The paper deals with the propagation of elastic and viscoelastic waves of planar and cylindrical bodies. In the three-dimensional formulation of the problem of elasticity theory, the variational equation (satisfies the Kirchhoff-Love hypothesis) reduces to solving. Neglecting this equation in terms that take into account the inertia of rotation of the normal to the median plane. After some non-complicated operations, a system of first-order differential equations with complex coefficients is obtained, which is subsequently solved by orthogonal sweep method with a combination of the Mueller method on complex arithmetic. The dispersion relation for the wedge-shaped plate is obtained. Detection of a new type of waves "Troyanovsky-Safarov" in plates of variable cross-section.
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