Viscoelastic Rayleigh waves
Authors:
P. K. Currie, M. A. Hayes and P. M. O’Leary
Journal:
Quart. Appl. Math. 35 (1977), 35-53
DOI:
https://doi.org/10.1090/qam/99648
MathSciNet review:
QAM99648
Full-text PDF Free Access
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References |
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Abstract: A general analysis is given of the propagation of surface waves over a half-space of homogeneous isotropic linearly-viscoelastic material. Particular emphasis is placed on the properties of the particle paths. The detailed examination of particular models shows that (in contrast with elastic materials) (i) more than one surface wave may be possible; (ii) the waves may be either direct or retrograde at the surface; (iii) the motion may change sense at many or no levels below the surface; (iv) the wave speed may be greater than the body-wave speeds.
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H. Jeffreys, The earth, Cambridge U. P., Cambridge, 1952, p. 34
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M. A. Hayes and R. S. Rivlin, Longitudinal waves in a linear viscoelastic material, ZAMP 23, 153–156 (1972)
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Lord Rayleigh, On waves propagated along the plane surface of an elastic solid, Proc. London Math. Soc. 17, 4–11 (1885)
H. Jeffreys, The earth, Cambridge U. P., Cambridge, 1952, p. 34
M. Hayes and R. S. Rivlin, A note on the secular equation for Rayleigh waves, ZAMP 13, 80–83 (1962)
A. N. Stroh, Steady state problems in anisotropic elasticity, J. Math. Phys. 41, 77–103 (1962)
D. M. Barnett and J. Lothe, Consideration of the existence of surface wave (Rayleigh wave) solutions in anisotropic elastic crystals, J. Phys. F: Metal Phys. 4, 671–686 (1974)
P. K. Currie, Rayleigh waves on elastic crystals, Quart. J. Mech. Appl. Math. 27, 489–496 (1974)
S. C. Hunter, Viscoelastic waves, in Progress in solid mechanics, vol. 1, edited by I. N. Sneddon and R. Hill, North-Holland, Amsterdam, 1962
F. J. Lockett, The reflection and refraction of waves at an interface between viscoelastic materials, J. Mech. Phys. Solids 10, 53–64 (1962)
M. A. Hayes and R. S. Rivlin, Propagation of sinusoidal small-amplitude waves in a deformed visco-elastic solid. I and II, J. Acoust. Soc. Amer. 46, 610–616 (1969), 51, 1652–1663 (1972)
M. A. Hayes and R. S. Rivlin, Longitudinal waves in a linear viscoelastic material, ZAMP 23, 153–156 (1972)
M. A. Hayes and R. S. Rivlin, Plane waves in linear viscoelastic materials, Quart. Appl. Math. 32, 113–121 (1974)
D. R. Bland, The theory of linear viscoelasticity, Pergamon Press, New York, 1960, p. 75
W. M. Ewing, W. S. Jardetzky and F. Press, Elastic waves in layered media, McGraw-Hill, New York, 1957, p. 274
R. S. Rivlin and J. L. Ericksen, Stress-deformation relations for isotropic materials, J. Rat. Mech. Anal. 4, 323–425 (1955)
A. E. Green and R. S. Rivlin, The mechanics of non-linear materials with memory, Arch. Rat. Mech. Anal, 1, 1–21 (1957)
J. W. Archbold, Algebra, Pitman, London, 1970
H. Kolsky, Stress waves in solids, Dover, New York, 1962, p. 22
P. Chadwick and D. W. Windle, Propagation of Rayleigh waves along isothermal and insulated boundaries, Proc. Roy. Soc. A280, 47–71 (1964)
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Article copyright:
© Copyright 1977
American Mathematical Society