsevier Ltd. All rights reserved.