An Algorithm to Calculate Dispersion Properties of Helical Waves in Radially Inhomogeneous Elastic Waveguides

The algorithm for dispersion curves calculation in radially inhomogeneous isotropic elastic waveguides is presented. Main attention is directed at helical waves, which propagate along cylindrical surface under arbitrary angle to its generatrix. They can be described by noninteger azimuthal wavenumbers. Such waves find expanding application in non-destructive testing, acoustic tomography, etc. Provided physical parameters of the medium are piecewise continuous functions of the radial coordinate, one can tackle the problem under consideration by matrix Riccati equation technique for elastic impedance matrix. It can be solved by parametric continuation method. Cayley transform was applied to avoid singularities in the course of computations.