Contributions to the integration of the magnetoelasticity equations

Abstract

This paper considers the magnetoelasticity equations for a homogeneous and isotropic elastic medium which satisfies the condition εμ e = ε 0 μ e0 . It is assumed that Maxwell's displacement currents are neglected. The equations are written in dimensionless variables. The linearization of the system of equations leads to the obtaining of a single equation for the current density. As a practical application, Cauchy's problem is solved for the perfectly conductive infinite plane in the presence of a homogeneous magnetic field. It is shown that the wave propagation takes place without dispersion. In the final part of the paper Cauchy's problem is solved for the elastic half-plane subjected to a normal pressure on the boundary. The solution is obtained by a continuous superposition of plane waves. ]It is demonstrated that in both cases Cauchy's problem is correctly set.