First Branch Dispersion of Torsional Waves in Bimaterial Rods

Torsional wave propagation is investigated for a rod consisting of two concentric, circular cylinders of dissimilar materials, perfectly bonded at the interface. Dispersion curves for the first branch of propagation are obtained from the frequency equation, which is derived through a solution satisfying the equations of linear elasticity. These dispersion curves are presented in dimensionless form with the ratio of constituent cylinder radii and ratios of like material properties as parameters. Only parameter values for which ρ2/ρ1>μ2/μ1 are considered. An expression for the first branch torsional wave velocity limit, as wavelength becomes infinite, is obtained from the exact frequency equation.