Large-scale deterministic simulations are performed in order to observe the band gap formation in composite models having quasirandom fiber arrangements. Unidirectional fiber-reinforced composite panels are modeled in two-dimensional space with quasirandom fiber arrangements that can be qualified as “essentially regular with slight randomness.” Different quasirandom fiber arrangements are computationally generated using the same control parameters. Statistical parameters are used to quantitatively describe the fiber arrangements. Subsequently, a series of arrangements is generated from each base line arrangement by scaling up the coordinates of fiber centers, while the fiber diameter remains unchanged in order to study the effects of fiber spacing. Simulation results are compared with the corresponding case of ideally regular fiber arrangement. The most interesting observation is that the slight randomness in the fiber arrangements enhances the band gap phenomenon by introducing a few secondary band gaps adjacent to the primary band gap.

1.
Miyashita
,
T.
, 2005, “
Sonic Crystals and Sonic Wave-Guides
,”
Meas. Sci. Technol.
0957-0233,
16
(
5
), pp.
R47
R63
.
2.
Kushwaha
,
M. S.
,
Halevi
,
P.
,
Martinez
,
G.
,
Dobrzynski
,
L.
, and
Djafari-Rouhani
,
B.
, 1994, “
Theory of Acoustic Band Structure of Periodic Elastic Composites
,”
Phys. Rev. B
0163-1829,
49
(
4
), pp.
2313
2322
.
3.
Suzuki
,
T.
, and
Yu
,
P. K. L.
, 1996, “
Suppression and Enhancement of Elastodynamic Radiation From a Point Source Load in Elastic Wave Band Structures
,”
J. Appl. Phys.
0021-8979,
80
(
10
), pp.
5665
5673
.
4.
Chen
,
Y. Y.
, and
Ye
,
Z.
, 2001, “
Theoretical Analysis of Acoustic Stop Bands in Two-Dimensional Periodic Scattering Arrays
,”
Phys. Rev. E
1063-651X,
64
(
3
), pp.
036616
.
5.
Wu
,
F. G.
,
Liu
,
J. Y.
,
Liu
,
Y. Z.
, and
Liu
,
Y. Y.
, 2004, “
Splitting and Tuning Characteristics of the Point Defect Modes in Two-Dimensional Phononic Crystals
,”
Phys. Rev. E
1063-651X,
69
(
6
), pp.
066609
.
6.
Lambin
,
Ph.
,
Khelif
,
A.
,
Vasseur
,
J. O.
, and
Dobrzynski
,
L.
, 2001, “
Stopping of Acoustic Waves by Sonic Polymer-Fluid Composites
,”
Phys. Rev. E
1063-651X,
63
(
6
), pp.
066605
.
7.
Tanaka
,
Y.
, and
Tamura
,
S.
, 2002, “
Band Structures of Acoustic Waves in Phononic Lattices
,”
Physica B
0921-4526,
316–317
, pp.
237
239
.
8.
Cao
,
Y. J.
,
Hou
,
Z. L.
, and
Liu
,
Y. Y.
, 2004, “
Finite Difference Time Domain Method for Band-Structure Calculations of Two-Dimensional Phononic Crystals
,”
Solid State Commun.
0038-1098,
132
(
8
), pp.
539
543
.
9.
Sigalas
,
M. M.
, and
Garcia
,
N.
, 2000, “
Theoretical Study of Three Dimensional Elastic Band Gaps With the Finite-Difference Time-Domain Method
,”
J. Appl. Phys.
0021-8979,
87
(
6
), pp.
3122
3125
.
10.
Zhang
,
S.
, and
Cheng
,
J. C.
, 2003, “
Existence of Broad Acoustic Bandgaps in Three-Component Composite
,”
Phys. Rev. B
0163-1829,
68
(
24
), pp.
245101
.
11.
Laude
,
V.
,
Khelif
,
A.
,
Benchabane
,
S.
,
Wilm
,
M.
,
Sylvestre
,
T.
, and
Kibler
,
B.
, 2005, “
Phononic Band-Gap Guidance of Acoustic Modes in Photonic Crystal Fibers
,”
Phys. Rev. B
0163-1829,
71
(
4
), pp.
045107
.
12.
Kafesaki
,
M.
, and
Economou
,
E. N.
, 1999, “
Multiple-Scattering Theory for Three-Dimensional Periodic Acoustic Composites
,”
Phys. Rev. B
0163-1829,
60
(
17
), pp.
