Abstract
We report a theoretical and experimental study of an array of Helmholtz resonators optimized to achieve both efficient sound absorption and diffusion. The analysis starts with a simplified 1D model where the plane wave approximation is used to design an array of resonators showing perfect absorption for a targeted range of frequencies. The absorption is optimized by tuning the geometry of the resonators, i.e., by tuning the viscothermal losses of each element. Experiments with the 1D array were performed in an impedance tube. The designed system is extended to 2D by periodically replicating the 1D array. The 2D system has been numerically modeled and experimentally tested in an anechoic chamber. It preserves the absorption properties of the 1D system and introduces efficient diffusion at higher frequencies due to the joint effect of resonances and multiple scattering inside the discrete 2D structure. The combined effect of sound absorption at low frequencies and sound diffusion at higher frequencies, may play a relevant role in the design of noise reduction systems for different applications.
Highlights
Periodic arrays of solid scatterers embedded in a solid host, known as phononic crystals, have been exploited in the last decades for acoustic wave control, giving rise to several applications ranging from the radiofrequency regime to seismic waves [1,2]
The design of the 1D system is performed by using an optimization technique (Sequential Quadratic Programming (SQP) method) employing Transfer Matrix Method (TMM)
To maximize the absorption coefficient for a range of frequencies f = [400, 560] Hz, in which the number of resonators is fixed to N = 5, including cavities in between the resonators
Summary
Periodic arrays of solid scatterers embedded in a solid host, known as phononic crystals, have been exploited in the last decades for acoustic wave control, giving rise to several applications ranging from the radiofrequency regime to seismic waves [1,2]. These systems have a particular dispersion relation with the presence of band gaps [3]. Combining the dispersion and the bandgaps, perhaps the most developed application of sonic crystals is design of acoustic barriers for the sound mitigation of traffic noise [12,13]
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