Accurate evaluation of lowest band gaps in ternary locally resonant phononic crystals

Based on a better understanding of the lattice vibration modes, two simple spring–mass models are constructed in order to evaluate the frequencies on both the lower and upper edges of the lowest locally resonant band gaps of the ternary locally resonant phononic crystals. The parameters of the models are given in a reasonable way based on the physical insight into the band gap mechanism. Both the lumped-mass methods and our models are used in the study of the influences of structural and the material parameters on frequencies on both edges of the lowest gaps in the ternary locally resonant phononic crystals. The analytical evaluations with our models and the theoretical predictions with the lumped-mass method are in good agreement with each other. The newly proposed heuristic models are helpful for a better understanding of the locally resonant band gap mechanism, as well as more accurate evaluation of the band edge frequencies.

[1]  C. Jianchun,et al.  Local resonant characteristics of a layered cylinder embedded in the elastic medium , 2005 .

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

[3]  Gang Wang,et al.  Quasi-one-dimensional phononic crystals studied using the improved lumped-mass method : Application to locally resonant beams with flexural wave band gap , 2005 .

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

[5]  José Sánchez-Dehesa,et al.  Two-dimensional phononic crystals studied using a variational method: Application to lattices of locally resonant materials , 2003 .

[6]  Philippe Lambin,et al.  Comparison of the sound attenuation efficiency of locally resonant materials and elastic band-gap structures , 2004 .

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

[8]  Z. Hou,et al.  Convergence problem of plane-wave expansion method for phononic crystals , 2004 .

[9]  B. Djafari-Rouhani,et al.  Evidence of fano-like interference phenomena in locally resonant materials. , 2002, Physical review letters.

[10]  Gang Wang,et al.  Lumped-mass method for the study of band structure in two-dimensional phononic crystals , 2004 .

[11]  Gang Wang,et al.  Two-dimensional locally resonant phononic crystals with binary structures. , 2004, Physical review letters.

[12]  M. Hirsekorn,et al.  Small-size sonic crystals with strong attenuation bands in the audible frequency range , 2004 .

[13]  B. Djafari-Rouhani,et al.  Acoustic band structure of periodic elastic composites. , 1993, Physical review letters.

[14]  N. K. Batra,et al.  Modelling and simulation of acoustic wave propagation in locally resonant sonic materials. , 2004, Ultrasonics.

[15]  王刚,et al.  Formation mechanism of the low-frequency locally resonant band gap in the two-dimensional ternary phononic crystals , 2006 .

[16]  R. Martínez-Sala,et al.  Sound attenuation by sculpture , 1995, Nature.