Propagation of Own Waves in a Viscoelastic Cylindrical Panel of Variable Thickness

Abstract

The paper considers the problem of propagation of natural waves in a viscoelastic cylindrical panel of variable thickness. A mathematical formulation, a solution technique and an algorithm for wave propagation problems in viscoelastic cylindrical panels of variable thickness are formulated. To derive the shell equations, the principle of possible displacements was used (within the framework of the Kirchhoff–Love hypotheses). Using the variational equation and physical equations, a system consisting of eight differential equations is obtained. After some transformations, a spectral boundary value problem on a complex parameter is constructed for a system of eight ordinary differential equations with respect to complex functions of the form. Dispersion relations for the cylindrical panel are obtained, numerical results are obtained and an analysis is made. It is established that in the case of a wedge-shaped cylindrical panel, for each mode, there are limiting propagation velocities with an increase in the wave number that coincide in magnitude with the corresponding velocities of normal waves in a wedge-shaped plate of zero curvature.