Spread waves in a viscoelastic cylindrical body of a sector cross section with cutouts

Abstract

In this article an analysis of well-known works related to wave propagation and dispersion dependences in a cylindrical waveguide are presented. A mathematical model, methodology and algorithm for solving the problem of wave propagation in a cylindrical waveguide, having a sector cut are developed. The obtained equations are solved by the orthogonal sweep method in combination with the Mueller and Gauss methods. The dispersion relation for a viscoelastic cylindrical waveguide, having a sector cut in cross section at an arbitrary angle is obtained. Based on the obtained results, it was found that, there are no waves in the elastic cylinder of a sector section with real parts of the phase velocity. It has been established that, in the case of a wedge-shaped viscoelastic cylindrical panel, for each mode, there are limiting wave propagation velocities and they change with a change in the radius of curvature. The spectral sets of normal waves with an increase in the angular parameter of the sector cut-out, corresponding to lower non-zero frequencies of wave locking, slowly decrease.