Abstract
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.
Highlights
Silencers are widely used in engineering applications in cars, aircrafts, ships, and submarines. e acoustic modes have significant effects on acoustic characteristics of silencers. e configuration of silencers can be improved to optimize the acoustic attenuation performance according to the acoustic modal characteristics
Many methods including analytical and numerical methods have been developed to predict the acoustic modes and transmission loss of silencers. e two-dimensional transversal modes of regular cross sections of silencers are calculated by using the analytical method in [1,2,3,4], and the transmission loss results are calculated by using the mode-matching method. e analytical methods have the advantage of high computational accuracy and efficiency but are confined to relatively simple and regular configurations
In [5,6,7,8,9,10,11,12], the two-dimensional transversal modes of the expansion chamber silencers and the perforated tube silencers with arbitrary cross section are calculated by using the 2D finite element method, and the effects of the structure parameters of chambers and perforated tubes on the transversal modes are investigated [9, 10]. e finite element method can be used for the acoustic modes of any complex silencers, but the numerical accuracy is largely determined by the quantity and quality of the mesh elements and are highly timeconsuming when the size of the silencer is large or the computational frequency range is wide
Summary
Silencers are widely used in engineering applications in cars, aircrafts, ships, and submarines. e acoustic modes have significant effects on acoustic characteristics of silencers. e configuration of silencers can be improved to optimize the acoustic attenuation performance according to the acoustic modal characteristics. E finite element method can be used for the acoustic modes of any complex silencers, but the numerical accuracy is largely determined by the quantity and quality of the mesh elements and are highly timeconsuming when the size of the silencer is large or the computational frequency range is wide. For this reason, the mesh-free methods are proposed to calculate the 2D acoustic problems [13,14,15,16,17,18,19,20]. Shock and Vibration e radial point interpolation method (RPIM) for the Helmholtz equation in the 2D case is studied by Wentreodt [14]. ree different radial basis function point interpolation methods (RPIMs) were studied in that work, and all of them showed a significant reduction of the dispersion error compared with that of the FEM. e dual reciprocity hybrid boundary node method (DRHBNM), combining the hybrid boundary node method (HBNM) with the dual reciprocity method (DRM), is applied for solving acoustic eigenvalue problems by Li et al [15]. e numerical examples of several acoustic cavities with different boundary conditions were provided, and suitable accuracy was demonstrated in that paper. e meshless Galerkin least-squares (MGLS) method [16] is proposed to a 2D acoustic problems, and the numerical examples of an L-shaped cavity demonstrated the MGLS method had higher computational efficiency than the EFGM
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