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.