The study of reactive silencers by shape and parametric optimization techniques

The aim of this work is to show the application of shape and parametric optimization techniques in the study of reactive silencers with extended inlet and outlet ducts. Parametric optimization is employed to evaluate the appropriate size of the inlet and outlet ducts. Shape optimization is employed to establish the proper profile of these ducts in order to improve the acoustic features of these mufflers in a specific frequency range. The objective function used in the optimization processes is defined through the average transmission loss (TL) for the desired frequency range. This type of objective function is strongly non-linear and the genetic algorithm, GA, was chosen as a mathematical method for determining the maximum of this function. The Finite Element Method with an axisymmetric formulation along with the modified four-parameter method are used to calculate the TL(ω). The Hermite polynomials were used in the shape optimization in order to obtain local boundary approximations with C1 continuity. The results showed the optimization efficiency of the inlet ducts profile for acting in specific frequency ranges with gains up to 20 dB with respect to silencers without shape optimization. The numerical analyses agree well with experimental results.