Guided circumferential waves in layered cylinders

This paper examines the propagation of time harmonic circumferential waves in a two-dimensional (infinitely long) hollow cylinder with an inner shaft. The boundary condition at the interface (between the inner shaft and the outer cylinder) is assumed as free-sliding; that is, the interfacial shear stresses are assumed to be zero, and the normal stress and radial displacements are continuous. The dispersion relationship is obtained from linear elasticity theory, and numerical results for the dispersion curves of the first several modes are presented. In addition, displacement profiles along the radial directions are provided. These results show that, at higher frequencies, the first mode asymptotically tends to a Rayleigh wave on a flat surface, while the second mode also approaches a Rayleigh wave propagating along the free-sliding interface.