Czech Technical University in Prague, Faculty of Electrical Engineering, Technicka 2, 166 27 Prague 6, Czech Republic.
J Acoust Soc Am. 2013 Aug;134(2):933-8. doi: 10.1121/1.4813223.
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.
本研究关注具有特殊重点的任意轴对称平面源的参数辐射，即低频差频场。作为一个考虑非线性、衍射和耗散的模型方程，采用了 Westervelt 方程。通过逐次逼近法，在准线性近似下计算差频场模式。通过使用多高斯光束展开对主场进行近似解析描述，将用于计算声场的多层积分简化为三维积分。随后，在傍轴近似下，将该积分简化为一维形式，该形式以前已在文献中发表，代表了快速计算次级声场的一种手段。三维积分通过数值计算得到，数值结果预测了在源附近低频场的非零幅度，这是傍轴近似无法正确包含的一种效应。
