Longitudinal waves in an elastic medium with a piecewise-linear dependence of the stress on the strain
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.
scientific article; zbMATH DE number 56381