Laboratoire d'Acoustique de l'Université du Maine, UMR6613 CNRS/Univ. du Maine, Avenue Olivier Messiaen, F-72085 Le Mans Cedex 9, France.
J Acoust Soc Am. 2013 Feb;133(2):821-31. doi: 10.1121/1.4773276.
This papers reports a three-dimensional (3D) extension of the model proposed by Groby et al. [J. Acoust. Soc. Am. 127, 2865-2874 (2010)]. The acoustic properties of a porous layer backed by a rigid plate with periodic rectangular irregularities are investigated. The Johnson-Champoux-Allard model is used to predict the complex bulk modulus and density of the equivalent fluid in the porous material. The method of variable separation is used together with the radiation conditions and Floquet theorem to derive the analytical expression for the acoustic reflection coefficient from the porous layer with 3D inhomogeneities. Finite element method is also used to validate the proposed analytical solution. The theoretical and numerical predictions agree well with the experimental data obtained from an impedance tube experiment. It is shown that the measured acoustic absorption coefficient spectrum exhibits a quasi-total absorption peak at the predicted frequency of the mode trapped in the porous layer. When more than one irregularity per spatial period is considered, additional absorption peaks are observed.
本文对 Groby 等人提出的模型进行了三维（3D）扩展[J. Acoust. Soc. Am. 127, 2865-2874（2010）]。研究了具有周期性矩形不规则性的刚性板背衬多孔层的声学特性。Johnson-Champoux-Allard 模型用于预测多孔材料中等效流体的复体积模量和密度。采用变量分离法和辐射条件以及 Floquet 定理，推导出具有 3D 非均匀性的多孔层的声反射系数的解析表达式。还使用有限元法验证了所提出的解析解。理论和数值预测与阻抗管实验获得的实验数据吻合良好。结果表明，测量的吸声系数谱在预测的多孔层中陷波模式的频率处表现出准全吸收峰。当每个空间周期考虑多个不规则性时，会观察到额外的吸收峰。
