Shear Waves in an Elastic Plate with a Hole Resting on a Rough Base

Anatoly Nikolaevich Filippov ()
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Anatoly Nikolaevich Filippov: Department of Higher Mathematics, Gubkin University, Leninsky Prospect 65, Bld. 1, 119991 Moscow, Russia

Mathematics, 2024, vol. 12, issue 1, 1-16

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 elastic thin plate with a circular orifice of radius r 0 lying on a rough base. Considering the friction forces and their influence on the sample of wave propagation in extended rods or thin plates is important for calculating the stress–strain state in them and the size of the area of motion. An exact analytical solution of a nonlinear boundary value problem for tangential stresses and velocities is obtained in quadratures by the Laplace transform, with respect to time. It turned out that the complete exhaustion of the wave front of a strong rupture occurs at a finite distance r * from the center of the orifice, and an elementary formula is given for this distance (the case of tangential shock stresses suddenly applied to the orifice boundary is considered). For various ratios of the magnitude of the limiting friction force to the amplitude of the applied load, the stopping (trailing) wave fronts are calculated. After passing them, a state of static equilibrium between the elastic and friction forces with a nonlinear distribution of residual stresses is established in the region r 0 ≤ r ≤ r * . For the first time, a precise analytical solution was obtained for the boundary value problem of the propagation of elastic shear waves in an infinite isotropic space with a cylindrical cavity, when a tangential shock load is set on its surface.

Keywords: shear wave; dry friction; elastic plate with orifice; non-linear partial equations; residual stresses; trailing wave front (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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