Wave propagation in a cylindrical body in the presence of surface forces depending on the relative displacement

Abstract

Studies of wave propagation in extended bodies with external friction have a wide range of applications and are significant for various engineering and scientific fields. They contribute to the development of new technologies, improve the design and construction of structures, and expand our understanding of the physical processes occurring in various materials and media. In this article, axisymmetric two-dimensional problems of the propagation of longitudinal waves in a cylindrical body are numerically solved in the presence of surface friction forces of the Winkler and Kelvin-Voigt types. For the numerical solution, the Wilkins scheme of the finite difference method was used. The influence of friction forces on the wave parameters is revealed. It is determined that the results of the considered problems are between solutions using slippery contact without friction and with friction according to the Coulomb law. A 5-7% deviation of the hypothesis of flat sections is shown, which makes it possible to reduce such a problem to a one-dimensional formulation.