Normal Modes Characterizing Magnetoelastic Plane Waves

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Abstract
The general theory of magnetohydrodynamic waves in an ideal conducting fluid embedded in a uniform field of magnetic induction, and the application of the theory to the systematic analysis of the various modes of propagation in incompressible and compressible fluids have been presented by the author in two earlier papers. The techniques developed there have now been extended to the study of homogeneous plane waves in an unbounded conducting solid. It is found that, in the presence of a uniform static magnetic field, the elastic medium sustains five distinct modes of propagation as already pointed out by Knopoff. The first two modes are pure shear waves, one of which is a slightly attenuated shear mode with phase velocity modified anisotropically by magnetoelastic coupling, whereas the companion shear mode is highly attenuated and exhibits a propagation constant which is essentially that of an electromagnetic wave of the same frequency. The remaining three modes are shear-compression waves of which one mode exhibits a phase velocity intermediate between the phase velocity of shear and compressional waves, the second mode has a phase velocity exceeding that of compressional waves, and the third shear-compression mode is again highly attenuated with the propagation characteristics of an electromagnetic wave.

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