A hybrid mathematical model for predicting the noise attenuation of rectangular baffle silencers

A hybrid mathematical model is applied to predict the noise attenuation of rectangular baffle-type silencers. The Euler-Maclaurin summation formula is used to obtain an approximate closed form solution to the acoustic wave equation in a thin rectangular duct with rigid walls. The plane wave component is extracted from the solution leaving a closed form solution to represent the infinite number of higher order modes resulting from duct wall reflections. A dissipative baffle silencer consisting of standard high performance sound absorption material with a thin perforated cover is considered to define the rectangular duct. The noise attenuation of the plane wave component is obtained by interpolation of standard splitter silencer curves based on percent open area. The noise attenuation of the higher mode component is obtained by considering equivalent ray reflection and the random incidence sound coefficient of the baffle. End reflection loss is considered by evaluating the acoustic radiation impedance. The hybrid analytical/numerical mathematical model is especially applicable to cases of short silencers where both plane wave and higher order modes are readily excited, such as a silencer providing broadband attenuation that is directly attached to an opening in a plenum. Theoretical results are compared with experiments for two silencer sizes applied to an axial fan plenum. The model provides computationally efficient equations that may be used in optimization studies of more complex silencer systems.