Dispersion properties of helical waves in radially inhomogeneous elastic media

In this paper, a method describing dispersion curve calculation for waves propagating in radially layered, inhomogeneous isotropic elastic waveguides is developed. Particular emphasis is placed on the helical waves with noninteger azimuthal wavenumbers, which can be potentially applied in such fields as nondestructive evaluation, acoustic tomography, etc., stipulating their practical importance. To solve the problem under consideration, the matrix Riccati equation is formulated for an impedance matrix. The use of the latter yields a simple form of the dispersion equation. Numerical computation of dispersion curves can encounter difficulties, which are due to potential singularities of the impedance matrix and the necessity to separate roots of the dispersion equation. These difficulties are overcome by employing the Cayley transform and invoking the parametric continuation method. The method developed by the authors is demonstrated by calculating dispersion diagrams in support of helical waves for several models of practical interest. Such computations for an inhomogeneous layer and its approximation by a set of homogeneous layers using a transfer matrix and Riccati equation methods revealed higher computational accuracy of the latter. Dispersion curves calculated for layers with different types of inhomogeneity demonstrated significant discrepancies at low frequencies.