11993
12001
.
13.
Caballero
,
D.
,
Sanchez-Dehesa
,
J.
,
Rubio
,
C.
,
Martinez-Sala
,
R.
,
Sanchez-Perez
,
J. V.
, and
Meseguer
,
F.
, 1999, “
Large Two-Dimensional Sonic Band Gaps
,”
Phys. Rev. E
1063-651X,
60
(
6
), pp.
R6316
R6319
.
14.
Maslov
,
K.
,
Kinra
,
V. K.
, and
Henderson
,
B. K.
, 2000, “
Elastodynamic Response of a Coplanar Periodic Layer of Elastic Spherical Inclusions
,”
Mech. Mater.
0167-6636,
32
(
12
), pp.
785
795
.
15.
Liu
,
Z. Y.
,
Chan
,
C. T.
,
Sheng
,
P.
, and
Goertzen
,
A. L.
, 2000, “
Elastic Wave Scattering by Periodic Structures of Spherical Objects: Theory and Experiment
,”
Phys. Rev. B
0163-1829,
62
(
4
), pp.
2446
2457
.
16.
Platts
,
S. B.
,
Movchan
,
N. V.
,
McPhedran
,
R. C.
, and
Movchan
,
A. B.
, 2003, “
Band Gaps and Elastic Waves in Disordered Stacks: Normal Incidence
,”
Proc. R. Soc. London, Ser. A
1364-5021,
459
(
2029
), pp.
221
240
.
17.
Sainidou
,
R.
,
Stefanou
,
N.
,
Psarobas
,
I. E.
, and
Modinos
,
A.
, 2005, “
A Layer-Multiple-Scattering Method for Phononic Crystals and Heterostructures of Such
,”
Comput. Phys. Commun.
0010-4655,
166
, pp.
197
240
.
18.
Psarobas
,
I. E.
,
Stefanou
,
N.
, and
Modinos
,
A.
, 2000, “
Scattering of Elastic Waves by Periodic Arrays of Spherical Bodies
,”
Phys. Rev. B
0163-1829,
62
(
1
), pp.
278
291
.
19.
Cai
,
L.-W.
, 2006, “
Evaluation of Layered Multiple-Scattering Method for Antiplane Shear Wave Scattering From Gratings
,”
J. Acoust. Soc. Am.
0001-4966,
120
(
1
), pp.
49
61
.
20.
Sigalas
,
M. M.
,
Soukoulis
,
C. M.
,
Chan
,
C. T.
,
Biswas
,
R.
, and
Ho
,
K. M.
, 1999, “
Effect of Disorder on Photonic Band Gaps
,”
Phys. Rev. B
0163-1829,
59
(
20
), pp.
12767
12770
.
21.
Li
,
Z.-Y.
,
Zhang
,
X.
, and
Zhang
,
Z.-Q.
, 2000, “
Disordered Photonic Crystals Understood by a Perturbation Formalism
,”
Phys. Rev. B
0163-1829,
61
(
23
), pp.
15738
15748
.
22.
Frei
,
W. R.
, and
Johnson
,
H. T.
, 2004, “
Finite-Element Analysis of Disorder Effects in Photonic Crystals
,”
Phys. Rev. B
0163-1829,
70
(
16
), pp.
165116
.
23.
Cai
,
L.-W.
, and
Williams
,
J. H.
, Jr.
, 1999, “
Large Scale Multiple Scattering Problems
,”
Ultrasonics
0041-624X,
37
(
7
), pp.
453
462
.
24.
Cai
,
L.-W.
, and
Williams
,
J. H.
, Jr.
, 1999, “
Full-Scale Simulations of Elastic Wave Scattering in Fiber Reinforced Composites
,”
Ultrasonics
0041-624X,
37
(
7
), pp.
463
482
.
25.
Cai
,
L.-W.
, and
Williams
,
J. H.
, Jr.
, 1999, “
NDE via Stopband Formation in Fiber Reinforced Composites Having Square Fiber Arrangements
,”
Ultrasonics
0041-624X,
37
(
7
), pp.
483
492
.
26.
Cai
,
L.-W.
, 2004, “
Scattering of Antiplane Shear Waves by Layered Elastic Circular Cylinders
,”
J. Acoust. Soc. Am.
0001-4966,
115
(
2
), pp.
515
522
.
You do not currently have access to this content.