Contact Problem for a Cylindrical Waveguide With a Periodic Structure

Abstract

The axially symmetric problem of a stamp excitation of torsional oscillations in a cylindrical waveguide with periodically changing mechanical properties along the longitudinal coordinate has been studied. A section of waveguide, corresponding to the minimal period of change in mechanical properties, can consist of any number of homogeneous regions (finite cylinders) with a different length and with various elastic constants. The method, related to the construction of the special “transition operator”, which allows finding the values of the displacement vector and stress tensors on one cross-section of a waveguide by their values on another. The distance between waveguide sections equals the value of the minimal period of changing properties of the waveguide. Relations for calculating the eigenvalues of the transition operator are obtained. The study of these eigenvalues allows defining the range of frequencies when both damping and continuous oscillations can propagate in the waveguide. Contact strains under a stamp are determined for relatively large radii of the cylinder.