Wave Processes in Viscoelastic Topographic Waveguides

The natural vibrations of an orthotropic viscoelastic waveguide are investigated. The statement of the problem on an elastic waveguide in the operator form is formulated; the concept of complex modules is used to pass to the viscoelastic case. A weak formulation of the problem, on the basis of which a variational principle similar to the Hamilton-Ostrogradsky principle is formulated, is performed. A simplified functional built on the basis of Kirchhoff-type hypotheses for wedge-shaped waveguides is used to form an approach to constructing a dispersion set based on the Ritz method. Computational experiments have been carried out for topographic waveguides with a trapezoidal, triangular, and rectangular cross-sections. The graphs of dispersion dependences are plotted, a comparison with the elastic case is made.