Phononic gaps induced by inertial amplification in BCC and FCC lattices

Abstract In this study, infinite and finite periodic body centered cubic (BCC) and face centered cubic (FCC) lattices with and without inertial amplification mechanisms are investigated. These three-dimensional lattices are modeled with mass and spring elements that are parametrically varied to observe their effect on phononic gap (stop band) limits. When inertial amplification mechanisms are used in both of the infinite periodic lattices, wide low frequency band gaps are generated. Moreover, wide and deep phononic gaps are obtained by using moderate amount of unit cells in the case of finite periodic lattices.

[1]  Massimo Ruzzene,et al.  Wave Propagation in Auxetic Tetrachiral Honeycombs , 2010 .

[2]  Fugen Wu,et al.  Elastic wave band gaps for three-dimensional phononic crystals with two structural units , 2003 .

[3]  A. Modinos,et al.  Formation of absolute frequency gaps in three-dimensional solid phononic crystals , 2002 .

[4]  Yuesheng Wang,et al.  Wave band gaps in three-dimensional periodic piezoelectric structures , 2009 .

[5]  Gregory M. Hulbert,et al.  Phononic band gaps induced by inertial amplification in periodic media , 2007 .

[6]  Massimo Ruzzene,et al.  Phononic properties of hexagonal chiral lattices , 2009 .

[7]  Tsung-Tsong Wu,et al.  Three-dimensional phononic band gap calculations using the FDTD method and a PC cluster system. , 2006, IEEE transactions on ultrasonics, ferroelectrics, and frequency control.

[8]  B. Djafari-Rouhani,et al.  Sonic stop-bands for cubic arrays of rigid inclusions in air , 1998 .

[9]  Ole Sigmund,et al.  Systematic design of phononic band–gap materials and structures by topology optimization , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[10]  Gregory M. Hulbert,et al.  Theory of phononic gaps induced by inertial amplification in finite structures , 2010 .

[11]  Brian R. Mace,et al.  Formation and coupling of band gaps in a locally resonant elastic system comprising a string with attached resonators , 2011 .

[12]  Eleftherios N. Economou,et al.  Stop bands for elastic waves in periodic composite materials , 1994 .

[13]  N. Fleck,et al.  Wave propagation in two-dimensional periodic lattices. , 2006, The Journal of the Acoustical Society of America.

[14]  Yaozong Liu,et al.  Low frequency torsional vibration gaps in the shaft with locally resonant structures , 2006 .

[15]  Michael J. Leamy,et al.  Exact wave-based Bloch analysis procedure for investigating wave propagation in two-dimensional periodic lattices , 2012 .

[16]  O. Bou Matar,et al.  Tunable magnetoelastic phononic crystals , 2009 .

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

[18]  R. Sprik,et al.  Acoustic band gaps in composites of solids and viscous liquids , 1998 .

[19]  Yuesheng Wang,et al.  Band gaps of elastic waves in three-dimensional piezoelectric phononic crystals with initial stress , 2010 .

[20]  HighWire Press.  Philosophical Transactions of the Royal Society of London , 1781, The London Medical Journal.

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

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

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

[24]  Jakob Søndergaard Jensen,et al.  Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures , 2003 .

[25]  Zhengyou Liu,et al.  The optimum elastic wave band gaps in three dimensional phononic crystals with local resonance , 2004 .

[26]  Wen Ji-Hong,et al.  Accurate evaluation of lowest band gaps in ternary locally resonant phononic crystals , 2006 .

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

[28]  Huijie Shen,et al.  Propagation of flexural wave in periodic beam on elastic foundations , 2012 .

[29]  P. Sheng,et al.  Three-component elastic wave band-gap material , 2002 .

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

[31]  P. Yu,et al.  Complex elastic wave band structures in three-dimensional periodic elastic media , 1998 .

[32]  M. Sigalas,et al.  Elastic wave band gaps in 3-D periodic polymer matrix composites , 1995 .