School of Engineering Design and Technology, University of Bradford, Bradford, United Kingdom.
J Acoust Soc Am. 2013 Aug;134(2):939-49. doi: 10.1121/1.4812757.
In this paper a derivation of the attenuation factor in a waveguide with stochastic walls is presented. The perturbation method and Fourier analysis are employed to derive asymptotically consistent boundary-value problems at each asymptotic order. The derived approximation predicts the attenuation of the propagating mode in a rough waveguide through a correction to the eigenvalue corresponding to smooth walls. The proposed approach can be used to derive results that are consistent with those obtained by Bass et al. [IEEE Trans. Antennas Propag. 22, 278-288 (1974)]. The novelty of the method is that it does not involve the integral Dyson-type equation and, as a result, the large number of statistical moments included in the equation in the form of the mass operator of the volume scattering theory. The derived eigenvalue correction is described by the correlation function of the randomly rough surface. The averaged solution in the plane wave regime is approximated by the exponential function dependent on the derived eigenvalue correction. The approximations are compared with numerical results obtained using the finite element method (FEM). An approach to retrieve the correct deviation in roughness height and correlation length from multiple numerical realizations of the stochastic surface is proposed to account for the oversampling of the rough surface occurring in the FEM meshing procedure.
本文给出了具有随机壁的波导中衰减因子的推导。采用微扰法和傅里叶分析，在每一渐近阶推导出渐近一致的边值问题。所得到的近似预测了粗糙波导中传播模式的衰减，方法是对光滑壁对应的特征值进行修正。所提出的方法可以用来推导与 Bass 等人获得的结果一致的结果。[IEEE 天线与传播汇刊，22，278-288（1974）]。该方法的新颖之处在于它不涉及积分 Dyson 型方程，因此，在体积散射理论的质量算子形式中，方程包含大量的统计矩。所得到的特征值修正由随机粗糙表面的相关函数描述。在平面波情况下的平均解用依赖于导出的特征值修正的指数函数来近似。将这些近似与使用有限元方法（FEM）获得的数值结果进行了比较。提出了一种从随机表面的多个数值实现中提取正确的粗糙度高度和相关长度偏差的方法，以考虑到在 FEM 网格剖分过程中发生的粗糙表面过采样。
