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Shear Waves in an Elastic Plate with a Hole Resting on a Rough Base
Version 1
: Received: 21 November 2023 / Approved: 23 November 2023 / Online: 23 November 2023 (09:31:58 CET)
A peer-reviewed article of this Preprint also exists.
Filippov, A.N. Shear Waves in an Elastic Plate with a Hole Resting on a Rough Base. Mathematics 2024, 12, 165. Filippov, A.N. Shear Waves in an Elastic Plate with a Hole Resting on a Rough Base. Mathematics 2024, 12, 165.
Abstract
The article is devoted to the analytical and numerical study of the pattern of propagation and attenuation, due to Coulomb friction, of shear waves in an infinite thin elastic plate with a circular orifice of radius lying on a rough base. In the field of motion, an exact analytical solution of a nonlinear boundary value problem for tangential stresses and transversal velocities is obtained in quadratures by the method of Laplace transformations. It turned out that the complete exhaustion of the wave front of a strong rupture occurs at a finite distance from the center of the hole and an elementary formula is given for this distance (the case of tangential forces instantly applied to the orifice boundary, and then constant in time, is considered). For various ratios of the magnitude of the limiting friction force to the amplitude of the applied load, the trailing wave fronts are obtained, after which a state of static equilibrium between the elastic and friction forces with a nonlinear distribution of residual deformations is established in the region .
Keywords
shear wave; dry friction; elastic plate with orifice; non-linear partial equations; residual stresses; trailing wave front
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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