In order to avoid the dependence of mesh method on grids, a 3D global weak-form mesh-free method (MFM) is applied to study the three-dimensional acoustic characteristics of silencers. For the expansion chamber silencers, the 3D acoustic modes are extracted and the transmission loss results are computed by using the 3D global weak-form (MFM), which is based on the radial basis function point interpolation method (RPIM) for calculating the shape functions and Galerkin method for discretizing the system equation. The first 15 order 3D acoustic modes and TL results of a special expansion chamber silencer are presented to validate the computational accuracy of the proposed technique, and the relative errors are controlled within 0.5% by comparing with the 3D finite element method (FEF) calculations. Additionally, the effects of axial modes on the acoustic characteristics are investigated, and the pass through frequencies can be eliminated to enhance the acoustic attenuation performance by locating the side branch outlet on the nodal lines of axial modes.

中文翻译：

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膨胀室声衰减分析的3D全局弱形式无网格方法

为了避免网格方法对网格的依赖性，使用3D全局弱形式无网格方法（MFM）研究消音器的三维声学特性。对于膨胀室消音器，使用基于径向基函数点插值法（RPIM）的3D整体弱形式（MFM）提取3D声模并计算传输损耗结果，以计算形状函数和Galerkin方法离散化系统方程。给出了特殊膨胀室消声器的前15阶3D声模和TL结果，以验证所提出技术的计算精度，并且与3D有限元方法（FEF）计算相比，相对误差控制在0.5％以内。另外，