Circumferential propagation of S H waves in hollow cylinders

Abstract

This paper concerns the circumferential propagation of shear horizontally polarized waves in hollow, infinite, elastic cylinders. The exact solution of this classical problem expressed in terms of Bessel and Hankel functions gives rise to serious numerical difficulties when the circumferential wavenumber takes large values. A different method is developed to treat such cases. The method is based on a direct integration of the problem cast in the Sturm–Liouville form. Calculations performed with the Sturm–Liouville solver of Bailey et al. [ACM Trans. Math. Software 4, 193–208 (1978)] allow accurate determinations of SH modes for a wide range of geometrical parameters, reduced frequencies, and circumferential wavenumbers. This direct approach may be extended to other modal problems which are amenable to a standard Sturm–Liouville formulation.