Nonlinear King integral for arbitrary axisymmetric sound beams at finite amplitude. II. Derivation of uniformly accurate expressions
Nonlinear King integral for arbitrary axisymmetric sound beams at finite amplitude. II. Derivation of uniformly accurate expressions
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有限振幅下任意轴对称声束的非线性 King 积分。
DOI：
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发表时间：
1984
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通讯作者：
J. Ginsberg
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作者：
J. Ginsberg
本研究的第一部分[J。美国社会76，1201-1207（1984）]导出了复变函数形式的轴对称单色声束速度势的微扰表示。该结果使用汉克尔变换来描述对横向位置的依赖性，在相应的波数以及距换能器的距离方面缺乏统一的有效性。从势导出的状态变量的表达式具有相同的行为。一个平面波的例子是用来适应奇异摄动法重整化的情况下，潜在的是在复杂的形式。由此产生的技术是用来获得一个坐标应变变换，使状态变量一致准确。压力的表达式类似于线性理论中的King积分，除了被积函数是应变坐标的函数。预测的波形特性与实验数据的比较[Gallego‐J.
The first part of this investigation [J. Acoust. Soc. Am. 76, 1201–1207 (1984)] derived a perturbation representation of the velocity potential for an axisymmetric, monochromatic sound beam in the form of a complex function. That result, which used Hankel transforms to describe the dependence on transverse position, lacked uniform validity in the corresponding wavenumber, as well as the distance from the transducer. Expressions for the state variables derived from the potential have the same behavior. The example of a planar wave is used to adapt the singular perturbation method of renormalization to the case where the potential is in complex form. The resulting technique is used to obtain a coordinate straining transformation that makes the state variables uniformly accurate. The expression for the pressure is similar to the King integral in linear theory, except that the integrand is a function of the strained coordinates. Comparison of the predicted waveform properties with experimental data [Gallego‐J...