Recently, research on new techniques of single-chamber mufflers equipped with perforated tubes has been addressed. However, research work on shape optimization of multichamber silencers hybridized with perforated plug/non-plug tubes along with work on the maximal allowable back pressure of mufflers has been neglected. Therefore, we will not only analyze the sound transmission loss (STL) of a spaceconstrained two-chamber muffler hybridized with perforated plug/non-plug tubes but also optimize the best design shape under a specified pressure drop. In this paper, both the numerical decoupling technique and simulated annealing (SA) for solving the coupled acoustical problem of perforated plug/ non-plug tubes are used. A numerical case in eliminating a broadband fan noise is also introduced. To verify the reliability of SA optimization, optimal noise abatements for the pure tone (500 Hz) are exemplified. However, before the SA operation can be carried out, the accuracy of the mathematical model must be checked using the experimental data. Results indicate that the maximum STL is precisely located at the desired target tones. The optimal result of one case study for eliminating broadband noise also revealed that the overall noise reductions with respect to the muffler, which are under various maximum allowable pressure drops (100, 200, 300, 400, 500 (Pa), and infinity) can reach 68.4, 52.7, 45.4, 40.4, 36.0, and 33.2 dB. Furthermore, both the pressure drop and the acoustical performance increase when the diameters (at inlet tubes as well as perforated holes), the perforated ratio, and the length of perforated tube decrease. Consequently, a successful approach used for the optimal design of the twochamber mufflers equipped with perforated plug/non-plug tubes under space and back pressure constrained conditions has been demonstrated.

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