Love waves in stratified monoclinic media
Author:
Sergey V. Kuznetsov
Journal:
Quart. Appl. Math. 62 (2004), 749-766
MSC:
Primary 74J15; Secondary 74E10
DOI:
https://doi.org/10.1090/qam/2104272
MathSciNet review:
MR2104272
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Abstract: A mathematical model for analysis of Love waves propagating in stratified anisotropic (monoclinic) media is presented; this model is based on a newly developed Modified Transfer Matrix (MTM) method. Closed form dispersed relations are obtained for media consisting of one or two orthotropic layers lying on orthotropic substrate. Conditions for existence of Love waves are analyzed. Horizontally polarized shear surface waves of non-Love type are constructed. A numerical algorithm is worked out for obtaining dispersion relations for Love waves propagating in stratified media containing a large number of layers.
A. E. H. Love, Some Problems of Geodynamics, Cambridge University Press, London, 1911
E. Dieulesaint and D. Royer, Elastic Waves in Solids, Wiley, N. Y., 1980
P. R. Sengupta and S. Nath, Surface waves in fiber-reinforced anisotropic elastic media, Sadhana 26, 363–370 (2001)
- William T. Thomson, Transmission of elastic waves through a stratified solid medium, J. Appl. Phys. 21 (1950), 89–93. MR 35191
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L. Knopoff, A matrix method for elastic wave problems, Bull. Seism. Soc. Am. 54, 431–438 (1964)
A. K. Mal and L. Knopoff, A differential equation for surface waves in layers with varying thickness, J. Math. Anal. Appl. 21, 431–441 (1968)
J. W. Dunkin, Computation of model solutions in layered elastic media at high frequencies, Bull. Seism. Soc. Am. 55, 335–358 (1965)
T. Kundu and A. K. Mal, Elastic waves in a multilayered solid due to a dislocation source, Wave Motion 7, 459–471 (1985)
R. B. Evans, The decoupling of seismic waves, Wave Motion 8, 321–328 (1986)
M. Castaings and B. Hosten, Delta operator technique to improve the Thomson-Haskell method stability for propagation in multilayered anisotropic absorbing plates, J. Acoust. Soc. Am. (1994)
M. J. S. Lowe, Matrix techniques for modeling ultrasonic waves in multilayered media, IEEE Trans. Ultrasonics, Ferroelectrics, and Frequency Control 42, 525–542 (1995)
M. Mallah, L. Philippe, and A. Khater, Numerical computations of elastic wave propagation in anisotropic thin films deposited on substrates, Comp. Mater. Sci. 15, 411–421 (1999)
- R. Wobst, The generalized eigenvalue problem and acoustic surface wave computations, Computing 39 (1987), no. 1, 57–69 (English, with German summary). MR 908556, DOI https://doi.org/10.1007/BF02307713
M. E. Gurtin, The Linear Theory of Elasticity, In: Handbuch der Physik, Bd. VIa/2, Springer, Berlin, 1972
- Sergey V. Kuznetsov, “Forbidden” planes for Rayleigh waves, Quart. Appl. Math. 60 (2002), no. 1, 87–97. MR 1878260, DOI https://doi.org/10.1090/qam/1878260
- Sergey V. Kuznetsov, Subsonic Lamb waves in anisotropic plates, Quart. Appl. Math. 60 (2002), no. 3, 577–587. MR 1914442, DOI https://doi.org/10.1090/qam/1914442
- Sergey V. Kuznetsov, Surface waves of non-Rayleigh type, Quart. Appl. Math. 61 (2003), no. 3, 575–582. MR 1999838, DOI https://doi.org/10.1090/qam/1999838
A. E. H. Love, Some Problems of Geodynamics, Cambridge University Press, London, 1911
E. Dieulesaint and D. Royer, Elastic Waves in Solids, Wiley, N. Y., 1980
P. R. Sengupta and S. Nath, Surface waves in fiber-reinforced anisotropic elastic media, Sadhana 26, 363–370 (2001)
W. T. Thomas, Transmission of elastic waves through a stratified solid medium, J. Appl. Phys. 21, 89–93 (1950)
N. A. Haskell, Dispersion of surface waves on multilayered media, Bull. Seism. Soc. Am. 43, 17–34 (1953)
L. Knopoff, A matrix method for elastic wave problems, Bull. Seism. Soc. Am. 54, 431–438 (1964)
A. K. Mal and L. Knopoff, A differential equation for surface waves in layers with varying thickness, J. Math. Anal. Appl. 21, 431–441 (1968)
J. W. Dunkin, Computation of model solutions in layered elastic media at high frequencies, Bull. Seism. Soc. Am. 55, 335–358 (1965)
T. Kundu and A. K. Mal, Elastic waves in a multilayered solid due to a dislocation source, Wave Motion 7, 459–471 (1985)
R. B. Evans, The decoupling of seismic waves, Wave Motion 8, 321–328 (1986)
M. Castaings and B. Hosten, Delta operator technique to improve the Thomson-Haskell method stability for propagation in multilayered anisotropic absorbing plates, J. Acoust. Soc. Am. (1994)
M. J. S. Lowe, Matrix techniques for modeling ultrasonic waves in multilayered media, IEEE Trans. Ultrasonics, Ferroelectrics, and Frequency Control 42, 525–542 (1995)
M. Mallah, L. Philippe, and A. Khater, Numerical computations of elastic wave propagation in anisotropic thin films deposited on substrates, Comp. Mater. Sci. 15, 411–421 (1999)
R. Wobst, The generalized eigenvalue problem and acoustic surface wave computations, Computing 39, 57–69 (1987)
M. E. Gurtin, The Linear Theory of Elasticity, In: Handbuch der Physik, Bd. VIa/2, Springer, Berlin, 1972
S. V. Kuznetsov, "Forbidden” planes for Rayleigh waves, Quart. Appl. Math, 60, 87–97 (2002)
S. V. Kuznetsov, Subsonic Lamb waves in anisotropic plates, Quart. Appl. Math. 60, 577–587 (2002)
S. V. Kuznetsov, Surface waves of Non-Rayleigh type, Quart. Appl. Math. 61, 575–582 (2003)
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© Copyright 2004
American Mathematical Society
