Asymptotic Analysis of Higher Order Peripheral Modes in Acoustic Wave Scattering by an Elastic Cylinder or Sphere

  • J. Kaplunov
  • V. Kovalev
  • M. Wilde
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 113)


Higher order partial modes are studied in the case of harmonic scattering of plane acoustic waves by an elastic cylinder or sphere. Short-wavelength asymptotic models are developed for localized Rayleigh and whispering gallery peripheral waves and non-localized distortion peripheral waves. Approximate formulae are obtained including local estimations for resonant curves. An asymptotic classification is proposed for modal resonances. Comparison with exact solutions is presented.


Asymptotic scattering Rayleigh whispering gallery elastic cylinder sphere 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Babich, V M and V.S. Buldyrev, V S (1991) Short-wavelength di raction theory. Asymptotic methods. Berlin: Springer-Verlag.Google Scholar
  2. [2]
    Kaplunov, J D, Kossovich, L Yu and Nolde, E V (1998) Dynamics of thin walled elastic bodies. San Diego: Academic Press.Google Scholar
  3. [3]
    Kaplunov, J D and Kovalev, V A (2000) Approximation of the resonances of the Rayleigh wave in scattering of acoustic waves by elastic circular cylinders and spheres, Izv. Ross. Akad. Nauk. Mekhanika Tverdogo Tela, 35(4), 180–186 (Engl.transl.: Mechanics of Solids).Google Scholar
  4. [4]
    Olver, F W J (1974) Introduction to asymptotic and special functions. NY: Academic Press.Google Scholar
  5. [5]
    Veksler, N D (1993) Resonance acoustic spectroscopy. Berlin: Springer-Verlag.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • J. Kaplunov
    • 1
  • V. Kovalev
    • 2
  • M. Wilde
    • 3
  1. 1.Department of MathematicsThe University of ManchesterManchesterUK
  2. 2.Department of MathematicsMoscow State Academy of Device Building and Computer ScienceMoscowRussia
  3. 3.Department of Mathematical Elasticity and BiomechanicsSaratov State UniversitySaratovRussia

Personalised recommendations