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Rayleigh-gravity waves in a heavy elastic medium. (English) Zbl 0698.73011

Summary: A plane wave travelling through an elastic incompressible medium with a plane boundary is considered. The motion is confined largely to the neighbourhood of the latter. In addition to elastic forces, gravitational ones are accounted for as well. The velocity of propagation is calculated applying a Lagrangian description of the problem.

MSC:

74J15 Surface waves in solid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Full Text: DOI

References:

[1] Graff, K. F.: Wave motion in elastic solids. Oxford: Clarendon Press 1975. · Zbl 0314.73022
[2] Kolsky, H.: Stress waves in solids. Oxford: Clarendon Press 1953. · Zbl 0052.42502
[3] Lamb, H.: Hydrodynamics. Cambridge: University Press 1962. · Zbl 0828.01012
[4] Stoker, J. J.: Water waves. New York: Interscience Publishers 1957. · Zbl 0078.40805
[5] Truesdell, C., Noll, W.: The non-linear field theories of mechanics. In: Encyclopedia of physics, Vol. III/3. Berlin: Springer-Verlag 1965. · Zbl 0779.73004
[6] Trefftz, E.: Zur Theorie der Stabilit?t des elastischen Gleichgewichts. Zeitschr. f. angew. Math. und Mech.13, 160-165 (1933). · JFM 59.0737.07 · doi:10.1002/zamm.19330130224
[7] Pearson, C. E.: Theoretical elasticity. Cambridge: Harvard University Press 1959.
[8] Green, A. E., Adkins, J. E.: Large elastic deformations. Oxford: Clarendon Press 1960. · Zbl 0090.17501
[9] Timoshenko, S., Gere, J. M.: Theory of elastic stability. New York: McGraw-Hill 1961.
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