Radiation and scattering of waves on an elastic half-space; a non-commutative matrix Wiener-Hopf problem

Journal of the Mechanics and Physics of Solids

Volumn 44, Issue 12, 1996, Pages 2125-2154

  Abrahams, I D ^a  

^a KEELE UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; ELASTICITY; MATRIX ALGEBRA; WAVE TRANSMISSION;

ELASTIC WAVE RADIATION;

ELASTIC WAVES;

EID: 0030403727     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(96)00064-6     Document Type: Article

References (22)

1. Abrahams, I. D. (1996a) On the solution of Wiener-Hopf problems involving non-commutative matrix kernel decompositions. SIAM J. Appl. Math., to be published.
2. Abrahams, I. D. (1996b) An approximate factorization technique for scalar and matrix Wiener-Hopf kernels. Proc. Roy. Soc. Lond. A., submitted.
3. Abrahams, I. D. and Lawrie, J. B. (1995) On the factorization of a class of Wiener-Hopf kernels. IMA J. Appl. Math. 55, 35-47.
4. Abrahams, I. D. and Wickham, G. R. (1992) Scattering of elastic waves by a small inclined surface breaking crack. J. Mech. Phys. Solids 40, 1707-1733.
5. Achenbach, J. D. and Gautesen, A. K. (1977) Elastodynamic stress intensity factors for a semi-infinite crack under 3-D loading. J. Appl. Mech. 44, 243-249.
6. Atkinson, C. (1977) Dynamic crack problems in dissimilar media. Mechanics of Fracture 4 (ed. G. C. Sih), pp. 213-248. Noordhoff, Leyden.
7. Baker, G. A. Jr. (1975) Essentials of Padé Approximants. Academic Press, New York.
8. Bedford, A. and Drumheller, D. S. (1994) Elastic Wave Propagation. Wiley, Chichester.
9. Crighton, D. G., Dowling, A. P., Ffowcs Williams, J. E., Heckl, M. and Leppington, F. G. (1992) Modern Methods in Analytical Acoustics. Springer Verlag, London.
10. de Hoop, A. T. (1962) A modification of Cagniard's method for solving seismic pulse problems. Appl. Sci. Res. B8, 349-356.
11. Freund, L. B. (1993) Dynamic Fracture Mechanics. Cambridge University Press, Cambridge.
12. Green, A. E. and Zerna, W. (1954) Theoretical Elasticity. Clarendon Press, Oxford.
13. Khrapkov, A. A. (1971) Certain cases of the elastic equilibrium of an infinite wedge with a non-symmetric notch at the vertex, subjected to concentrated forces. Appl. Math. Mech. (P M M) 35, 625-637.
14. Lawrie, J. B. and Abrahams, I. D. (1994) Acoustic radiation from two opposed semi-infinite coaxial cylindrical waveguides. II : Separated ducts. Wave Motion 19, 83-109.
15. Movchan, A. B. and Willis, J. R. (1995) Dynamic weight-functions for a moving crack, 2. Shear loading. J. Mech. Phys. Solids 43, 1369-1383.
16. Muskhelishvili, N. I. (1953) Some basic Problems of the Mathematical Theory of Elasticity, 3rd. edn. Noordhoff, Leyden.
17. Noble, B. (1988) Methods Based on the Wiener-Hopf Technique, 2nd. edn. Chelsea, New York.
18. Rawlins, A. D. (1975) The solution of a mixed boundary value problem in the theory of diffraction by a semi-infinite plane. Proc. Roy. Soc. Lond. A 346, 469-484.
19. Wickham, G. R. (1977) The forced two dimensional oscillations of a rigid strip in smooth contact with a semi-infinite elastic solid. Proc. Camb. Phil. Soc. 81, 291-311.
20. Wickham, G. R. (1980) Short-wave radiation from a rigid strip in smooth contact with a semi-infinite elastic solid. Quart. J. Mech. Appl. Math. 33, 409-433.
21. Wickham, G. R. (1995) Mode conversion, corner singularities and matrix Wiener-Hopf factorization in diffraction theory. Proc. Roy. Soc. Lond. A 451, 399-423.
22. Zhang, B. and Abrahams, I. D. (1995) The radiation of sound from a finite ring-forced cylindrical elastic shell. I : Wiener-Hopf analysis. Proc. Roy. Soc. Lond. A 450, 89-108.