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

In this paper, the propagation of time-harmonic torsional waves in composite elastic cylinders is investigated. An imperfect interface is considered where tractions are continuous across the interface and the displacement jump is proportional to the stress acting on the interface. A frequency equation is derived for the rod and dispersion curves of normalized frequency as a function of normalized wave number for elastic bimaterials with varying values 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 correct limiting behavior for large F. It is shown that the modes, at any given frequency, are orthogonal, and it is outlined how the problem of reflection of a torsional mode by a planar defect (such as a circumferential crack) can be treated.