Finite Amplitude Sound Beams Resulting from Nonlinear Vibration of a Circular Membrane Undergoing Axisymmetric Resonant Excitation

  • J. H. Ginsberg
Conference paper
Part of the IUTAM Symposia book series (IUTAM)

Summary

This paper analyses the interaction between a vibrating circular membrane contained in an infinite baffle and the resulting sound field radiated into a fluid medium contained in the half-space above the membrane. The case of resonant excitation of the membrane leads to nonlinear coupling between transverse and in-plane displacement. Nonlinearity within the fluid medium is described by a recent general treatment of finite amplitude sound beams resulting from boundary motion. The vibratory response of the membrane is evaluated in a perturbation technique based on the modes of free vibration. The results give amplitude-frequency relations for the plate that account for the inertial and damping impedances of the fluid, as well as expressions that may be solved for the pressure signal in the fluid.

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References

  1. 1.
    Ginsberg, J. H.: Nonlinear King integral for arbitrary axisymmetric sound beams at finite amplitudes. II. Derivation of uniformly accurate results. J. Acoust. Soc. Am. 76 (1984) 1208–1214.ADSMATHCrossRefGoogle Scholar
  2. 2.
    Chobotov, V. A. and Binder, R. C.: Nonlinear response of a circular membrane to sinusoidal excitation. J. Acoust. Soc. Am. 36 (1964) 59–73.ADSCrossRefGoogle Scholar
  3. 3.
    Bouwkamp, C. J.: A contribution to the theory of acoustic radiation. Phillips Research Reports 1 (1946) 251–277.MathSciNetGoogle Scholar

Copyright information

© Springer, Berlin Heidelberg 1986

Authors and Affiliations

  • J. H. Ginsberg
    • 1
  1. 1.School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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