In the present paper, the Dirichlet-to-Neumann map method is employed to compute the band structures of two-dimensional phononic crystals with smoothly sliding connection conditions between the matrix and the scatterers, which are composed of square or triangular lattices of circular solid cylinders in a solid matrix. The solid/solid systems of various material parameters with sliding interface conditions are considered. The influence of sliding interface conditions on the band structures is analyzed and discussed. The results show that the smoothly sliding interface condition has significant effect on the band structure.
Issue Section:
Technical Brief
References
1.
Kushwaha
, M. S.
, Halevi
, P.
, Dobrzynski
, L.
, and Djafari-Rouhani
, B.
, 1993
, “Acoustic Band Structure of Periodic Elastic Composites
,” Phys. Rev. Lett.
, 71
, pp. 2022
–2025
.10.1103/PhysRevLett.71.20222.
Goffaux
, C.
, and Vigneron
, J. P.
, 2001
, “Theoretical Study of a Tunable Phononic Band Gap System
,” Phys. Rev. B
, 64
, p. 075118
.10.1103/PhysRevB.64.0751183.
Bian
, Z. G.
, Peng
, W.
, and Song
, J. Z.
, 2013
, “Thermal Tuning of Band Structures in a One-Dimensional Phononic Crystal
,” ASME J. Appl. Mech.
, 81
, p. 041008
.10.1115/1.40250584.
Liu
, Z.
, Chan
, C. T.
, Sheng
, P.
, Goertzen
, A. L.
, and Page
, J. H.
, 2000
, “Elastic Wave Scattering by Periodic Structures of Spherical Objects: Theory and Experiment
,” Phys. Rev. B
, 62
, pp. 2446
–2457
.10.1103/PhysRevB.62.24465.
Montero de Espinosa
, F. R.
, Jimenez
, E.
, and Torres
, M.
, 1998
, “Ultrasonic Band Gap in a Periodic Two-Dimensional Composite
,” Phys. Rev. Lett.
, 80
, pp. 1208
–1211
.10.1103/PhysRevLett.80.12086.
Liu
, Z.
, Zhang
, X.
, Mao
, Y.
, Zhu
, Y. Y.
, Yang
, Z.
, Chan
, C. T.
, and Sheng
, P.
, 2000
, “Locally Resonant Sonic Materials
,” Science
, 289
, pp. 1734
–1736
.10.1126/science.289.5485.17347.
Goffaux
, C.
, and Sanchez-Dehesa
, J.
, 2003
, “Two-Dimensional Phononic Crystals Studied Using a Variational Method: Application to Lattices of Locally Resonant Materials
,” Phys. Rev. B
, 67
, p. 144301
.10.1103/PhysRevB.67.1443018.
Liu
, Z.
, Chan
, C. T.
, and Cheng
, P.
, 2002
, “Three-Component Elastic Wave Band-Gap Material
,” Phys. Rev. B
, 65
, p. 165116
.10.1103/PhysRevB.65.1651169.
Cervera
, F.
, Sanchis
, L.
, Sanchez-Perez
, J. V.
, Martinez-Sala
, R.
, Rubio
, C.
, Meseguer
, F.
, Lopez
, C.
, Caballero
, D.
, and Sanchez-Dehesa
, J.
, 2001
, “Refractive Acoustic Devices for Airborne Sound
,” Phys. Rev. Lett.
, 88
, p. 023902
.10.1103/PhysRevLett.88.02390210.
Vasseur
, J. O.
, Deymier
, P. A.
, Frantziskonis
, G.
, Chenni
, B.
, Djafari-Rouhani
, B.
, Dobrzynski
, L.
, and Prevost
, D.
, 2001
, “Experimental and Theoretical Evidence for the Existence of Absolute Acoustic Band Gaps in Two-Dimensional Solid Phononic Crystals
,” Phys. Rev. Lett.
, 86
, pp. 3012
–3015
.10.1103/PhysRevLett.86.301211.
Torres
, M.
, Montero de Espinosa
, F. R.
, and Aragon
, J. L.
