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Abstract:The acoustic properties of a three-dimensional sonic crystal made of square-rod rigid scatterers incorporating a periodic arrangement of quarter wavelength resonators are theoretically and experimentally reported in this work. The periodicity of the system produces Bragg band gaps that can be tuned in frequency by modifying the orientation of the square-rod scatterers with respect to the incident wave. In addition, the quarter wavelength resonators introduce resonant band gaps that can be tuned by coupling the neighbor resonators. Bragg and resonant band gaps can overlap allowing the wave propagation control inside the periodic resonant medium. In particular, we show theoretically and experimentally that this system can produce a broad frequency band gap exceeding two and a half octaves (from 590 Hz to 3220 Hz) with transmission lower than 3%. Finite element methods were used to calculate the dispersion relation of the locally resonant system. The visco-thermal losses were accounted for in the quarter wavelength resonators to simulate the wave propagation in the semi-infinite structures and to compare the numerical results with the experiments performed in an echo-free chamber. The simulations and the experimental results are in good agreement. This work motivates interesting applications of this system as acoustic audible filters.

The acoustic properties of a three-dimensional sonic crystal made of square-rod rigid scatterers incorporating a periodic arrangement of quarter wavelength resonators are theoretically and experimentally reported in this work. The periodicity of the system produces Bragg band gaps that can be tuned in frequency by modifying the orientation of the square-rod scatterers with respect to the incident wave. In addition, the quarter wavelength resonators introduce resonant band gaps that can be tuned by coupling the neighbor resonators. Bragg and resonant band gaps can overlap allowing the wave propagation control inside the periodic resonant medium. In particular, we theoretically and experimentally show that this system can produce a broad frequency band gap exceeding two and a half octaves (from 590 Hz to 3220 Hz) with transmission lower than 3%. Finite element methods were used to calculate the dispersion relation of the locally resonant system. The visco-thermal losses were accounted for in the quarter wavelength resonators to simulate the wave propagation in the semi-infinite structures and to compare the numerical results with the experiments performed in an echo-free chamber. The simulations and the experimental results are in good agreement. This work motivates interesting applications of this system as acoustic audible filters.