Shape Optimization Of Extended Tube Muffler Using Threshold Acceptance, Simulated Annealing And FEM Methods


  • khamchane abdelkader university of Bejaia
  • Youcef Khelfaoui Laboratoire de Mcanique, Matériaux et Energétique
  • Brahim Hamtache Laboratoire de Mécanique, Matériaux et Energétique


Silencieux réactif, Méthode des éléments finis, Acceptation du seuil, Recuit simulé, Méthode de la matrice de transfert, Puissance acoustique acoustique


Exhaust noise must meet customer expectations, legislation targets, and cost reduction which call for design optimization of the exhaust systems in the design phase. Shape optimization of reactive mufflers using algorithms became as one of important solutions to improve the acoustic performance of compact mufflers used in a limited space.
In this paper, a numerical assessment of single expansion-chamber muffler with extended tube under limited space is performed by the maximization of the sound transmission loss (STL) using the Transfer Matrix Method (TMM) and Finite Element Method (FEM). This shape optimization analysis is performed using novel schemes called Threshold Acceptance (TA) and Simulated Annealing (SA), a robust schemes used to search for the global optimum by imitating the metal’s heating process, an accuracy check on the mathematical model is performed. Also, for reliability check on the TA and SA methods, the STL’s maximization with respect to a one-tone noise is introduced, the best designs obtained by the two methods are compared and analyzed by Finite Element Method (FEM). The Transfer Matrix Method (TMM) is a modelling method based on the plane wave propagation model and the FEM solution used to analyze the STL of the shape optimized mufflers is based on the Acoustic Power method. A standard computational code COMSOL Multiphysics is used to analyze in 3D the sound attenuation of the muffler by the FEM method. The acoustical ability of the muffler obtained is than assessed by comparing the FEM solution with the analytical method. Results show that the best acoustical performance is obtained with TA optimizer and the maximal STL is precisely located at the desired targeted tone. Consequently, the optimal approach on the design of single expansion-chamber muffler with extended tube presented in this study provides quick and novel schemes for the shape optimization of muffler under limited space.

Additional Files



How to Cite

abdelkader khamchane, Khelfaoui Y, Hamtache B. Shape Optimization Of Extended Tube Muffler Using Threshold Acceptance, Simulated Annealing And FEM Methods. Canadian Acoustics [Internet]. 2021 Jul. 7 [cited 2024 May 27];49(2). Available from:



Article - Engineering Acoustics / Noise Control

Most read articles by the same author(s)