Dispersion of torsional waves in a thick-walled transversely isotropic circular cylinder of infinite length

The dispersion properties of torsional waves of a thick-walled transversely isotropic circular cylinder of infinite length are investigated. The assumed waves are axisymmetric and propagate along the x-axis of the cylinder. The wall of the cylinder consists of a transversely isotropic material with the axis of isotropy parallel to the x-axis of the cylinder. The dispersion curves for both the phase and group velocities are determined and graphically illustrated. The amplitudes of the tangential displacements for some dispersion branches are shown. The purpose of the paper is to show the present technique is useful in solving some energy flow problems when torsional waves travel along arbitrarily laminated cylinders with various kinds of anisotropy. It seems that by controlling the anisotropy of a shell-like structure, the optimisation of amplitude and energy flow distributions in different parts of the structure can be achieved.