Numerical Analysis and Parametric Study of Phononic Band Gap Structures

Abstract:

Phononic band gap crystals (PnCs) are periodic composite materials and well known for their novel property that can prohibit the propagation of mechanical waves in certain range of frequency. This paper develops the finite element method to calculate band structures of bi-material phononic crystals. Through finite element analysis, complete band gap for longitudinal and transverse waves are obtained by characterizing the dispersion relation in phononic crystals. Phononic crystals with different inclusion shapes in a square and hexagonal unit cell are investigated to study the influence of unit cell topology on band gap size. For a specific pattern, the existence of complete band gap in relation to the density and Lamé constant modulus of composites is studied and critical density ratio and Lamé constant ratio of inclusions versus base material for opening complete band gap are given. The results provide theoretical guidance for designing phononic crystals in practical applications.

• Periodical: Applied Mechanics and Materials (Volume 846)
• Pages: 120-126
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.846.120
• Online since: July 2016
• Authors: Yang Fan Li*, Xiao Dong Huang, Shi Wei Zhou
• Keywords: Finite Element Method, Lattice Type, Phononic Band Gap Crystals

References

[1] Y. Pennec, J.O. Vasseur, B. Djafari-Rouhani, L. Dobrzyński, P.A. Deymier, Two-dimensional phononic crystals: Examples and applications, Surface Science Reports 65 (2010) 229.

DOI: 10.1016/j.surfrep.2010.08.002

[2] M. Sigalas, E. Economou, Elastic and acoustic wave band structure, J. Sound. Vib. 158 (1992) 377.

DOI: 10.1016/0022-460x(92)90059-7

[3] M.S. Kushwaha, P. Halevi, L. Dobrzynski, B. Djafari-Rouhani, Acoustic band structure of periodic elastic composites, Phys. Rev. Lett. 71 (1993) (2022).

DOI: 10.1103/physrevlett.71.2022

[4] M.S. Kushwaha, Classical band structure of periodic elastic composites, Int. J. Mod. Phys. B 10 (1996) 977.

DOI: 10.1142/s0217979296000398

[5] M. Sigalas, E. Economou, Attenuation of multiple-scattered sound, EPL 36 (1996) 241.

DOI: 10.1209/epl/i1996-00216-4

[6] M. Kafesaki, E.N. Economou, Multiple-scattering theory for three-dimensional periodic acoustic composites, Phys. Rev. B 60 (1999) 11993.

DOI: 10.1103/physrevb.60.11993

[7] M. Sigalas, N. Garcıa, Theoretical study of three dimensional elastic band gaps with the finite-difference time-domain method, J. Appl. Phys. 87 (2000) 3122.

DOI: 10.1063/1.372308

[8] Y. Tanaka, Y. Tomoyasu, S. -i. Tamura, Band structure of acoustic waves in phononic lattices: Two-dimensional composites with large acoustic mismatch, Phys. Rev. B 62 (2000) 7387.

DOI: 10.1103/physrevb.62.7387

[9] Y. Cao, Z. Hou, Y. Liu, Finite difference time domain method for band-structure calculations of two-dimensional phononic crystals, Solid State Commun. 132 (2004) 539.

DOI: 10.1016/j.ssc.2004.09.003

[10] W. Axmann, P. Kuchment, An Efficient Finite Element Method for Computing Spectra of Photonic and Acoustic Band-Gap Materials: I. Scalar Case, J. Comput. Phys. 150 (1999) 468.

DOI: 10.1006/jcph.1999.6188

[11] W. Kuang, Z. Hou, Y. Liu, The effects of shapes and symmetries of scatterers on the phononic band gap in 2D phononic crystals, Phys. Lett. A 332 (2004) 481.

DOI: 10.1016/j.physleta.2004.10.009

[12] M.S. Kushwaha, P. Halevi, G. Martínez, L. Dobrzynski, B. Djafari-Rouhani, Theory of acoustic band structure of periodic elastic composites, Phys. Rev. B 49 (1994) 2313.

DOI: 10.1103/physrevb.49.2313

[13] Y. -H. Liu, C.C. Chang, R. -L. Chern, C.C. Chang, Phononic band gaps of elastic periodic structures: A homogenization theory study, Phys. Rev. B 75 (2007) 054104.

DOI: 10.1103/physrevb.75.054104

[14] M. Sigalas, E.N. Economou, Band structure of elastic waves in two dimensional systems, Solid State Commun. 86 (1993) 141.

DOI: 10.1016/0038-1098(93)90888-t

[15] J. Vasseur, B. Djafari-Rouhani, L. Dobrzynski, M. Kushwaha, P. Halevi, Complete acoustic band gaps in periodic fibre reinforced composite materials: the carbon/epoxy composite and some metallic systems, J. Phys: Condensed Matter 6 (1994) 8759.

DOI: 10.1088/0953-8984/6/42/008

[16] X. -Z. Zhou, Y. -S. Wang, C. Zhang, Effects of material parameters on elastic band gaps of two-dimensional solid phononic crystals, J. Appl. Phys. 106 (2009) 014903.

DOI: 10.1063/1.3159644

[17] C. Kittel, P. McEuen, P. McEuen, Introduction to solid state physics, Wiley New York, (1976).