Simple calculation approach for the second harmonic sound field generated by an arbitrary axial-symmetric source

In a linear approximation, an arbitrary axial-symmetric source can be expressed as the linear superposition of a set of Gaussian sources and the corresponding radiated sound held can be represented as the superposition of this set of Gaussian beams. The analysis is extended to the second harmonic generation due to nonlinear effects under a quasilinear approximation, then the second harmonic sound field could be considered as a sum of self- and cross-interaction terms produced by a series of Gaussian beams. Therefore, the calculation of the second harmonic sound field of an axial-symmetric source can be reduced to a simple linear combination of a set of exponential integral functions, instead of a complicated triple integral. In order to verify this calculation approach, the second harmonic generation of a focused and a simple piston source is examined, and the result is in good agreement with that in earlier paper by complicated computation. (C) 1996 Acoustical Society of America.