Use of slow sound to design perfect and broadband passive sound absorbing materials.

Perfect (100%) absorption by thin structures consisting of a periodic arrangement of rectangular quarter-wavelength channels with side detuned quarter-wavelength resonators is demonstrated. The thickness of these structures is 13-17 times thinner than the acoustic wavelength. This low frequency absorption is due to a slow sound wave propagating in the main rectangular channel. A theoretical model is proposed to predict the complex wavenumber in this channel. It is shown that the speed of sound in the channel is much lower than in the air, almost independent of the frequency in the low frequency range, and it is dispersive inside the induced transparency band which is observed. The perfect absorption condition is found to be caused by a critical coupling between the rectangular channel (sub-wavelength resonators) and the incoming wave. It is shown that the width of a large absorption peak in the frequency spectrum can be broadened if several rectangular channels in the unit cell are detuned. The detuning is achieved by varying the length of the side resonators for each channel. The predicted absorption coefficients are validated experimentally. Two resonant cells were produced with stereolithography which enabled the authors to incorporate curved side resonators.

[1]  W. Lauriks,et al.  Acoustic wave propagation and internal fields in rigid frame macroscopically inhomogeneous porous media , 2007 .

[2]  W Lauriks,et al.  Total absorption peak by use of a rigid frame porous layer backed by a rigid multi-irregularities grating. , 2010, The Journal of the Acoustical Society of America.

[3]  V. Tournat,et al.  Enhancing the absorption properties of acoustic porous plates by periodically embedding Helmholtz resonators. , 2015, The Journal of the Acoustical Society of America.

[4]  Yves Aurégan,et al.  The use of slow waves to design simple sound absorbing materials , 2015 .

[5]  Raymond Panneton,et al.  Acoustic properties of air-saturated porous materials containing dead-end porosity , 2011 .

[6]  S. Bozhevolnyi,et al.  Demonstration of slow sound propagation and acoustic transparency with a series of detuned resonators , 2014 .

[7]  Sergey I. Bozhevolnyi,et al.  Acoustic transparency and slow sound using detuned acoustic resonators , 2011 .

[8]  Claude Boutin,et al.  Acoustics of porous media with inner resonators. , 2013, The Journal of the Acoustical Society of America.

[9]  Jean-François Mercier,et al.  Non‐reflecting boundary conditions for acoustic propagation in ducts with acoustic treatment and mean flow , 2011 .

[10]  G. Theocharis,et al.  Limits of slow sound propagation and transparency in lossy, locally resonant periodic structures , 2013, 1312.2851.

[11]  M. R. Stinson.  The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross- sectional shape , 1991 .

[12]  D. Maa,et al.  Potential of microperforated panel absorber , 1998 .

[13]  W Lauriks,et al.  Absorption of a rigid frame porous layer with periodic circular inclusions backed by a periodic grating. , 2011, The Journal of the Acoustical Society of America.

[14]  Claude Boutin,et al.  Acoustic wave propagation in double porosity media. , 2003, The Journal of the Acoustical Society of America.

[15]  Jeremy B. Wright,et al.  Directional perfect absorption using deep subwavelength low-permittivity films , 2014, 1405.5569.

[16]  A. Maurel,et al.  Enhanced transmission through gratings: Structural and geometrical effects , 2013 .

[17]  D. Lafarge,et al.  Check on a nonlocal Maxwellian theory of sound propagation in fluid-saturated rigid-framed porous media , 2014 .

[18]  Mustafa YILMAZ,et al.  Slow sound propagation in a sonic crystal linear waveguide , 2012 .

[19]  Lei Xiong,et al.  Acoustical behaviour of purely reacting liners , 2013 .

[20]  J. Groby,et al.  Absorption of sound by porous layers with embedded periodic arrays of resonant inclusions. , 2013, The Journal of the Acoustical Society of America.

[21]  G. Theocharis,et al.  Perfect and broadband acoustic absorption by critically coupled sub-wavelength resonators , 2016, Scientific Reports.

[22]  G. Hu,et al.  Ultrathin low-frequency sound absorbing panels based on coplanar spiral tubes or coplanar Helmholtz resonators , 2014 .

[23]  P. Sheng,et al.  Membrane-type acoustic metamaterial with negative dynamic mass. , 2008, Physical review letters.

[24]  W. Robertson,et al.  Slow group velocity propagation of sound via defect coupling in a one-dimensional acoustic band gap array , 2004 .

[25]  Constantin R. Simovski,et al.  On electromagnetic characterization and homogenization of nanostructured metamaterials , 2010 .

[26]  Gaokun Yu,et al.  Acoustical “transparency” induced by local resonance in Bragg bandgaps , 2014 .

[27]  P. Sheng,et al.  Dark acoustic metamaterials as super absorbers for low-frequency sound , 2012, Nature Communications.

[28]  P. Sheng,et al.  Acoustic metasurface with hybrid resonances. , 2014, Nature materials.

[29]  N. Fang,et al.  Ultrasonic metamaterials with negative modulus , 2006, Nature materials.

[30]  P Leclaire,et al.  Acoustical properties of air-saturated porous material with periodically distributed dead-end pores. , 2015, The Journal of the Acoustical Society of America.

[31]  I. David Abrahams,et al.  An Orthogonality Relation for a Class of Problems with High-Order Boundary Conditions , 1999 .

[32]  S. Cummer,et al.  Tapered labyrinthine acoustic metamaterials for broadband impedance matching , 2013 .