Three-dimensional multiresonant lossy sonic crystal for broadband acoustic attenuation: Application to train noise reduction

Abstract Broadband acoustic attenuation produced by a three dimensional (3D) locally resonant sonic crystal (LRSC), exploiting both the multiple coupled resonances and the Bragg band gaps, is numerically and experimentally reported in this work. The LRSC is made of square cross-section scatterers arranged on a square lattice and periodically incorporating both quarter-wavelength and Helmholtz resonators along their heights. Local resonators of different types are combined with the periodicity of the system generating multiple coupled resonances at low frequencies and opening Bragg band gaps respectively. This twofold coupling produces a strong broadband attenuation: a large insertion loss (IL), with an average value of 16.8 dB, covering three and a half octaves from 350 Hz to 5000 Hz with a LRSC of 30 cm width. This frequency band corresponds to one of the several railway noise sources (rolling noise, traction auxiliaries, etc.). A simplified 2D LRSC is finally analyzed numerically in a real train-track configuration, showing the efficiency of the proposed design to attenuate the railway rolling noise.

[1]  J. Groby,et al.  Sustainable sonic crystal made of resonating bamboo rods. , 2013, The Journal of the Acoustical Society of America.

[2]  Xinhua Hu,et al.  Two-dimensional sonic crystals with Helmholtz resonators. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  P. Sheng,et al.  Locally resonant sonic materials , 2000, Science.

[4]  K. Attenborough,et al.  Predictions and measurements of sound transmission through a periodic array of elastic shells in air. , 2010, The Journal of the Acoustical Society of America.

[5]  José Sánchez-Dehesa,et al.  Optimum control of broadband noise by arrays of cylindrical units made of a recycled material , 2013 .

[6]  Philippe Jean,et al.  Acoustical efficiency of a sonic crystal assisted noise barrier , 2013 .

[7]  Daniel Torrent,et al.  Noise control by sonic crystal barriers made of recycled materials. , 2010, The Journal of the Acoustical Society of America.

[8]  Vincent Pagneux,et al.  Rainbow-trapping absorbers: Broadband, perfect and asymmetric sound absorption by subwavelength panels for transmission problems , 2017, Scientific Reports.

[9]  Lawrence E. Kinsler,et al.  Fundamentals of acoustics , 1950 .

[10]  Sergio Castiñeira-Ibáñez,et al.  Environmental noise control during its transmission phase to protect buildings. Design model for acoustic barriers based on arrays of isolated scatterers , 2015 .

[11]  Overlapping of acoustic bandgaps using fractal geometries , 2010 .

[12]  G. Theocharis,et al.  Use of complex frequency plane to design broadband and sub-wavelength absorbers. , 2016, The Journal of the Acoustical Society of America.

[13]  Mathias Fink,et al.  Soda Cans Metamaterial: A Subwavelength-Scaled Phononic Crystal , 2016 .

[14]  C. Zwikker,et al.  Sound Absorbing Materials , 1949 .

[15]  C. Bradley Acoustic Bloch Wave Propagation in a Periodic Waveguide , 1991 .

[16]  J. Kergomard,et al.  Simple discontinuities in acoustic waveguides at low frequencies: Critical analysis and formulae , 1987 .

[17]  J. Groby,et al.  Broadband Transmission Loss Using the Overlap of Resonances in 3D Sonic Crystals , 2016 .

[18]  Vincent Pagneux,et al.  Ultra-thin metamaterial for perfect and omnidirectional sound absorption , 2016, 1606.07776.

[19]  J. V. Sánchez-Pérez,et al.  Acoustic barriers based on periodic arrays of scatterers , 2002 .

[20]  Douglas H. Keefe,et al.  Theory of sound propagation in a duct with a branched tube using modal decomposition , 1999 .

[21]  J. Groby,et al.  Complex dispersion relation of surface acoustic waves at a lossy metasurface , 2017 .

[22]  R. Martínez-Sala,et al.  Control of noise by trees arranged like sonic crystals , 2006 .

[23]  Mathias Fink,et al.  Acoustic resonators for far-field control of sound on a subwavelength scale. , 2011, Physical review letters.

[24]  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 .

[25]  Nobumasa Sugimoto,et al.  Dispersion characteristics of sound waves in a tunnel with an array of Helmholtz resonators , 1995 .

[26]  C. Goffaux,et al.  Theoretical study of a tunable phononic band gap system , 2001 .

[27]  Victor M. García-Chocano,et al.  Broadband sound absorption by lattices of microperforated cylindrical shells , 2012 .

[28]  G. Lerosey,et al.  Resonant metalenses for breaking the diffraction barrier. , 2010, Physical review letters.

[29]  A. Krynkin,et al.  Multi-resonant scatterers in Sonic Crystals: Locally Multi-resonant Acoustic Metamaterial , 2011, 1103.6283.

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