Semi-weak-form mesh-free method for acoustic attenuation analysis of silencers with arbitrary but axially uniform transversal sections

Abstract

To reduce the computational requirements of full multidimensional numerical calculations for silencers with arbitrary but uniform cross sections, a semi-weak-form mesh-free method (MFM) that combines the axial and transversal solutions of the wave equation is developed. Because perforated tube silencers contain more Neumann boundaries than other silencers, the transversal modes are extracted using the weak-form MFM, which is based on the radial basis function point interpolation method (RPIM) for creating shape functions and the Galerkin method for obtaining the weak formulation of transversal governing equations, as well as the Gauss integration scheme for computing the system matrices. The mode-matching approach employs the modal expansion of transversal modes and then matches the sound pressure and particle velocity at the cross sections to predict the transmission loss (TL). Several test cases are presented to validate the computational accuracy and efficiency of the proposed combined technique. Additionally, the stability and efficiency of the weak-form and strong-form MFMs are compared.