In this work, the scaled boundary finite element method (SBFEM) is used to predict the frequency response of an acoustic cavity with a porous layer based on Biot–Allard theory. For the porous material, both the solid and the fluid displacements are considered as the primary variables. Scaled boundary shape functions are used to interpolate the acoustic pressure within the acoustic cavity, and the solid and fluid displacements in the porous material. The material matrices of the porous material are decomposed in such a way that the elemental matrices are real and frequency independent. This allows the elemental matrices to be computed and stored for a given mesh and is used for each frequency increment thus reducing the number of computations. Numerical examples are presented to show the computational efficiency of the SBFEM in predicting the frequency response of a porous material excited with acoustic cavity.

中文翻译：

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具有多孔层的声腔的缩放边界有限元方法


在这项工作中，缩放边界有限元法 （SBFEM） 用于基于 Biot-Allard 理论预测具有多孔层的声腔的频率响应。对于多孔材料，固体和流体位移都被视为主要变量。缩放边界形状函数用于插值声腔内的声压，以及多孔材料中的固体和流体位移。多孔材料的材料矩阵以这样的方式分解，即元素矩阵是实数且与频率无关的。这允许为给定网格计算和存储单元矩阵，并用于每个频率增量，从而减少计算次数。通过数值实例展示了 SBFEM 在预测用声腔激发的多孔材料的频率响应方面的计算效率。