Longitudinal waves in an elastic medium with a piecewise-linear dependence of the stress on the strain
type: Item
instance of: scholarly article
title: Longitudinal waves in an elastic medium with a piecewise-linear dependence of the stress on the strain
zbMATH Open document ID: 0757.73011
DOI: 10.1016/0021-8928(90)90114-P
author: A. G. Kulikoskij
author: L. A. Pekuroskaya
published in: Journal of Applied Mathematics and Mechanics
publication date: 1992-09-26T00:00:00Z
review text: The longitudinal wave propagation in an elastic body, whose elasticity coefficient (the derivative of the stress with respect to the strain) undergoes a discontinuity, is considered. The assumed discontinuity is a piecewise-linear, namely, the reference velocity is \(c_ 1=\text{const}\) for \(x<0\) and \(c_ 2=\text{const}> c_ 1\) for \(x>0\). It is shown that there are five possible domains for the values of the front velocity \(W\), some of them corresponding to the so-called fast waves, the others to the so-called slow ones. The main result says that if the front velocity reaches the value of one of the velocities of the characteristics, then the reconstruction of the motion occurs. A special case is constituted by the conversion of the type of waves (fast into slow and conversely). The paper is of a real interest for those working in the area of elastic wave propagation in media with jumps in the physical parameters.
Mathematics Subject Classification ID: 74J10
Mathematics Subject Classification ID: 74B99
zbMATH DE Number: 56381
zbMATH Keywords: slow waves
zbMATH Keywords: elasticity coefficient
zbMATH Keywords: discontinuity
zbMATH Keywords: fast waves
zbMATH Keywords: velocities of the characteristics
reviewed by: Dumitru Stanomir
MaRDI profile type: Publication
cites work: A boundary value problem in the theory of plastic wave propagation
cites work: On fronts of strong and weak discontinuities in solutions of the equations of different-modulus elasticity theory
cites work: General theory of the solutions of the equations of motion of an elastic medium of different moduli
cites work: Q3844581
description: scientific article; zbMATH DE number 56381