Ds. Ding et al., SIMPLE CALCULATION APPROACH FOR THE 2ND-HARMONIC SOUND FIELD GENERATED BY AN ARBITRARY AXIAL-SYMMETRICAL SOURCE, The Journal of the Acoustical Society of America, 100(2), 1996, pp. 727-733
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 super
position of this set of Gaussian beams. The analysis is extended to th
e second harmonic generation due to nonlinear effects under a quasilin
ear approximation, then the second harmonic sound field could be consi
dered as a sum of self- and cross-interaction terms produced by a seri
es of Gaussian beams. Therefore, the calculation of the second harmoni
c 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 pi
ston source is examined, and the result is in good agreement with that
in earlier paper by complicated computation. (C) 1996 Acoustical Soci
ety of America.