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

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 deriv...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2024-03, Vol.45 (3), p.1246-1253
Main Authors: Safarov, Ismoil, Nuriddinov, Bakhtiyor, Nuriddinov, Zhavlon
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Analysis
Boundary value problems
Cylindrical shells
Cylindrical waves
Differential equations
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Ordinary differential equations
Probability Theory and Stochastic Processes
Propagation
Propagation modes
Propagation velocity
Variable thickness
Viscoelasticity
Wave propagation
Wedge shaped plates
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Summary: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.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080224600663