Time-harmonic torsional waves in a composite cylinder with an imperfect interface

In this paper, the propagation of time-harmonic torsional waves in composit e elastic cylinders is investigated. An imperfect interface is considered w here tractions are continuous across the interface and the displacement jum p is proportional to the stress acting on the interface. A frequency equati on is derived for the rod and dispersion curves of normalized frequency as a function of normalized wave number for elastic bimaterials with varying v alues for the interface constant F are presented. The analysis is shown to recover the dispersion curves for a bimaterial rod with a perfect (welded) interface (F = 0), and has the corner limiting behavior for large F. It is shown that the modes, at any given frequency, are orthogonal, and it is out lined how the problem of reflection of a torsional mode by a planar defect (such as a circumferential crack) can be treated. (C) 2000 Acoustical Socie ty of America. [S0001-4966(00)04402-7].