Eigenvalue of a semi-infinite elastic strip

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 462, Issue 2068, 2006, Pages 1255-1270

  Zernov, V ^a,c   Pichugin, A V ^b   Kaplunov, J ^a,c  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b UNIVERSITY OF SHEFFIELD   (United Kingdom)

^c BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

Edge resonance; Semi infinite strip; Vibration

Indexed keywords

EID: 33748083255     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2005.1615     Document Type: Article

References (23)

1. Auld, B. A. & Tsao, E. M. 1977 A variational analysis of edge resonance in a semi-infinite plate. IEEE Trans. Sonics Ultrason. 24, 317-320.
2. Gazis, D. G. & Mindlin, R. D. 1960 Extensional vibrations and waves in a circular disk and a semi-infinite plate. J. Appl. Mech. 27, 541-547.
3. Graff, K. F. 1991 Wave motion in clastic solids. New York: Dover.
4. Gregory, R. D. & Gladwell, J. 1983 The reflection of a symmetric Rayleigh-Lamb wave at the fixed or free edge of a plate. J. Elast. 13, 185-206. (doi:10.1007/BF00043002)
5. Grinchenko, V. T. & Meleshko, V. V. 1981 Harmonic oscillations and waves in elastic bodies. Kiev: Nankova Dumka. [In Russian.]
6. Kamotskii, I. V. & Nazarov, S. A. 1999b Wood's anomalies and surface waves in the problem of scattering by a periodic boundary, II. Sb. Math. 190, 111-141. (doi:10.1070/ SM1999v100n02ABEH000379)
7. Kamotskii, I. V. & Nazarov, S. A. 1999b Wood's anomalies and surface waves in the problem of scattering by a periodic boundary, II. Sb. Math. 190, 205-231. (doi:10.1070/ SM1999v190n02ABEH000383)
8. Kamotskii, I. V. & Nazarov, S. A. 2002 An augmented scattering matrix and exponentially decreasing solutions of an elliptic problem in a cylindrical domain. J. Math. Sci. 111, 3657-3666. (doi:10.1023/A:101G377707919)
9. Kaplunov, J. D., Kossovich, L. Y. & Wilde, M. V. 2000 Free localized vibrations of a semi-infinite cylindrical shell. J. Acoust. Soc. Am. 107, 1383-1393. (doi:10.1121/1.428426)
10. Kirrmann, P. 1995 On the completeness of Lamb modes. J. Elast. 37, 39-69. (doi:10.1007/ BF00043418)
11. Kostyuchenko, A. G. & Orazov, M. B. 1977 The completeness of root vectors in certain self-adjoint quadratic bundles. Funct. Anal. Appl. 11, 317-319. (doi:10.1007/BF01077154)
12. Kovalenko, M. D. 1992 Biorthogonal expansions in the first fundamental problem of elasticity theory. J. Appl. Math. Mech. 55, 836-843. (doi:10.101G/0021-8928(91)9013G-I)
13. Lamb, H. 1917 On waves in an elastic plate. Proc. R. Soc. A 93, 114-128.
14. Le Clézio, E., Predoi, M. V., Castaings, M., Hosten, B. & Rousseau, M. 2003 Numerical predictions and experiments on the free-plate edge mode. Ultrasonics 41, 25-40. (doi:10.1016/S0041-624X(02)00391-8)
15. Markenscoff, X. & Paukshto, M. 1998 The Cosserat spectrum in the theory of elasticity and applications. Proc. R. Soc. A 454, 631-643. (doi:10.1098/rspa.l998.0177)
16. Mindlin, R. D. & Onoe, M. 1957 Mathematical theory of vibrations of elastic plates. Proc. 11th Ann. Symp. Freq. Cont, pp. 17-40. Monmouth, NJ: US Army Signal Engineering Labs.
17. Nazarov, S. A. & Plamenevsky, B. A. 1994 Elliptic problems in domains with piecewise smooth boundaries. Berlin: Walter de Grnytcr fe Co.
18. Roitberg, I., Vassiliev, D. & Weidl, T. 1998 Edge resonance in an elastic semi-strip. Q. J. Mech. Appl. Math. 51, 1-13. (doi:10.1093/qjmam/51.1.1)
19. Shaw, E. A. G. 1956 On the resonant vibrations of thick barium titanate disks. J. Acoust. Soc. Am. 28, 38-50. (doi:10.1121/1.1908218)
20. Torvik, P. J. 1967 Reflection of wave trains in semi-infinite plate. J. Acoust. Soc. Am. 41, 346-353. (doi:10.1121/1.1910344)
21. Ustinov, I. A. & Iudovich, V. I. 1973 On the completeness of a system of elementary solutions of the biharmonic equation in a semi-strip. J. Appl. Math. Mech. 37, 665-674. (doi:10.1016/0021-8928(73)90116-0)
22. Veksler, N. D. 1993 Resonance acoustic spectroscopy. Berlin: Springer.
23. Wilde, M. V. 2004 D.Sc. thesis, Saratov State University. [In Russian.]