Previous studies on photonic crystals raise the exciting topic of phononic crystals. This paper presents the results of tunable band gaps in the acoustic waves of two-dimensional phononic crystals with reticular geometric structures using the 2D and 3D finite element methods. This paper calculates and discusses the band gap variations of the bulk modes due to different sizes of reticular geometric structures. Results show that adjusting the orientation of the reticular geometric structures can increase or decrease the total elastic band gaps for mixed polarization modes. The band gap phenomena of elastic or acoustic waves can potentially be utilized to achieve vibration-free, high-precision mechanical systems, and sound insulation.

1.
Johnson
,
S. G.
, and
Joannopoulos
,
J. D.
, 2003,
Photonic Crystals: The Road From Theory to Practice
,
Kluwer Academic
,
Boston
.
2.
Joannopoulos
,
J. D.
,
Meade
,
R. D.
, and
Winn
,
J. N.
, 1995,
Photonic Crystals: Molding the Flow of Light
,
Princeton University Press
,
Princeton, NJ
.
3.
Leung
,
K. M.
, and
Liu
,
Y. F.
, 1990, “
Full Vector Wave Calculation of Photonic Band Structures in Face-Centered-Cubic Dielectric Media
,”
Phys. Rev. Lett.
0031-9007,
65
, pp.
2646
2649
.
4.
Johnson
,
S.
, and
Joannopoulos
,
J.
, 2001, “
Block-Iterative Frequency-Domain Methods for Maxwell’s Equations in a Planewave Basis
,”
Opt. Express
1094-4087,
8
, pp.
173
190
.
5.
Hussein
,
M. I.
, 2009, “
Reduced Bloch Mode Expansion for Periodic Media Band Structure Calculations
,”
Proc. R. Soc. London, Ser. A
0950-1207,
465
, pp.
2825
2848
.
6.
Kushwaha
,
M. S.
,
Halevi
,
P.
,
Dobrzynski
,
L.
, and
Djafari-Rouhani
,
B.
, 1993, “
Acoustic Band Structure of Periodic Elastic Composites
,”
Phys. Rev. Lett.
0031-9007,
71
, pp.
2022
2025
.
7.
Vasseur
,
J. O.
,
Deymier
,
P. A.
,
Frantziskonis
,
G.
,
Hong
,
G.
,
Djafari-Rouhani
,
B.
, and
Dobrzynski
,
L.
, 1998, “
Experimental Evidence for the Existence of Absolute Acoustic Band Gaps in Two-Dimensional Periodic Composite Media
,”
J. Phys.: Condens. Matter
0953-8984,
10
, pp.
6051
.
8.
Goffaux
,
C.
, and
Vigneron
,
J. P.
, 2001, “
Theoretical Study of a Tunable Phononic Band Gap System
,”
Phys. Rev. B
0556-2805,
64
, p.
075118
.
9.
Tanaka
,
Y.
, and
Tamura
,
S. i.
, 1998, “
Surface Acoustic Waves in Two-Dimensional Periodic Elastic Structures
,”
Phys. Rev. B
0556-2805,
58
, pp.
7958
7965
.
10.
Wu
,
T. -T.
,
Huang
,
Z. G.
, and
Lin
,
S.
, 2004, “
Surface and Bulk Acoustic Waves in Two-Dimensional Phononic Crystals Consisting of Materials With General Anisotropy
,”
Phys. Rev. B
0556-2805,
69
, p.
094301
.
11.
Huang
,
Z. -G.
, and
Wu
,
T. -T.
, 2005, “
Temperature Effect on the Bandgaps of Surface and Bulk Acoustic Waves in Two-Dimensional Phononic Crystals
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
0885-3010,
52
, pp.
365
370
.
12.
Wu
,
T. -T.
, and
Huang
,
Z. G.
, 2004, “
Level Repulsion of Bulk Acoustic Waves in Composite Materials
,”
Phys. Rev. B
0556-2805,
70
, p.
214304
.
13.
Wu
,
T. -T.
,
Hsu
,
Z. C.
, and
Huang
,
Z. G.
, 2005, “
Band Gaps and the Electromechanical Coupling Coefficient of a Surface Acoustic Wave in a Two-Dimensional Piezoelectric Phononic Crystal
,”
Phys. Rev. B
0556-2805,
71
, p.
064303
.
14.
Laude
,
V.
,
Wilm
,
M.
,
Benchabane
,
S.
, and
Khelif
,
A.
, 2005, “
Full Band Gap for Surface Acoustic Waves in a Piezoelectric Phononic Crystal
,”
Phys. Rev. E
1063-651X,
71
, p.
036607
.
15.
Wang
,
X.
,
Zhang
,
X. -G.
,
Yu
,
Q.
, and
Harmon
,
B. N.
, 1993, “
Multiple-Scattering Theory for Electromagnetic Waves
,”
Phys. Rev. B
0556-2805,
47
, pp.
4161
4167
.
16.
Leung
,
K. M.
, and
Qiu
,
Y.
, 1993, “
Multiple-Scattering Calculation of the Two-Dimensional Photonic Band Structure
,”
Phys. Rev. B
0556-2805,
48
, pp.
7767
7771
.
17.
Kafesaki
,
M.
