Subsonic Lamb waves in anisotropic plates
Author:
Sergey V. Kuznetsov
Journal:
Quart. Appl. Math. 60 (2002), 577-587
MSC:
Primary 74J15; Secondary 74E10, 74K20
DOI:
https://doi.org/10.1090/qam/1914442
MathSciNet review:
MR1914442
Full-text PDF Free Access
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Abstract: A six-dimensional complex formalism for analysis of Lamb waves propagating with subsonic speed in anisotropic plates is formulated. Conditions for nonexistence of certain Lamb waves in anisotropic plates are obtained. An example of a transversely isotropic plate having “forbidden” speed at which no subsonic Lamb wave propagates is presented.
H. Lamb, On waves in an elastic plate, Proc. Roy. Soc. A93, 114–128 (1917)
J. W. Strutt (Lord Rayleigh), On wave propagating along the plane surface of an elastic solid, Proc. London Math. Soc. 17, 4–11 (1885)
G. W. Farnell, Properties of elastic surface waves, Phys. Acoust. 6, 109–166 (1970)
D. M. Barnett and J. Lothe, Synthesis of the sextic and the integral formalism for dislocations, Greens functions, and surface waves in anisotropic elastic solids, Phys. Norv. 7, 13–19 (1973)
P. Chadwick and G. D. Smith, Foundations of the theory of surface waves in anisotropic elastic materials, In: Advances in Applied Mechanics 17, Academic Press, New York, 1977, pp. 303–376
G. T. Mase and G. C. Johnson, An acoustic theory for surface waves in anisotropic media, J. Appl. Mech. 54, 127–135 (1987)
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- T. C. T. Ting and D. M. Barnett, Classifications of surface waves in anisotropic elastic materials, Wave Motion 26 (1997), no. 3, 207–218. MR 1482220, DOI https://doi.org/10.1016/S0165-2125%2897%2900027-9
R. Stoneley, Elastic waves at the surface of separation of two solids, Proc. Roy. Soc. London A106, 416–428 (1924)
E. Dieulesaint and D. Royer, Elastic Waves in Solids, John Wiley and Sons, New York, 1980
P. Chadwick and P. Borejko, Existence and uniqueness of Stoneley waves, Geophys. J. Internat. 118, 279–284 (1994)
- P. Chadwick, Interfacial and surface waves in pre-strained isotropic elastic media, Z. Angew. Math. Phys. 46 (1995), no. Special Issue, S51–S71. Theoretical, experimental, and numerical contributions to the mechanics of fluids and solids. MR 1359313
W. Lin and L. M. Keer, A study of Lamb waves in anisotropic plates, J. Acoust. Soc. Amer. 92, 888–894 (1992)
N. Guo and P. Cawley, Lamb wave propagation in composite laminates and its relationship with acousto-ultrasonics, NDT & E Internat. 26, 75–84 (1993)
D. E. Chimenti, Lamb waves in microstructured plates, Ultrasonics 32, 255–260 (1994)
O. Poncelet and M. Deschamps, Lamb waves generated by inhomogeneous plane waves, J. Acoust. Soc. Amer. 102, 292–300 (1997)
- A. N. Stroh, Steady state problems in anisotropic elasticity, J. Math. and Phys. 41 (1962), 77–103. MR 139306
- Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
P. Chadwick, Some remarks on the existence of one-component surface waves in elastic materials with symmetry, Physica Scripta 44, 94–97 (1992)
H. Lamb, On waves in an elastic plate, Proc. Roy. Soc. A93, 114–128 (1917)
J. W. Strutt (Lord Rayleigh), On wave propagating along the plane surface of an elastic solid, Proc. London Math. Soc. 17, 4–11 (1885)
G. W. Farnell, Properties of elastic surface waves, Phys. Acoust. 6, 109–166 (1970)
D. M. Barnett and J. Lothe, Synthesis of the sextic and the integral formalism for dislocations, Greens functions, and surface waves in anisotropic elastic solids, Phys. Norv. 7, 13–19 (1973)
P. Chadwick and G. D. Smith, Foundations of the theory of surface waves in anisotropic elastic materials, In: Advances in Applied Mechanics 17, Academic Press, New York, 1977, pp. 303–376
G. T. Mase and G. C. Johnson, An acoustic theory for surface waves in anisotropic media, J. Appl. Mech. 54, 127–135 (1987)
S. A. Gundersen, D. M. Barnett, and J. Lothe, Rayleigh wave existence theory: A supplementary remark, Wave Motion 9, 319–321 (1987)
T. C. T. Ting and D. M. Barnett, Classifications of surface waves in anisotropic elastic materials, Wave Motion 26, 207–218 (1997)
R. Stoneley, Elastic waves at the surface of separation of two solids, Proc. Roy. Soc. London A106, 416–428 (1924)
E. Dieulesaint and D. Royer, Elastic Waves in Solids, John Wiley and Sons, New York, 1980
P. Chadwick and P. Borejko, Existence and uniqueness of Stoneley waves, Geophys. J. Internat. 118, 279–284 (1994)
P. Chadwick, Interfacial and surface waves in pre-strained isotropic elastic media, Z. Angew. Math. Phys. 46, 51–71 (1995)
W. Lin and L. M. Keer, A study of Lamb waves in anisotropic plates, J. Acoust. Soc. Amer. 92, 888–894 (1992)
N. Guo and P. Cawley, Lamb wave propagation in composite laminates and its relationship with acousto-ultrasonics, NDT & E Internat. 26, 75–84 (1993)
D. E. Chimenti, Lamb waves in microstructured plates, Ultrasonics 32, 255–260 (1994)
O. Poncelet and M. Deschamps, Lamb waves generated by inhomogeneous plane waves, J. Acoust. Soc. Amer. 102, 292–300 (1997)
A. N. Stroh, Steady state problems in anisotropic elasticity, J. Math. Phys. 41, 77–103 (1962)
P. Hartman, Ordinary Differential Equations, John Wiley and Sons, New York, 1964
P. Chadwick, Some remarks on the existence of one-component surface waves in elastic materials with symmetry, Physica Scripta 44, 94–97 (1992)
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© Copyright 2002
American Mathematical Society
