Analysis of nonlinear harmonic generation for arbitrary dual frequency transducer excitation

Abstract

An earlier study of finite amplitude axisymmetric sound beams [J. H. Ginsberg, J. Acoust. Soc. Am. Suppl. 1 73, S83 (1983)] considered the case of monochromatic excitation. That work featured a singular perturbation analysis combining asymptotic integration and the renormalization version of the method of strained coordinates. The present paper initiates an extension of those techniques to the case of a dual frequency source. The parametric array, in which the primary beams are at closely spaced frequencies, has already received much attention. The system discussed here permits disparate frequencies. Aside from a restriction to axisymmetry, the excitation at each frequency is arbitrary. The analysis thus far has obtained the first two orders of approximation for the velocity potential. This expression describes the manner in which nonlinear effects accumulate for the various sum and difference frequencies. It is the foundation for a future derivation of an expression for the pressure that is descriptive of the entire field. In addition, the trend for harmonic generation indicated by the analysis suggests that conversion efficiency in the parametric array might be improved by altering the transverse vibration pattern of the individual primary beams. [Work supported by ONR, code 425-UA.]