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Application and Extension of an Analytical Model of the Confined Acoustic Beam Generated by a Transducer

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Final rept.

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The primary goal of this project was to develop an overall description of transducer radiation in which finite amplitude effects, diffraction, and spherical spreading are treated consistently, without limitation to a specific spatial domain or a specific type of input to the projector. Initially, the mathematical tools for this work were those used to develop the nonlinear King integral for nonlinear effects arising in the sound beam generated by a harmonic input. These techniques combined singular perturbation theory and asymptotic analysis of the behavior in specific domains. The general approach uses King integral in linear theory, which is a Fourier- Bessel integral transform, to develop the second order source terms that generate nonlinearities in the response. There are two kinds of nonlinear effects that arise at the second order. Some produce terms that remain bounded as the signal propagates. One such effect is associated with the fact that the input from the transducer originates from a moving boundary, rather than the much simpler description, z 0. The smallness of the acoustic Mach number leads to the conclusion that these fixed magnitude effects cannot account for measured levels of distortion. The other group of nonlinear effects arise from resonance-like phenomena. These terms lead to distortion that grows with increasing distance. Shocks ultimately form this effect, unless dissipation is adequate to overcome the nonlinear distortion process. It is this cumulative growth effect that needs to be evaluated.

Subject Categories:

  • Acoustic Detection and Detectors
  • Acoustics

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