Maximov German A, Podjachev Eugenii V, Horoshenkov Kirill V
Moscow Engineering Physics Institute, Kashirskoe Shosse 31, Moscow, 115409 Russian Federation.
J Acoust Soc Am. 2008 Mar;123(3):1248-59. doi: 10.1121/1.2831932.
The attenuation of axisymmetric eigenmodes in a cylindrical, elastic, fluid-filled waveguide with a statistically rough elastic wall is studied. It is shown that small perturbation theory can be used to relate explicitly the statistical characteristics of the internal wall surface roughness of an elastic pipe to the attenuation and scattering coefficients of the acoustic modes in the filling fluid. Analytical expressions for modal attenuation coefficients are obtained. The analysis of the frequency dependent attenuation coefficients and the ratio between the roughness correlation length and the inner radius of the pipe is made for different correlation functions of the roughness. It is shown that two scale parameters control the overall behavior of the modal attenuation coefficients. These are the ratios of the roughness correlation length and the inner pipe radius to the acoustic wavelength. The numerical results for sound propagation in a pipe and in a borehole with statistically rough, elastic walls are obtained and discussed.
研究了具有统计粗糙弹性壁的圆柱形、弹性、充液波导中轴对称本征模的衰减。结果表明，小扰动理论可用于明确地将弹性管道内壁表面粗糙度的统计特性与填充流体中声模的衰减和散射系数联系起来。得到了模态衰减系数的解析表达式。针对不同粗糙度相关函数，分析了频率相关的衰减系数以及粗糙度相关长度与管道内半径之比。结果表明，两个尺度参数控制着模态衰减系数的整体行为。这两个参数分别是粗糙度相关长度与管道内半径和声波长的比值。给出并讨论了在具有统计粗糙弹性壁的管道和钻孔中声音传播的数值结果。
