Matrix condensation and transfer matrix techniques in the 3-D analysis of expansion chamber mufflers

A truly three-dimensional (3-D) finite element model for the analysis of a complex commercial automotive muffler requires several hundred nodes and elements, resulting in tedious data preparation and solution of a large number of simultaneous equations. Researchers have generally restricted themselves to l-D, 2-D or axisymmetric 3-D analyses owing to the high core memory and CPU time requirements. In this paper, two efficient solution techniques, viz., the matrix condensation technique and the transfer matrix technique, are presented in conjunction with the substructuring principle for reducing these requirements substantially. The results obtained in the form of muffler performance parameters show excellent agreement with the analytical and experimental results. These techniques are then applied to the analysis of mufflers of any geometry including offset extended inlet/outlet.