On a Method in Dynamic Elasticity Problems for Heterogeneous Wedge-Shaped Medium

Vyacheslav Berkovich,Viсtor Poltinnikov,D Rudoy,N Ugrekhelidze,A Olshevskaya

doi:10.1051/e3sconf/202127304002

Vyacheslav Berkovich, Viсtor Poltinnikov + Show 3 more

Open Access

https://doi.org/10.1051/e3sconf/202127304002

Copy DOI

Abstract

The method of analysis of steady oscillations arising in the piecewise homogeneous wedge-shaped medium composed by two homogeneous elastic wedges with different mechanical and geometric characteristics is presented. Method is based on the distributions’ integral transform technique and allows reconstructing the wave field in the whole medium by displacement oscillations given in the domain on the boundary of the medium. The problem in question is reduced to a boundary integral equation (BIA). Solvability problems of the BIA are examined and the structure of its solution is established.

Highlights

The aim of the present paper is mathematical modeling the dynamics of a massive body of composite material under harmonic oscillations
Аnalogous problems arise in seismic prospects when analyzing the wave propagation in the skew-layered medium near the earth crust surface
The problems mentioned above are reduced to mixed dynamic boundary value problems for the elastic wedge-shaped composite body

Summary

Introduction

The aim of the present paper is mathematical modeling the dynamics of a massive body of composite material under harmonic oscillations. The investigation of the stressed and deformable state for such a body is of great interest for theoretical and practical analysis of strength of materials and reliability problems of technical constructions under long exploitation both in hard industry enterprises and agricultural machinery ones. The problem in question appears when analyzing construction elements by nondestructive testing as well. Аnalogous problems arise in seismic prospects when analyzing the wave propagation in the skew-layered medium near the earth crust surface. The problems mentioned above are reduced to mixed dynamic boundary value problems for the elastic wedge-shaped composite body. Investigation of such problems for the homogeneous medium has been usually based on Kontorovich-Lebedev integral transform techniques:

Objectives

Methods

Results

Conclusion