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J Acoust Soc Am. 2013 Aug;134(2):933-8. doi: 10.1121/1.4813223.

Non-paraxial model for a parametric acoustic array.

Author information

1
Czech Technical University in Prague, Faculty of Electrical Engineering, Technicka 2, 166 27 Prague 6, Czech Republic. milan.cervenka@fel.cvut.cz

Abstract

This study is concerned with parametric radiation from an arbitrary axisymmetric planar source with a special focus on low-frequency difference-frequency fields. As a model equation accounting for nonlinearity, diffraction, and dissipation, the Westervelt equation is used. The difference-frequency-field patterns are calculated in the quasi-linear approximation by the method of successive approximations. A multi-layer integral for calculation of the acoustic field is reduced to a three-dimensional one by employing an approximate analytical description of the primary field with the use of a multi-Gaussian beam expansion. This integral is subsequently reduced in the paraxial approximation to a one-dimensional form which has previously been published in literature and which represents a means for fast calculations of secondary acoustic fields. The three-dimensional integral is calculated numerically and the numerical results predict nonzero amplitude of the low-frequency field in the vicinity of the source which is an effect that cannot be correctly encompassed in the paraxial approximation.

PMID:
23927092
DOI:
10.1121/1.4813223
[Indexed for MEDLINE]
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