Recently, research on new techniques of single-chamber perforated silencers has been addressed. However, the research work on shape optimization of multi-chamber silencers within a compact volume is rare. Work on the maximal allowable back pressure of mufflers has also been neglected. Therefore, the main purpose of this paper is to analyze the sound transmission loss (STL) of a space-constrained multi-chamber muffler and to optimize the best design shape under a specified pressure drop. In this paper, both the generalized decoupling technique and plane wave theory used to solve the coupled acoustical problem of multi-chamber perforated mufflers are presented. The four-pole system matrix used to evaluate the acoustic performance of sound transmission loss STL, is also presented in conjunction with the genetic algorithm (GA). In addition, numerical cases of sound elimination with respect to three kinds of multi-chamber mufflers (one-chamber, twochamber, and three-chamber mufflers) at various pure tones (200, 500 Hz) are discussed. Before the GA operation can be carried out, the accuracy of the mathematical models is checked using Crocker’s experimental data. The result reveals that to achieve a better acoustical performance under a specified maximal allowable pressure drop, a sacrifice of the acoustical performance to depress the muffler’s back pressure is required. As a result, the optimal STL of three kinds of mufflers under a specified maximal allowable pressure drop of 600 (Pa) can be achieved at the targeted frequencies. Consequently, the approach used for the optimal design of the multichamber mufflers under space and back-pressure’s constrained conditions is quite effective.

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