Steady waves in an anisotropic elastic layer attached to a half-space or between two half-spaces - A generalization of Love waves and Stoneley waves

Mathematics and Mechanics of Solids

Volumn 14, Issue 1-2, 2009, Pages 52-71

  Ting, T C T ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Anisotropic; Bimaterials; Bonded layer; Dispersion equations; Half spaces; Love waves; Plates; Slip waves; Steady waves; Stoneley waves

Indexed keywords

HYDROELASTICITY;

ANISOTROPIC; BIMATERIALS; BONDED LAYER; DISPERSION EQUATIONS; HALF-SPACES; LOVE WAVES; PLATES; SLIP WAVES; STEADY WAVES; STONELEY WAVES;

ANISOTROPY;

EID: 58149109009     PISSN: 10812865     EISSN: 17413028     Source Type: Journal    
DOI: 10.1177/1081286508092602     Document Type: Article

References (27)

1. Bovik, P. On the modeling of thin interface layers in elastic and acoustic scattering problems. Quarterly Journal of Mechanics and Applied Mathematics, 47, 17-40 (1994).
2. Niklasson, A.J., Datta, S.K. and Dunn, M.L. On approximate guided waves in plates with thin anisotropic coatings by means of effective boundary conditions. Journal of Acoustic Society of America, 108 (3), 924-933 (2000).
3. Niklasson, A.J., Datta, S.K. and Dunn, M.L. On ultrasonic guided waves in a thin anisotropic layer lying between two isotropic layers. Journal of Acoustic Society of America, 108 (5), 2005-2011 (2000).
4. Benveniste, Y. A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media. Journal of Mechanics and Physics of Solids, 54, 708-734 (2006).
5. Ting, T.C.T. Mechanics of a thin anisotropic elastic layer and a layer that is bonded to an anisotropic elastic body or bodies. Proceedings of the Royal Society of London A, 463, 2223-2239 (2007).
6. Ting, T.C.T. Green's functions for a half-space and two half-spaces bonded to a thin anisotropic elastic layer. Journal of Applied Mechanics, 75, 051103 (2008).
7. Benveniste, Y. An O(hn) interface model of a three-dimensional curved interphase in conduction phenomena. Proceedings of the Royal Society of London A, 462, 1593-1617 (2006).
8. Stroh, A.N. Steady state problems in anisotropic elasticity. Journal of Mathematical Physics, 4, 77-103 (1962).
9. Ingebrigtsen, K.A. and Tonning, A. Elastic surface waves in crystal. Physics Review, 184, 942-951 (1969).
10. Barnett, D.M. and Lothe, J. Synthesis of the sextic and the integral formalism for dislocations, Greens function and surface waves in anisotropic elastic solids. Physica Norvegica, 7, 13-19 (1973).
11. Barnett, D.M. and Lothe, J. Consideration of the existence of surface wave (Rayleigh wave) solutions in anisotropic elastic crystals. Journal of Physics F: Metal Physics, 4, 671-686 (1974).
12. Chadwick, P. and Smith, G.D. Foundations of the theory of surface waves in anisotropic elastic materials. Advances in Applied Mechanics, 17, 303-376 (1977).
13. Barnett, D.M. and Lothe, J. The existence of Rayleigh (surface) wave solutions in anisotropic elastic half-spaces, in Modern Problems in Elastic Wave Propagation, ed. J. Miklowitz and J. D. Achenbach, pp. 445-457, Wiley, New York, 1978.
14. Barnett, D.M. and Lothe, J. Free surface (Rayleigh) waves in anisotropic elastic half-spaces: The surface impedance methods. Proceedings of the Royal Society of London A, 402, 135-152 (1985).
15. Ting, T.C.T. Anisotropic Elasticity: Theory and Applications, Oxford University Press, New York, 1996.
16. Ting, T.C.T. Some identities and the structure of Ni in the Stroh formalism of anisotropic elasticity. Quarterly of Applied Mathematics,. 46, 109 - 120 (1988).
17. Nayfeh, A.H. Wave Propagation in Layered Anisotropic Media. North-Holland, Amsterdam, 1995.
18. Ting, T.C.T. and Chadwick, P. Harmonic waves in periodically layered anisotropic elastic composites. In Symposium on Wave Propagation in Structures Composites, ed. A. K. Mal and T. C. T. Ting, Vol. 90, pp. 69-79, ASME, New York, 1988.
19. Shuvalov, A.L.: On the theory of wave propagation in anisotropic plates. Proceedings of the Royal Society of London A, 456, 2197-2222 (2000).
20. Gilbert, F. and Backus, G.E. Propagator matrices in elastic wave and vibration problems. Geophysics, 31, 326-332 (1966).
21. Peace, M.C. III. Methods of Matrix Algebra. Academic Press, New York, 1965.
22. Shuvalov, A.L. and Every, A.G. Some properties of surface acoustic waves in anisotropic-coated solids, studied by the impedance method. Wave Motion, 36, 257-273 (2002).
23. Bovik, P. A comparison between the Tiersten model and O(H) boundary conditions for elastic surface waves guided by thin layers. Journal of Applied Mechanics, 63, 162-167 (1996).
24. Barnett, D.M., Gavazza, S.D. and Lothe, J. Slip waves along the interface between two anisotropic elastic half-spaces in sliding contact. Proceedings of the Royal Society of London A, 415, 389-1419 (1988).
25. Ting, T.C.T. Dispersion equations for steady waves in an anisotropic elastic plate or a layered plate. Proceedings of the Royal Society of London A, 464 (2091), 613-629 (2008).
26. Barnett, D.M., Lothe, J., Musgrave, M.J.P., and Gavazza, S.D. Interfacial (Stoneley) waves in bonded anisotropic elastic half-spaces. Proceedings of the Royal Society of London A, 402, 153-166 (1985).
27. Ting, T.C.T. Existence of one-component Rayleigh waves, Stoneley waves, Love waves, slip waves and one-component waves in a plate or a layered plate. Journal of Mechanics of Materials and Structures, in press (2008).