Propagation of elastic surface waves along a cylindrical cavity of arbitrary cross section

A. Bamberger; P. Joly; M. Kern

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1991)

  • Volume: 25, Issue: 1, page 1-30
  • ISSN: 0764-583X

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Bamberger, A., Joly, P., and Kern, M.. "Propagation of elastic surface waves along a cylindrical cavity of arbitrary cross section." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 25.1 (1991): 1-30. <http://eudml.org/doc/193619>.

@article{Bamberger1991,
author = {Bamberger, A., Joly, P., Kern, M.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {existence of hierarchy of guided modes; free surface; infinitely long cylinder; eigenvalue problem; unbounded selfadjoint operator},
language = {eng},
number = {1},
pages = {1-30},
publisher = {Dunod},
title = {Propagation of elastic surface waves along a cylindrical cavity of arbitrary cross section},
url = {http://eudml.org/doc/193619},
volume = {25},
year = {1991},
}

TY - JOUR
AU - Bamberger, A.
AU - Joly, P.
AU - Kern, M.
TI - Propagation of elastic surface waves along a cylindrical cavity of arbitrary cross section
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1991
PB - Dunod
VL - 25
IS - 1
SP - 1
EP - 30
LA - eng
KW - existence of hierarchy of guided modes; free surface; infinitely long cylinder; eigenvalue problem; unbounded selfadjoint operator
UR - http://eudml.org/doc/193619
ER -

References

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  1. [1] M. ABRAMOWITZ, I. STEGUN, Handbook of mathematical functions Dover publications (1968) 
  2. [2] A. R. ADAMS, Sobolev spaces Academic Press (1975) Zbl0314.46030MR450957
  3. [3] A. BAMBERGER, A. S. BONNET, Calcul des modes guidés d'une fibre optique Analyse numérique Report n° 143, CMAP, Ecole Polytechnique (1986) 
  4. [4] A. BAMBERGER, Y. DERMENJIAN, P. JOLY, « Mathematical Analysis of the Propagation of Elastic Guided Waves in Heterogeneous Media », INRIA Report n° 1013 (1989) to appear in Journal of Differential Equations (1990) Zbl0714.35045MR1079862
  5. [5] A. BAMBERGER, P. JOLY, M. KERN, Etude mathématique des modes élastiques guidés par l'extérieur d'une cavité cylindrique de section arbitraire Report n° 650, INRIA (1987) Zbl0617.73029
  6. [6] A. BAMBERGER, P. JOLY, M. KERN, Propagation d'ondes élastiques guidées par la surface d'une cavité cylindrique de section arbitraire CRAS, Paris, série I, t 504, n° 3, pp 59-62 (1987) Zbl0617.73029MR878826
  7. [7] M. BIOT, Propagation of elastic waves in a liquid filled cylindrical bore surrounded by an elastic solid J Appl Physics, 24, pp 515-521 (1953) Zbl0053.31804MR55893
  8. [8] A. BOSTROM, A. D. BURDEN, Propagation of elastic surface waves and their excitation by a point force J Acoust Soc Amer, 72, pp 998-1004 (1982) 
  9. [9] A. D. BURDEN, The propagation of elastic surface waves along cylindrical cavities of general cross section Wave Motion, 7, pp 153-168 (1985) Zbl0553.73015
  10. [10] R. COURANT, D. HILBERT, Methods of Mathematical Physics. Vol. I, Wiley (1962). Zbl0729.00007MR1013360
  11. [11] Y. DERMENJIAN, J. C. GUILLOT, Scattering of elastic waves in a perturbed isotropic half-space with a free boundary. The limiting absorption principle. Report n° 491, INRIA (1986). Zbl0647.73011
  12. [12] N. DUNFORD, J. T. SCHWARTZ, Linear operators. Vol. II, Wiley (1963). 
  13. [13] P. JOLY, Analyse numérique des ondes de Rayleigh. 3rd cycle Thesis, University Paris IX (1983). 
  14. [14] P. E. LAGASSE, Higher order finite element analysis of topographic guides supporting elastic surface waves. J. Acoust. Soc. Amer., 53, pp. 1116-1122 (1973). 
  15. [15] P. E. LAGASSE, I. M. MASON, E. A. ASH, Acoustic surface wave guides. Analysis and assessment. IEEE Trans. Microwave Theory Tech. 21, pp. 225-236 (1973). 
  16. [16] D. MARCUSE, Theory of dielectric optical waveguides. Academic Press (1974). 
  17. [17] J. MIKLOWITZ, The theory of elastic waves and waveguides. North-Holland (1980). Zbl0565.73025MR515886
  18. [18] I. A. MINDLIN, Free elastic waves on the surface of a tube of infinite thickness. J. Appl. Math. Mech., 27, pp. 823-828 (1963). Zbl0127.41502
  19. [19] J. A. MORRISON, Propagation of high frequency surface waves along cylinders of general cross section. J. Math. Phys., 16, pp. 1786-1794 (1975). Zbl0309.73025MR381436
  20. [20] J. A. NITSCHE, On Korn's second inequality. RAIRO Analyse Numérique, 15, pp. 237-248 (1981). Zbl0467.35019MR631678
  21. [21] Lord RAYLEIGH, On waves propagating along the plane surface of an elastic solid. Proc. London Math. Soc., 17, p. 411 (1885). JFM17.0962.01
  22. [22] M. REED, B. SIMON, Methods of modern mathematical physics. Academic Press (1981). Zbl0459.46001
  23. [23] F. RELLICH, Uber das asymptotiche Verhalten der Lösungen von Δu + ku = 0 in unendlichen Gebieten. Jber. Deutsche Math. Verein., 53, pp. 57-64 (1943). Zbl0028.16401MR17816
  24. [24] F. SANTOSA, On the solution of elastodynamics problems for infinite cylinders. Report ONR/SRO, Cornell University (1986). 
  25. [25] M. SCHECHTER, Operator methods in quantum mechanics. North Holland (1981). Zbl0456.47012MR597895
  26. [26] SCHULENBERGER, Elastic waves in the half-space R2+. J. Diff. Eq., 29, pp. 405-438 (1978). Zbl0404.35066MR507488
  27. [27] J. WEIDMAN, Linear operators in Hilbert Spaces. Springer (1981). Zbl0434.47001
  28. [28] C. H. WILCOX, Scattering theory for the d'Alembert equation in unbounded domains. Lecture Notes in Mathematics No. 442, Springer (1975). Zbl0299.35002MR460927
  29. [29] L. O. WILSON, J. A. MORRISON, Propagation of high frequency elastic surface waves along cylinders of general cross section. J. Math. Phys., 16, pp. 1795-1805 (1975). Zbl0313.73020MR381437

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