On the vibration problem for an elastic body surrounded by a slightly compressible fluid

R. Ohayon; E. Sanchez-Palencia

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1983)

  • Volume: 17, Issue: 3, page 311-326
  • ISSN: 0764-583X

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Ohayon, R., and Sanchez-Palencia, E.. "On the vibration problem for an elastic body surrounded by a slightly compressible fluid." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 17.3 (1983): 311-326. <http://eudml.org/doc/193420>.

@article{Ohayon1983,
author = {Ohayon, R., Sanchez-Palencia, E.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {elastic bounded body; immersed in ideal fluid; small compressibility; scattering frequencies converge as epsilon -> 0 to eigenfrequencies of selfadjoint problem; incompressible fluid; asymptotic behaviour; implicit function theorem; scattering theory},
language = {eng},
number = {3},
pages = {311-326},
publisher = {Dunod},
title = {On the vibration problem for an elastic body surrounded by a slightly compressible fluid},
url = {http://eudml.org/doc/193420},
volume = {17},
year = {1983},
}

TY - JOUR
AU - Ohayon, R.
AU - Sanchez-Palencia, E.
TI - On the vibration problem for an elastic body surrounded by a slightly compressible fluid
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1983
PB - Dunod
VL - 17
IS - 3
SP - 311
EP - 326
LA - eng
KW - elastic bounded body; immersed in ideal fluid; small compressibility; scattering frequencies converge as epsilon -> 0 to eigenfrequencies of selfadjoint problem; incompressible fluid; asymptotic behaviour; implicit function theorem; scattering theory
UR - http://eudml.org/doc/193420
ER -

References

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  2. [2] S. CERNEAU and E. SANCHEZ-PALENCIA, Sur les vitrations libres des corps élastiquesplongés dans les fluides, Jour. Méca., 15(1976), pp. 399-425. Zbl0332.76058MR428884
  3. [3] T. KATO, Perturbation theory for linear operators, Springer, Berlin (1966). Zbl0148.12601
  4. [4] K. KNOPP, Theory offunctions, Part II, Dover, New-York. 
  5. [5] R. KRESS, On the limiting behaviour of solutions to intégral équations associatedwith time harmonie wave équations for small frequencies, Math. Meth. Appl. Sci.7 (1979), pp. 89-100. Zbl0418.35031MR548408
  6. [6] G. HACHEM, Sur les fréquences de diffusion(scattering) d'un corps élastique coupléavec l'air, Anna. Fac. Sci. Toulouse, 2 (1980), pp. 193-218. Zbl0481.35070MR614012
  7. [7] P. LAX and R. PHILLIPS, Scattering theory, cad. Press, New-York (1967). Zbl0186.16301MR217440
  8. [8] H. MORAND and R. OHAYON, Substructure variational analysis of the vibrations ofcoupled fluid-structure Systems. Finite element results, Int. J. for Num. Meth. inEngng., 14 (1979), pp. 741-755. Zbl0402.73052
  9. [9] B. NICOLAS-VULLIERME, R. OHAYON, R. VALID, Vibrations harmoniques de struc-tures élastiques immergées dans unliquide, 81e session A.T.M.A., Paris (mai 1981), T. P.,O.N.E.R.A., n° 1981-40. 
  10. [10] R. OHAYON, R. VALID, True symmetrie formulations offree vibrations of fluid-structure interaction, Proc. Int.Conf. on Num. Meth. forCoupled Problems. Univ.of Swansea (sept. 1981) T.P., O.N.E.R.A., n° 1981-78. 
  11. [11] E. SANCHEZ-PALENCIA, Non homogeneous media and vibration theory, Lect. Notes Phys., 127, Springer, Berlin (1980). Zbl0432.70002
  12. [12] V. I. SMIRNOV, A course ofhigher mathematics, vol. IV,Pergamon, Oxford (1964). 
  13. [13] S. STEINBERG, Meromorphic families of compact operators, Arch. Rat.Mech. Anal.,31 (1968), pp. 372-379. Zbl0167.43002MR233240
  14. [14] T. C. Su, The effect ofviscosïty onfree vibrations of submerged fluid-fïlled sphericalshells, Jour. Sound Vibr., 77(1981), pp. 101-126. Zbl0477.73051

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