A transversal substructuring mode matching method applied to the acoustic analysis of dissipative mufflers

Abstract

To carry out the acoustic analysis of dissipative silencers with uniform cross-section, the application of the mode matching method at the geometrical discontinuities is an attractive option from a computational point of view. The consideration of this methodology assumes, in general, that the modes associated with the transversal geometry of each element with uniform cross-section are known for the excitation frequencies considered in the analysis. The calculation of the transversal modes is not, however, a simple task when the acoustic system involves perforated elements and absorbent materials. The current work presents a modal approach to calculate the transversal modes and the corresponding axial wavenumbers for dissipative mufflers of uniform (but arbitrary) cross-section. The proposed technique is based on the division of the transversal section into subdomains and the subsequent use of a substructuring procedure with two sets of modes to improve the convergence. The former set of modes fulfils the condition of zero pressure at the common boundary between transversal subdomains while the latter satisfies the condition of zero derivative in the direction normal to the boundary. The approach leads to a versatile methodology with a moderate computational effort that can be applied to mufflers commonly found in real applications. To validate the procedure presented in this work, comparisons are provided with finite element predictions and results available in the literature, showing a good agreement. In addition, the procedure is applied to an example of practical interest.