Lumped-mass method for the study of band structure in two-dimensional phononic crystals

A lumped-mass method is introduced to study the propagation of elastic waves in two-dimensional periodic systems. First, it is used to calculate the band structure of an array of Pb columns in an epoxy background. Second, the method is applied to the same array of Pb columns in a soft rubber background. The results are compared with those calculated with the well-known plane-wave expansion formalism, where the advantages of the lumped-mass method are pointed out and analyzed. These advantages make it possible for easy calculations of band structures of phononic crystals with interfaces of large contrast of elastic constants as well as units of any shapes.

[1]  Eleftherios N. Economou,et al.  Elastic and acoustic wave band structure , 1992 .

[2]  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.

[3]  Z. Ye,et al.  ACOUSTIC ATTENUATION BY TWO-DIMENSIONAL ARRAYS OF RIGID CYLINDERS , 2001, cond-mat/0101442.

[4]  John H. Page,et al.  Elastic Wave Scattering by Periodic Structures of Spherical Objects: Theory and Experiment , 2000 .

[5]  B. Djafari-Rouhani,et al.  Experimental evidence for the existence of absolute acoustic band gaps in two-dimensional periodic composite media , 1998 .

[6]  Han Xiao-Yun,et al.  Finite difference time domain method for the study of band gap in two-dimensiona l phononic crystals , 2003 .

[7]  M. Kafesaki,et al.  Air bubbles in water: a strongly multiple scattering medium for acoustic waves. , 2000, Physical review letters.

[8]  Ultrasonic wedges for elastic wave bending and splitting without requiring a full band gap. , 2001, Physical review letters.

[9]  R. Martínez-Sala,et al.  Refractive acoustic devices for airborne sound. , 2001 .

[10]  B. Djafari-Rouhani,et al.  Theory of acoustic band structure of periodic elastic composites. , 1994, Physical review. B, Condensed matter.

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

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

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

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

[15]  Eleftherios N. Economou,et al.  Band structure of elastic waves in two dimensional systems , 1993 .

[16]  Yukihiro Tanaka,et al.  Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch , 2000 .

[17]  M. Torres,et al.  ULTRASONIC BAND GAP IN A PERIODIC TWO-DIMENSIONAL COMPOSITE , 1998 .

[18]  Mihail M. Sigalas,et al.  Theoretical study of three dimensional elastic band gaps with the finite-difference time-domain method , 2000 .

[19]  Andreas Håkansson,et al.  ACOUSTIC INTERFEROMETERS BASED ON TWO-DIMENSIONAL ARRAYS OF RIGID CYLINDERS IN AIR , 2003 .

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

[21]  Steven G. Johnson,et al.  Photonic Crystals: The Road from Theory to Practice , 2001 .

[22]  P A Deymier,et al.  Experimental and theoretical evidence for the existence of absolute acoustic band gaps in two-dimensional solid phononic crystals. , 2001, Physical review letters.

[23]  Eleftherios N. Economou,et al.  Multiple-scattering theory for three-dimensional periodic acoustic composites , 1999 .