, 2002
, “Ultrasonic Wedges for Elastic Wave Bending and Splitting Without Requiring a Full Band Gap
,” Phys. Rev. Lett.
, 86
, pp. 4282
–4285
.10.1103/PhysRevLett.86.428212.
Wu
, T. T.
, Huang
, Z. G.
, and Lin
, S.
, 2004
, “Surface and Bulk Acoustic Waves in Two-Dimensional Phononic Crystal Consisting of Materials With General Anisotropy
,” Phys. Rev. B
, 69
, p. 094301
.10.1103/PhysRevB.69.09430113.
Tanaka
, Y.
, Tomoyasu
, Y.
, and Tamura
, S.
, 2000
, “Band Structure of Acoustic Waves in Phononic Lattices: Two-Dimensional Composites With Large Acoustic Mismatch
,” Phys. Rev. B
, 62
, pp. 7387
–7392
.10.1103/PhysRevB.62.738714.
Sigalas
, M. M.
, and Gálvez
, N.
, 2000
, “Importance of Coupling Between Longitudinal and Transverse Components for the Creation of Acoustic Band Gaps: The Aluminum in Mercury Case
,” Appl. Phys. Lett.
, 76
, pp. 2307
–2309
.10.1063/1.12632815.
Yan
, Z. Z.
, Wang
, Y. S.
, and Zhang
, Ch.
, 2008
, “A Method Based on Wavelets for Band Structure Analysis of Phononic Crystals
,” Comput. Model Eng. Sci.
, 38
, pp. 59
–87
10.3970/cmes.2008.038.059.16.
Yan
, Z. Z.
, Wang
, Y. S.
, and Zhang
, Ch.
, 2008
, “Wavelet Method for Calculating the Defect States of Two-Dimensional Phononic Crystals
,” Acta Mech. Solida Sinica
, 21
, pp. 104
–109
.10.1007/s10338-008-0813-617.
Mei
, J.
, Liu
, Z. Y.
, and Shi
, J.
, 2003
, “Theory for Elastic Wave Scattering by a Two Dimensional Periodical Array of Cylinders: An Ideal Approach for Band-Structure Calculations
,” Phys. Rev. B
, 67
, p. 245107
.10.1103/PhysRevB.67.24510718.
Cai
, B.
, and Wei
, P. J.
, 2013
, “Surface/Interface Effect on Dispersion Relations of 2D Phononic Crystals With Parallel Nanoholes or Nanofibers
,” Acta Mech.
, 224
, pp. 2749
–2758
.10.1007/s00707-013-0886-219.
Qiu
, C. Y.
, Liu
, Z. Y.
, and Mei
, J.
, 2005
, “The Layer Multiple Scattering Method for Calculating Transmission Coefficients of 2D Phononic Crystals
,” Solid State Commun.
, 134
, pp. 765
–770
.10.1016/j.ssc.2005.02.03420.
Mei
, J.
, Liu
, Z. Y.
, and Qiu
, C. Y.
, 2005
, “Multiple-Scattering Theory for Out-of-Plane Propagation of Elastic Waves in Two-Dimensional Phononic Crystals
,” J. Phys. Condens. Matter
, 17
, pp. 3735
–3757
.10.1088/0953-8984/17/25/00321.
Liu
, W.
, Chen
, J. W.
, Liu
, Y. Q.
, and Su
, X. Y.
, 2012
, “Effect of Interface/Surface Stress on the Elastic Wave Band Structure of Two-Dimensional Phononic Crystals
,” Phys. Lett. A
, 376
, pp. 605
–609
.10.1016/j.physleta.2011.11.04322.
Li
, F. L.
, Wang
, Y. S.
, Zhang
, Ch.
, and Yu
, G. L.
, 2013
, “Boundary Element Method for Band Gap Calculations of Two-Dimensional Solid Phononic Crystals
,” Eng. Anal. Boundary Elem.
, 37
, pp. 225
–235
.10.1016/j.enganabound.2012.10.00323.
Li
, F. L.
, Wang
, Y. S.
, Zhang
, Ch.
, and Yu
, G. L.
