The compact Green’s function for a semi‐infinite elastic plate, with application to trailing edge noise and blade–vortex interaction noise
The compact Green’s function for a semi‐infinite elastic plate, with application to trailing edge noise and blade–vortex interaction noise
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半无限弹性板的紧凑格林函数，应用于后缘噪声和叶片涡相互作用噪声
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发表时间：
1993
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通讯作者：
M. S. Howe
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作者：
M. S. Howe
本文推导了控制空气动力声源在薄型半无限弹性板边缘附近产生的格林函数的解析表达式。得到了紧凑的格林函数的简单封闭表达式，该表达式适用于源流在边缘附近的长度尺度远小于声波波长和弯曲波长的情况。这就要求特征流动马赫数M和频率f满足M2≪f/fc≪1，其中fc是重合频率，在此频率以上，真空中的弯曲波速度超过流体中的声速。在这样的频率下，板的弯曲响应可以显著地影响边缘附近的声源产生的声音水平。这可以通过以下在声音产生中的应用来说明：(i)弹性后缘上的湍流边界层流动（其中包括与适用于任意值f/fc > 1的更完整的预测的比较），以及（ii）相互作用…
Analytic representations are derived for the acoustic Green’s function governing the production of aerodynamic sound by sources near the edge of a thin, semi‐infinite elastic plate. Simple closed‐form expressions are obtained for the compact Green’s function, which is applicable when the length scale of the source flow near the edge is much smaller than both the acoustic and bending wavelengths. This requires that the characteristic flow Mach number M and frequency f satisfy M2≪f/fc≪1, where fc is the coincidence frequency, above which the bending wave speed in vacuo exceeds the speed of sound in the fluid. At such frequencies the flexural response of the plate can significantly affect the level of sound generation by sources in the neighborhood of the edge. This is illustrated by applications to sound production by (i) turbulent boundary layer flow over an elastic trailing edge (which includes a comparison with more complete predictions applicable for arbitrary values of f/fc≲1), and (ii) the interaction...