Broadband Transmission Loss Using the Overlap of Resonances in 3D Sonic Crystals

Abstract

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.

Complex Dispersion Relation Recovery from 2D Periodic Resonant Systems of Finite Size

“…Specifically, we consider the structure shown in Figure 1b, i.e., a periodic system composed of QWRs arranged in a square lattice embedded in air. Both lossless and lossy cases are considered with visco-thermal losses considered solely inside the QWR resonators [24,25]. Figure 4 shows the complex dispersion relation results of the 2D acoustic metamaterial.…”

“…The SC shown in Figure 1a consists of cylindrical rigid scatterers with radius r = 0.003 m. The second periodic system is a metamaterial consisting of square scatterers with QWRs, as shown in Figure 1b. The geometric parameters of the resonator are its external side length, L = 0.05 m, and internal dimensions, d qw = 0.035 m and l qw = 0.04 m. See Refs [24,25]. for specific details on the resonators.…”

Type of dike using C-shaped vertical cylinders

“…We first notice the quasi-identical results for configurations 1 and 2, which means that a scale factor on the lattice is passed on the wave number, that is, on the wavelength. For all cases, a band gap is observed between the first two bands corresponding to low frequencies, which is due to the presence of the slit (note that an extra path along X is required in the band diagram [22]). This behavior is not observed in the case of plain cylinders (see Fig.…”

Sound Absorption and Diffusion by 2D Arrays of Helmholtz Resonators

“…Ultra-thin meta-diffusers have also been designed showing very good performance at low frequencies [22,23]. Locally resonant materials have been also used for the mitigation of sound for traffic and railway noise showing their efficiency at low frequencies [15,[24][25][26][27][28][29][30][31][32].…”