Boltayev Zafar Iхtiyorovich, Doctor of physical-mechanical sciences, associated professor, leading Researcher of the Bukhara branch of the Institute of Mathematics named after V.I. Romanovsky Xudoyberdiyev Mirqosim Rashitovich, Ruziyeva Mavluda Anvar qizi, Doctor of philosophy in techanical sciences, assistant of department of “Mechanics” 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.
Keywords: variational equation, panel of variable thickness, shell equation,
natural waves, spectral boundary value problem, complex frequency
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