Geometrical Magnetoelasticity

An account is given of propagation phenomena in an electrically neutral, infinitely conducting, inhomogeneous elastic medium in the presence of a magnetic field. The linearized equations of magnetoelasticity are employed, the stress-strain relation being given by Hooke's law. Our discussion is based on the fact that these equations may be expressed as a first-order, symmetric-hyperbolic, system or one that is essentially so. This property implies, in advance, that the linearized equations possess a geometrical theory analogous to geometrical optics. A complete solution of the following basic problem in the geometrical theory is given. Let a small discontinuity be specified across a surface S0 in an otherwise an disturbed magnetoelastic medium. The problem is to determine the wave fronts that evolve from S0—there will be six of them in general-and to ascertain the polarizations of the field vectors and strengths of the discontinuities carried on these fronts. The solution of this problem is employed to obtain an explicit solution of a special magnetoelastic piston problem which is designed to illustrate a purely magnetic method for initiating magnetoelastic waves.