Elastic waves in rotating media
Authors:
Michael Schoenberg and Dan Censor
Journal:
Quart. Appl. Math. 31 (1973), 115-125
DOI:
https://doi.org/10.1090/qam/99708
MathSciNet review:
QAM99708
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Abstract: Plane harmonic waves in a rotating elastic medium are considered. The inclusion of centripetal and Coriolis accelerations in the equations of motion with respect to a rotating frame of reference leads to the result that the medium behaves as if it were dispersive and anisotropic. The general techniques of treating anistropic media are used with some necessary modifications. Results concerning slowness surfaces, energy flux and mode shapes are derived. These concepts are applied in a discussion of the behavior of harmonic waves at a free surface.
- J. L. Synge, Elastic waves in anisotropic media, J. Math. and Phys. 35 (1957), 323–334. MR 85782, DOI https://doi.org/10.1002/sapm1956351323
- J. L. Synge, Flux of energy for elastic waves in anisotropic media, Proc. Roy. Irish Acad. Sect. A 58 (1956), 13–21. MR 135319
- M. J. P. Musgrave, Reflexion and refraction of plane elastic waves at a plane boundary between aeolotropic media, Geophys. J. 3 (1960), 406–418. MR 0120918
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
J. L. Synge, Elastic waves in anisotropic media, J. Math. Physics 35, 323–334 (1957)
J. L. Synge, Flux of energy for elastic waves in anisotropic media, Proc. Roy. Irish Acad. A58, 13–21 (1956)
M. J. P. Musgrave, Elastic waves in anisotropic media, Prog. Solid Mech. 2, 63–85 (1960)
R. Courant and D. Hilbert, Methods of mathematical physics, Volume I, Interscience Publishers, Inc., New York, 1953
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Article copyright:
© Copyright 1973
American Mathematical Society
