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

Alexandre Lardeau,Vicente Romero-García,Jean-Philippe Groby

doi:10.3390/cryst6050051

Alexandre Lardeau, Vicente Romero-García + Show 1 more

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https://doi.org/10.3390/cryst6050051

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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.

Highlights

IntroductionPeriodic arrays of rigid scatterers embedded in a fluid are the analogues for the acoustic waves of the crystalline structures for the electrons or the photonic crystals for the electromagnetic waves
Periodic arrays of rigid scatterers embedded in a fluid are the analogues for the acoustic waves of the crystalline structures for the electrons or the photonic crystals for the electromagnetic waves.Such structures are known as Sonic Crystals (SCs) [1] and the exploitation of the periodic distribution of scatterers in such structures have been intensively used to control the acoustic wave propagation.Perhaps the most known property of such systems is the presence of band gaps, ranges of frequencies in which the wave propagation is forbidden
The band gaps appear at high symmetry points in the Brillouin zone due to the presence of a degeneracy of the band structure produced by the Bragg interferences in the diffractive regime (λ ' a/2, λ being the wavelength of the incident wave and a the lattice constant characterizing the periodicity of the structure)

Summary

Introduction

Periodic arrays of rigid scatterers embedded in a fluid are the analogues for the acoustic waves of the crystalline structures for the electrons or the photonic crystals for the electromagnetic waves. The pioneering works of Bradley [19] and Sugimoto [20] theoretically and experimentally examined the propagation of sound waves in a waveguide loaded periodically with local resonators (quarter wavelength and Helmholtz resonators). In these systems two different mechanisms are responsible of the generation of band gaps. We analyze different configurations in which the coupling between the resonators in the structure generates multiple resonances that are designed to be close to the Bragg band gap This combined effect produces an overlap of the stop bands that can be used to strongly reduce the transmission in a broadband range of frequencies. The visco-thermal losses are accounted for in the quarter wavelength resonators to study the wave propagation in the semi-infinite structures and to compare numerical results with the experimental ones performed in an echo-free chamber

Experimental Set-Up

Numerical Characterization

Eigenvalue Problem

Scattering Problem

Results

Conclusions