Muffler design as of late has been restricted to lower frequencies using the plane wave theory. This has led to an underestimation of acoustical performances at higher frequencies. To overcome the above shortcomings, an analysis of three-dimensional waves propagating for a simple muffler using the finite element method has been developed. However, there has been scant research on rectangular mufflers equipped with baffle plates that eliminate noise, nor has the space-constrained conditions of industrial muffler designs been properly addressed. Therefore, to improve the acoustical performance of a rectangular muffler within a constrained space, the shape optimization of rectangular mufflers using an eigen function, a four-pole system in conjunction with a Genetic Algorithm is proposed and assessed. Here, a numerical analysis of pure tone noise emitted from an induced fan using three kinds of rectangular mufflers hybridized with multiple chambers is introduced. Before the optimization process is carried out, an accuracy check of the mathematical models for two rectangular one-chamber/three-chamber mufflers with various allocations of inlets/outlets and partitioned bafflers is also performed. Simulated results reveal that the acoustical performance of a muffler with more geometric design parameter is found to be more efficient. And finally, the STL of the muffler will increase as the number of the rectangular chambers increases.

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