An explicit expression for the surface-impedance tensor of a compressible monoclinic material in a state of plane strain

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 71, Issue 3, 2006, Pages 434-445

  Fu, Y B ^a   Brookes, D W ^a  

^a KEELE UNIVERSITY   (United Kingdom)

Author keywords

Anisotropic elasticity; Interfacial waves; Stroh formalism; Surface waves; Surface impedance tensor

Indexed keywords

BIFURCATION (MATHEMATICS); COMPRESSIBILITY; STRAIN; SURFACE WAVES; TENSORS;

ANISOTROPIC ELASTICITY; INTERFACIAL WAVES; SURFACE-IMPEDANCE TENSOR;

ELASTICITY;

EID: 33748063620     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxh106     Document Type: Article

References (37)

1. Barnett, D. M., Gavazza, S. D. & Lothe, J. (1988) Slip waves along the interface between two anisotropic elastic half-spaces in sliding contact. Proc. R. Soc. Lond. A, 415, 389-419.
2. Barnett, D. M. & Lothe, J. (1973) Synthesis of the sextic and the integral formalism for dislocations, Greens function and surface waves in anisotropic elastic solids. Phys. Norv., 7, 13-19.
3. Barnett, D. M. & Lothe, J. (1985) Free surface (Rayleigh) waves in anisotropic elastic half-spaces: The surface impedance method. Proc. R. Soc. Lond. A, 402, 135-152.
4. Barnett, D. M., Lothe, J., Gavazza, S. D. & Musgrave, M. J. P. (1985) Considerations of the existence of interfacial (Stoneley) waves in bonded anisotropic elastic half-spaces. Proc. R. Soc. Lond. A, 402, 153-166.
5. Biryukov, S. V. (1985) Impedance method in the theory of elastic surface waves. Soy. Phys. Acoust., 31, 350-354.
6. Biryukov, S. V., Gulyaev, Y. V., Krylov, V. V. & Plessky, V. P. (1995) Surface Acoustic Waves in Inhomogeneous Media. Berlin: Springer.
7. Bronshtein, I. N. & Semendyayev, K. A. (1997) Handbook of Mathematics (translated by K. A. Hirsch). Berlin: Springer.
8. Chadwick, P. (1989) Wave propagation in transversely isotropic elastic media II. Surface waves. Proc. R. Soc. Lond. A, 422, 67-101.
9. Chadwick, P. & Ogden, R. W. (1971) On the definition of elastic moduli. Arch. Ration. Mech. Anal., 44, 41-53.
10. Chadwick, P. & Smith, G. D. (1977) Foundations of the theory of surface waves in anisotropic elastic materials. Adv. Appl. Mech., 17, 303-376.
11. Chadwick, P. & Wilson, N. J. (1992a) The behaviour of elastic surface waves polarized in a plane of material symmetry II. Monoclinic media. Proc. R. Soc. Lond. A, 438, 207-223.
12. Chadwick, P. & Wilson, N. J. (1992b) The behaviour of elastic surface waves polarized in a plane of material symmetry III. Orthorhombic and cubic media. Proc. R. Soc. Lond. A, 438, 225-247.
13. Destrade, M. (2001) The explicit secular equation for surface acoustic waves in monoclinic elastic crystals. J. Acoust. Soc. Am., 109, 1398-1402.
14. Destrade, M. & Fu, Y. B. (2005) The speed of interface waves for monoclinic materials. Int. J. Eng. Sci. (submitted).
15. Dongye, C. & Ting, T. C. T. (1989) Explicit expressions of Barnett-Lothe tensors and their associated tensors for orthotropic materials. Q. Appl. Math., 47, 723-734.
16. Dowaikh, M. A. & Ogden, R. W. (1991) Interfacial waves and deformations in pre-stressed elastic media. Proc. R. Soc. Lond. A, 433, 313-328.
17. Fu, Y. B. (2005) An explicit expression for the surface-impedance matrix of a generally anisotropic incompressible elastic material in a state of plane strain. Int. J. Nonlinear Mech., 40, 229-239.
18. Fu, Y. B. & Freidin, A. B. (2004) Characterization and stability of two-phase piecewise-homogeneous deformations. Proc. R. Soc. Lond. A, 460, 3065-3094.
19. Fu, Y. B. & Mielke, A. (2002) A new identity for the surface-impedance matrix and its application to the determination of surface-wave speeds. Proc. R. Soc. Lond. A, 458, 2523-2543.
20. Ingerbrigtsen, K. A. & Tonning, A. (1969) Elastic surface waves in crystals. Phys. Rev., 184, 942-951.
21. Lothe, J. & Barnett, D. M. (1976) On the existence of surface wave solutions for anisotropic half-spaces with free surface. J. Appl. Phys., 47, 428-433.
22. Maznev, A. A. & Every, A. G. (1997) Time-domain dynamic surface response of an anisotropic elastic solid to an impulsive line force. Int. J. Eng. Sci., 35, 321-327.
23. Mielke, A. & Fu, Y. B. (2003) Uniqueness of the surface-wave speed: A proof that is independent of the Stroh Formalism. Math. Mech. Solids, 9, 5-15.
24. Mielke, A. & Sprenger, P. (1998) Quasiconvexity at the boundary and a simple variational formulation of Agmon's condition. J. Elast., 51, 23-41.
25. Nakamura, G. & Tanuma, K. (1997) A formula for the fundamental solution of anisotropic elasticity. Q. J. Mech. Appl. Math., 50, 179-194.
26. Simpson, H. C. & Spector, S. J. (1989) Necessary conditions at the boundary for minimizers in finite elasticity. Arch. Ration. Mech. Anal., 107, 105-125.
27. Simpson, H. C. & Spector, S. J. (1991) Some necessary conditions at an internal boundary for minimizers in finite elasticity. J. Elast., 26, 203-222.
28. Stroh, A. N. (1958) Dislocations and cracks in anisotropic elasticity. Philos. Mag., 3, 625-646.
29. Stroh, A. N. (1962) Steady state problems in anisotropic elasticity. J. Math. Phys., 41, 77-103.
30. Suo, Z. (1990) Singularities, interfaces and cracks in dissimilar anisotropic media. Proc. R. Soc. Lond. A, 427, 331-358.
31. Tanuma, K. (1996) Surface-impedance tensors of transversely isotropic elastic materials. Q. J. Mech. Appl. Math., 49, 29-48.
32. Tanuma, K., Man, C.-S., Huang, M.-J. & Nakamura, G. (2002) Surface impedance tensors of textured polycrystals. J. Elast., 67, 131-147.
33. 3 = 0. J. Elast., 27, 143-165.
34. Ting, T. C. T. (1996) Anisotropic Elasticity: Theory and Applications. New York: Oxford University Press.
35. Ting, T. C. T. (1997) New explicit expression of Barnett-Lothe tensors for anisotropic linear elastic materials. J. Elast., 47, 23-50.
36. Ting, T. C. T. & Lee, V.-G. (1997) The three-dimensional elastostatic Green's function for general anisotropic linear elastic solids. Q. J. Mech. Appl. Math., 50, 407-426.
37. Wu, K.-C. (2000) Extension of Stroh's formalism to self-similar problems in two-dimensional elastodynamics. Proc. R. Soc. Lond. A, 456, 869-890.