, 2013
, “Bandgap Calculations of Two-Dimensional Solid–Fluid Phononic Crystals With the Boundary Element Method
,” Wave Motion
, 50
, pp. 525
–541
.10.1016/j.wavemoti.2012.12.00124.
Yuan
, J. H.
, and Lu
, Y. Y.
, 2006
, “Photonic Bandgap Calculations With Dirichlet-to-Neumann Maps
,” Opt. Soc. Am.
, 23
, pp. 3217
–3222
.10.1364/JOSAA.23.00321725.
Yuan
, J. H.
, and Lu
, Y. Y.
, 2007
, “Computing Photonic Band Structures by Dirichlet-to-Neumann Maps: The Triangular Lattice
,” Opt. Commun.
, 273
, pp. 114
–120
.10.1016/j.optcom.2007.01.00526.
Yuan
, J. H.
, Lu
, Y. Y.
, and Antoine
, X.
, 2008
, “Modeling Photonic Crystals by Boundary Integral Equations and Dirichlet-to-Neumann Maps
,” J. Comput. Phys.
, 227
, pp. 4617
–4629
.10.1016/j.jcp.2008.01.01427.
Li
, F. L.
, and Wang
, Y. S.
, 2011
, “Application of Dirichlet-to-Neumann Map to Calculation of Band Gaps for Scalar Waves in Two-Dimensional Phononic Crystals
,” Acta. Acust. Acust.
, 97
, pp. 284
–290
.10.3813/AAA.91840828.
Zhen
, N.
, Li
, F. L.
, Wang
, Y. S.
, and Zhang
, Ch.
, 2012
, “Bandgap Calculation for Mixed In-Plane Waves in 2D Phononic Crystals Based on Dirichlet-to-Neumann Map
,” Acta Mech. Sinica
, 28
, pp. 1143
–1153
.10.1007/s10409-012-0092-929.
Li
, F. L.
, Wang
, Y. S.
, and Zhang
, Ch.
, 2011
, “Bandgap Calculation of Two-Dimensional Mixed Solid–Fluid Phononic Crystals by Dirichlet-to-Neumann Maps
,” Phys. Scr.
, 84
, p. 055402
.10.1088/0031-8949/84/05/05540230.
Zhen
, N.
Wang
, Y. S.
and Zhang
, Ch.
, 2012
, “Surface/Interface Effect on Band Structures of Nanosized Phononic Crystals
,” Mech. Res. Commun.
, 46
, pp. 81
–89
.10.1016/j.mechrescom.2012.09.00231.
Zhen
, N.
, Wang
, Y. S.
, and Zhang
, Ch.
, 2013
, “Bandgap Calculation of In-Plane Waves in Nanoscale Phononic Crystals Taking Account of Surface/Interface Effects
,” Phys. Rev. E
, 54
, pp. 125
–132
.10.1016/j.physe.2013.06.01232.
Bostrom
, A.
, 1980
, “Scattering by a Smooth Elastic Obstacle
,” J. Acoust. Soc. Am.
, 67
, pp. 1904
–1913
.10.1121/1.38445533.
Olsson
, P.
, 1986
, “Scattering of Elastic Waves by a Smooth Rigid Movable Inclusion
,” J. Acoust. Soc. Am.
, 79
, pp. 1237
–1247
.10.1121/1.39370334.
Stagni
, L
, 1991
, “Elastic Field Perturbation by an Elliptic Inhomogeneity With a Sliding Interface
,” J. Appl. Mech. Phys.
, 42
, pp. 811
–816
.10.1007/BF0094456435.
Vijayakumar
, S.
, and Cormack
, D. E.
, 1987
, “Nuclei of Strain for Bi-Material Elastic Media With Sliding Interface
,” J. Elast.
, 17
, pp. 285
–290
.10.1007/BF0004945936.
Wang
, G.
, Shao
, L. H.
, Liu
, Y. Z.
, and Wen
, J. H.
, 2006
, “Accurate Evaluation of Lowest Band Gaps in Ternary Locally Resonant Phononic Crystals
,” Chin. Phys.
, 15
, pp. 1843
–1848
.10.1088/1009-1963/15/8/036Copyright © 2014 by ASME
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