Quantitative characterization of bandgap properties of sets of isolated acoustic scatterers arranged using fractal geometries

The improvement in the bandgap properties of a set of acoustic scatterers arranged according to a fractal geometry is theoretically quantified in this work using the multiple scattering theory. The analysis considers the growth process of two different arrangements of rigid cylinders in air created from a starting cluster: a classical triangular crystalline array and an arrangement of cylinders based on a fractal geometry called a Sierpinski triangle. The obtained results, which are experimentally validated, show a dramatic increase in the size of the bandgap when the fractal geometry is used.

[1]  Daniel Torrent,et al.  Anisotropic mass density by two-dimensional acoustic metamaterials , 2008 .

[2]  Zhengyou Liu,et al.  Highly directional liquid surface wave source based on resonant cavity , 2009 .

[3]  Economou,et al.  Classical wave propagation in periodic structures: Cermet versus network topology. , 1993, Physical review. B, Condensed matter.

[4]  Lien-Wen Chen,et al.  Experimental investigation of the acoustic pressure in cavity of a two-dimensional sonic crystal , 2009 .

[5]  Anne-Christine Hladky-Hennion,et al.  Absolute forbidden bands and waveguiding in two-dimensional phononic crystal plates , 2008 .

[6]  V. Romero-Garc'ia,et al.  Tunable wideband bandstop acoustic filter based on 2D multi-physical phenomena periodic systems , 2011, 1102.1593.

[7]  D. Torrent,et al.  Acoustic metamaterials for new two-dimensional sonic devices , 2007 .

[8]  Keiichi Edagawa,et al.  Photonic crystals, amorphous materials, and quasicrystals , 2014, Science and technology of advanced materials.

[9]  Zhengyou Liu,et al.  Point defect states in two-dimensional phononic crystals , 2001 .

[10]  Economou,et al.  Spectral gaps for electromagnetic and scalar waves: Possible explanation for certain differences. , 1994, Physical review. B, Condensed matter.

[11]  John,et al.  Strong localization of photons in certain disordered dielectric superlattices. , 1987, Physical review letters.

[12]  Liu Xiaojian,et al.  Band structure characteristics of T-square fractal phononic crystals , 2013 .

[13]  R. Martínez-Sala,et al.  SOUND ATTENUATION BY A TWO-DIMENSIONAL ARRAY OF RIGID CYLINDERS , 1998 .

[14]  Vicent Romero-García,et al.  Band gap creation using quasiordered structures based on sonic crystals , 2006 .

[15]  Sergio Castiñeira-Ibáñez,et al.  Design, Manufacture and Characterization of an Acoustic Barrier Made of Multi-Phenomena Cylindrical Scatterers Arranged in a Fractal-Based Geometry , 2012 .

[16]  Salvatore Torquato,et al.  Designer disordered materials with large, complete photonic band gaps , 2009, Proceedings of the National Academy of Sciences.

[17]  E. Yablonovitch,et al.  Inhibited spontaneous emission in solid-state physics and electronics. , 1987, Physical review letters.

[18]  Fractal phononic crystals in aluminum nitride: An approach to ultra high frequency bandgaps , 2011 .

[19]  Y Y Chen,et al.  Theoretical analysis of acoustic stop bands in two-dimensional periodic scattering arrays. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Y. Lai,et al.  Large sonic band gaps in 12-fold quasicrystals , 2002 .

[21]  V. Twersky,et al.  Multiple Scattering of Radiation by an Arbitrary Configuration of Parallel Cylinders , 1952 .

[22]  Zhengyou Liu,et al.  Effective medium of periodic fluid-solid composites , 2012 .

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