In the classic treatment of the line-driven, fluid-loaded, thin elastic plate, a branch cut integral typically needs to be evaluated. This branch cut arises due to a square root operator in the spectral form of the acoustic impedance. In a previous paper [J. Acoust. Soc. Am. 110, 3018 (2001)], DiPerna and Feit developed a methodology, complex layer analysis (CLA), to approximate this impedance. The resulting approximation was in the form of a rational function, although this was not explicitly stated. In this paper, a rational function approximation (RFA) to the acoustic impedance is derived. The advantage of the RFA as compared to the CLA approach is that a smaller number of terms are required. The accuracy of the RFA is examined both in the Fourier transform domain and the spatial domain. The RFA is then used to obtain a differential relationship between the pressure and velocity on the surface of the plate. Finally, using the RFA in conjunction with the equation of motion of the plate, an approximate expression for the Green's function for a line-driven plate is obtained in terms of a sum of propagating and evanescent waves. Comparisons of these results with the numerical inversion of the exact integral show reasonable agreement.
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机译：在对线驱动，流体加载的薄弹性板进行经典处理时，通常需要评估分支切割的整体性。该分支切口是由于声阻抗的频谱形式中的平方根算符引起的。在上一篇论文中[J. co Soc。上午。 110，3018（2001）]，DiPerna和Feit开发了一种方法，即复杂层分析（CLA），以近似此阻抗。尽管没有明确说明，但所得的近似值是有理函数的形式。本文推导了声阻抗的有理函数近似（RFA）。与CLA方法相比，RFA的优势在于所需的术语数量更少。在傅立叶变换域和空间域中都检查了RFA的准确性。然后，RFA用于获得板表面上的压力和速度之间的微分关系。最后，将RFA与板的运动方程式结合使用，可以根据传播波和sum逝波的总和来获得直线驱动板的格林函数的近似表达式。这些结果与精确积分的数值反演的比较显示出合理的一致性。
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