Coupling of sound and structural vibrations

  • C. Kauffmann
Part of the Mathematics and Its Applications book series (MAIA, volume 81)


Vibrational properties of hull plates of ships are considerably modified by the presence of the water. A simple model problem is presented that accounts for the fluid-loading, i.e. the coupling of the plate’s flexural vibrations and the acoustic field in the fluid. This model, consisting of a thin, transversely vibrating plate with a compressible fluid at one side and excited by a time-harmonic load, is analyzed in some detail. The model equations are solved by means of a Green integral representation along with a set of coupled boundary integral equations. The kernel of the integral representation is found by using the Fourier integral transform technique and by evaluating numerically the inverse transform in the complex wavenumber plane. For the two-dimensional case the boundary integral equations degenerate to a system of algebraic equations, thus yielding an exact representation for the solution. Numerical results show the fluid-loading effect on the resonance frequencies of the plate, which are shifted downwards relative to the in vacuo natural frequencies, while acoustic radiation contributes to the damping of the plate’s resonant modes.


Acoustic Field Acoustic Pressure Acoustic Radiation Structural Vibration Infinite Plate 
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General introductory literature on acoustics and structural vibrations

  1. 1.
    J.W. Strutt Lord Rayleigh The Theory of Sound (Dover, New York, 1945), second edition, Vols. I and II.Google Scholar
  2. 2.
    P.M. Morse and K.U. Ingard Theoretical Acoustics (McGraw-Hill, New York, 1968, reprint: Princeton University Press, 1986).Google Scholar
  3. 3.
    L. Cremer and M. Heckl Structure-Borne Sound (Berlin, Springer, 1988), second edition.Google Scholar
  4. 4.
    A.D. Pierce Acoustics: an introduction to its physical principles and applications (McGraw-Hill, New York, 1981, reprint: Acoustical Society of America/American Institute of Physics, 1989).Google Scholar

Specific literature on fluid-loaded plates and shells

  1. 5.
    M.C. Junger and D. Feit Sound Structures and Their Interaction (Cambridge MA, MIT-press, 1986), second edition.Google Scholar
  2. 6.
    D.G. Crighton The 1988 Rayleigh medal lecture: fluid-loading — the interaction between sound and vibration J. Sound Vib. 133 1–27 (1989).MathSciNetCrossRefGoogle Scholar
  3. 7.
    P.R. Nayak Line admittance of infinite isotropic fluid-loaded plates J. Acoust. Soc. Am. 47 191–201 (1970).CrossRefGoogle Scholar
  4. 8.
    D.G. Crighton The free and forced waves on a fluid-loaded elastic plate J. Sound Vib. 62 225–235 (1979).CrossRefGoogle Scholar
  5. 9.
    D. Feit and Y.N. Liu The nearfield response of a line-driven fluid-loaded plate J. Acoust. Soc. Am. 78 763–766 (1985).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1992

Authors and Affiliations

  • C. Kauffmann
    • 1
  1. 1.Faculty of Technical Mathematics and InformaticsDelft University of TechnologyDelftThe Netherlands

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