Optimization of a silencer design using an helmholtz resonators array in grazing incident waves for broadband noise reduction

•Relate analytically the transmission coefficient to the geometric parameters of the silencer permits the geometric optimization to achieve broadband high Transmission Loss (TL).•The staggered different array on a rectangular duct has the advantage of achieving flat transmission-loss curve over a considered frequency band.•By introducing more structural degrees of freedom in a fixed volume, it is possible to improve the broadband TL performance of the silencer.•The proposed design strategy has a potential to suppress broadband low frequency and can be easily generalized for waveguide with other cross-section shape, and thus can find broad applications in engineering projects. In this work, we propose a general design strategy of passive acoustic treatments dealing with low frequency, broadband noise. The acoustic treatment is realized by arrays of Helmholtz resonators along the walls of the considered rectangular waveguide. The transfer matrix method is used to explicitly relate the geometric parameters of the resonators and acoustical response of the system. Based on this analytical model, an optimization is carried out to find the optimized structural design that minimizes the transmission coefficient in the considered frequency range. By using this design method, two specific designs are provided; their acoustic performances are validated by both simulations and measurements. The proposed design method can be easily generalized for waveguide with other cross-section shape, and thus can find broad applications in engineering projects which consider noise reductions in heat ventilation and air conditioning systems. Note that this work does not consider the effect of an air flow in the waveguide, however the design strategy still applies when the mean flow Mach number is sufficiently small.