Open AccessSimple Wave Motion in Magnetoelasticity
Author(s) -
Bazer Jack,
Karal Frank
Publication year - 1971
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1971.tb02335.x
Subject(s) - simple (philosophy) , magnetic field , classical mechanics , physics , wave equation , field (mathematics) , wave propagation , motion (physics) , variable (mathematics) , equations of motion , space (punctuation) , mechanics , mathematical analysis , mathematics , optics , computer science , quantum mechanics , philosophy , epistemology , pure mathematics , operating system
Summary Simple one‐dimensional wave motion in an infinitely conducting, electrically neutral, elastic medium in the presence of a magnetic field is studied. All physical quantities are required to depend on only one space variable and time; however, no restriction is placed on the orientations of the velocity, magnetic and strain vectors. In this paper, the stress–strain relation is assumed to be given by Hooke'sLaw so that the non‐linearity of the governing equations is due essentially to the interaction of the magnetic field with the velocity field and with itself. In this case, despite the complexity of the equations, almost completely explicit simple wave solutions are obtained. As in magnetogasdynamics, there are slow, fast, and Alfvén‐like simple wave solutions. These waves afford a mechanism for generating intense magnetic fields and together with the corresponding magnetoelastic shocks they enable one to solve one‐dimensional propagation problems with sufficiently simple initial conditions.