Theory of a discrete element method for modeling parallel-coupled muffler components

Abstract

Parallel-coupled muffler designs incorporating lengths of perforated tubing, such as concentric tube resonators (bean cans) and expansion chambers with perforated tubes extending into the chamber, cannot be modeled by traditional methods. In a recent paper, [J. W. Sullivan and M. J. Crocker, J. Acoust. Soc. Am. 60, S123(A) (1976)] a closed form solution for the transmission loss of a concentric tube resonator was presented, but the solution was restricted to the perforate having a constant specific impedance along the length of the tube. If the perforate impedance should vary along the tube either by design or by nonlinear effects a closed form solution is no longer possible and it then becomes necessary to resort to an approximate solution. One such solution is presented in which the tube and its backing volume are subdivided into discrete elements (slices) each described by a 4 × 4 transmission matrix. The advantages and disadvantages of this rather simple method compared with finite difference or finite element methods are discussed.