Derivation of the one-dimensional radiation condition in elasticity theory by introducing infinitesimal viscosity

Abstract

With the rapid development of engineering science and technology, tasks related to the calculation of wave processes in elastic medium are becoming more and more relevant. One of the important problems is the search for effective methods for calculating the propagation of harmonic oscillations in elastic mediums, in particular, in semi-infinite spaces. One of these methods is the use of asymptotic boundary conditions of the “radiation conditions” type, which allow us to describe the processes of wave propagation outside the computational domain. In this paper we consider the application of infinitesimal viscosity to derive an asymptotic boundary condition of the “radiation condition” type for the propagation of harmonic oscillations in a semi-infinite elastic space. The results of the study can be used in the design of various devices and structures subjected to the influence of wave processes in elastic mediums, in particular, in the field of soil mechanics.