, and
Economou
,
E. N.
, 1999, “
Multiple-Scattering Theory for Three-Dimensional Periodic Acoustic Composites
,”
Phys. Rev. B
0556-2805,
60
, pp.
11993
12001
.
18.
Psarobas
,
I. E.
,
Stefanou
,
N.
, and
Modinos
,
A.
, 2000, “
Scattering of Elastic Waves by Periodic Arrays of Spherical Bodies
,”
Phys. Rev. B
0556-2805,
62
, pp.
278
291
.
19.
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
0556-2805,
62
, pp.
2446
2457
.
20.
Yang
,
H. Y. D.
, 1996, “
Finite Difference Analysis of 2-D Photonic Crystals
,”
IEEE Trans. Microwave Theory Tech.
0018-9480,
44
, pp.
2688
2695
.
21.
García-Pablos
,
D.
,
Sigalas
,
M.
,
Montero de Espinosa
,
F. R.
,
Torres
,
M.
,
Kafesaki
,
M.
, and
Garcia
,
N.
, 2000, “
Theory and Experiments on Elastic Band Gaps
,”
Phys. Rev. Lett.
0031-9007,
84
, pp.
4349
4352
.
22.
Sun
,
J. H.
, and
Wu
,
T. -T.
, 2005, “
Analyses of Mode Coupling in Joined Parallel Phononic Crystal Waveguides
,”
Phys. Rev. B
0556-2805,
71
, p.
174303
.
23.
Pendry
,
J. B.
, and
MacKinnon
,
A.
, 1992, “
Calculation of Photon Dispersion Relations
,”
Phys. Rev. Lett.
0031-9007,
69
, pp.
2772
2775
.
24.
Jun
,
S.
,
Cho
,
Y. -S.
, and
Im
,
S.
, 2003, “
Moving Least-Square Method for the Band-Structure Calculation of 2D Photonic Crystals
,”
Opt. Express
1094-4087,
11
, pp.
541
551
.
25.
Moreno
,
E.
,
Erni
,
D.
, and
Hafner
,
C.
, 2002, “
Band Structure Computations of Metallic Photonic Crystals With the Multiple Multipole Method
,”
Phys. Rev. B
0556-2805,
65
, p.
155120
.
26.
Checoury
,
X.
, and
Lourtioz
,
J. -M.
, 2006, “
Wavelet Method for Computing Band Diagrams of 2D Photonic Crystals
,”
Opt. Commun.
0030-4018,
259
, pp.
360
365
.
27.
Yan
,
Z. Z.
, and
Wang
,
Y. S.
, 2006, “
Wavelet-Based Method for Calculating Elastic Band Gaps of Two-Dimensional Phononic Crystals
,”
Phys. Rev. B
0556-2805,
74
, p.
224303
.
28.
Chiang
,
P. J.
,
Yu
,
C. P.
, and
Chang
,
H. C.
, 2007, “
Analysis of Two-Dimensional Photonic Crystals Using a Multidomain Pseudospectral Method
,”
Phys. Rev. E
1063-651X,
75
, p.
026703
.
29.
Dobson
,
D. C.
, 1999, “
An Efficient Method for Band Structure Calculations in 2D Photonic Crystals
,”
J. Comput. Phys.
0021-9991,
149
, pp.
363
376
.
30.
Axmann
,
W.
, and
Kuchment
,
P.
, 1999, “
An Efficient Finite Element Method for Computing Spectra of Photonic and Acoustic Band-Gap Materials: I. Scalar Case
,”
J. Comput. Phys.
0021-9991,
150
, pp.
468
481
.
31.
Wu
,
T. -T.
,
Huang
,
Z. G.
,
Tsai
,
T. C.
, and
Wu
,
T. C.
, 2008, “
Evidence of Complete Band Gap and Resonances in a Plate With Periodic Stubbed Surface
,”
Appl. Phys. Lett.
0003-6951,
93
, p.
111902
.
32.
Huang
,
G. L.
, and
Sun
,
C. T.
, 2010, “
Band Gaps in a Multiresonator Acoustic Metamaterial
,”
ASME J. Vibr. Acoust.
0739-3717,
132
, p.
031003
.
33.
Salehian
,
A.
, and
Inman
,
D. J.
, 2010, “
Micropolar Continuous Modeling and Frequency Response Validation of a Lattice Structure
,”
ASME J. Vibr. Acoust.
0739-3717,
132
, p.
011010
.
34.
Burger
,
M. S.
,
Osher
,
J.
, and
Yablonovitch
,
E.
, 2004, “
Inverse Problem Techniques for the Design of Photonic Crystals
,”
IEICE Trans. Electron.
0916-8524,”
E87C
, pp.
258
265
.
35.
COMSOL Multiphysics
, 2009,
Structural Mechanics, Manual
,
COMSOL AB
,
Stockholm, Sweden
.
36.
Tanaka
,
Y.
,
Tomoyasu
,
Y.
, and
Tamura
,
S. I.
, 2000, “
Band Structure of Acoustic Waves in Phononic Lattices: Two-Dimensional Composites With Large Acoustic Mismatch
,”
Phys. Rev. B
0556-2805,
62
(
11
), pp.
7387
7392
.
You do not currently have access to this content.