In the study, a retrieval approach is extended to determine the effective dynamic properties of a finite multilayered acoustic metamaterial based on the theoretical reflection and transmission analysis. The accuracy of the method is verified through a comparison of wave dispersion curve predictions from the homogeneous effective medium and the exact solution. A multiresonant design is then suggested for the desirable multiple wave band gaps by using a finite acoustic metamaterial slab. Finally, the band gap behavior and kinetic energy transfer mechanism in a multilayered composite with a periodic microstructure are studied to demonstrate the difference between the Bragg scattering mechanism and the locally resonant mechanism.

References

References
1.
Mártinez-Sala
,
R.
,
Sancho
,
J.
,
Sánchez
,
J. V.
,
Gómez
,
V.
,
Llinares
,
J.
, and
Meseguer
,
F.
, 1995, “
Sound Attenuation by Sculpture
,”
Nature (London)
,
378
, p.
241
.
2.
Huang
,
G. L.
and
Sun
,
C. T.
, 2010, “
Band Gaps in a Multiresonator Acoustic Metamaterial
,”
ASME J. Vib. Acoust.
,
132
, p.
031003
.
3.
Milton
G. W.
and
Willis
,
J. R.
, 2007, “
On Modification of Newton’s Second Law and Linear Continuum Elastodynamics
,”
Proc. R. Soc. London, Ser. A
,
463
, p.
855
.
4.
Sigalas
,
M. M.
and
Economou
,
E. N.
, 1992, “
Elastic and Acoustic Wave Band Structure
,”
J. Sound Vib.
,
158
, p.
377
.
5.
Kushwaha
,
M. S.
,
Halevi
,
P.
,
Dobrzynski
,
L.
, and
Djafari-Rouhani
,
B.
, 1993, “
Acoustic Band Structure of Periodic Elastic Composites
,”
Phys. Rev. Lett.
,
71
, p.
2022
.
6.
Montero de Espinosa
,
F. R.
,
Jimenez
,
E.
, and
Torres
,
M.
, 1998, “
Ultrasonic Band Gap in a Periodic Two-dimensional Composite
,”
Phys. Rev. Lett.
,
80
, p.
1208
.
7.
Liu
,
Z. Y.
,
Zhang
,
X. X.
,
Mao
,
Y. W.
,
Zhu
,
Y. Y.
,
Yang
,
Z. Y.
,
Chan
,
C. T.
, and
Sheng
,
P.
, 2000, “
Locally Resonant Sonic Materials
,”
Science
,
289
, p.
1734
.
8.
Sheng
,
P.
,
Zhang
,
X. X.
,
Liu
,
Z. Y.
, and
Chan
,
C. T.
, 2003, “
Locally Resonant Sonic Materials
,”
Physica B
,
338
, p.
201
.
9.
Zhou
,
X. M.
,
Hu
,
G. K.
, and
Lu
,
T. J.
, 2008, “
Elastic Wave Transparency of a Solid Sphere Coated with Metamaterials
,”
Phys. Rev. B
,
77
, p.
024101
.
10.
Yao
,
S. S.
,
Zhou
,
X. M.
, and
Hu
,
G. K.
, 2008, “
Experimental Study on Negative Effective Mass in a 1D Mass-Spring System
,”
New J. Phys.
,
10
, p.
043020
.
11.
Lee
,
S. H.
,
Kim
,
C. K.
,
Park
,
C. M.
,
Seo
,
Y. M.
,
Wang
,
Z. G.
, and
Kim
,
C. K.
, 2009, “
Acoustic Metamaterial with Negative Modulus
,”
J. Phys.: Condens. Matter
,
21
, p.
175704
.
12.
Lee
,
S. H.
,
Park
,
C. M.
,
Seo
,
Y. M.
,
Wang
,
Z. G.
, and
Kim
,
C. K.
, 2009, “
Acoustic Metamaterial with Negative Density
,”
Phys. Lett. A
,
373
, p.
4464
.
13.
Huang
,
H. H.
,
Sun
,
C. T.
, and
Huang
,
G. L.
, 2009, “
On the Negative Effective Mass Density in Acoustic Metamaterials
,”
Int. J. Eng. Sci.
,
47
, p.
610
.
14.
Li
,
J.
and
Chan
,
C. T.
, 2004, “
Double-Negative Acoustic Metamaterial
,”
Phys. Rev. E
,
70
, p.
055602
.
15.
Pai
,
P. F.
, 2010, “
Metamaterial-Based Broadband Elastic Wave Absorber
,”
J. Intell. Mater. Syst. Struct.
,
21
, p.
517
.
16.
Zhang
,
S.
Yin
,
L. L.
, and
Fang
,
N.
, 2009, “
Focusing Ultrasound with an Acoustic Metamaterial Network
,”
Phys. Rev. Lett.
,
102
, p.
194301
.
17.
Torrent
,
D.
and
Sánchez-Dehesa
,
J.
, 2007, “
Acoustic Metamaterials for New Two Dimensional Sonic Devices
,”
New J. Phys.
,
9
, p.
323
.
18.
Torrent
,
D.
and
Sánchez-Dehesa
,
J.
, 2008, “
Acoustic Cloaking in Two Dimensions: A Feasible Approach
,”
New J. Phys.
,
10
, p.
063015
.
19.
Zhu
,
J.
,
Christensen
,
J.
,
Jung
,
J.
,
Martín-Moreno
,
L.
,
Yin
,
X.
,
Fok
,
L.
,
Zhang
,
X.
, and
García-Vidal
,
F. J.
, 2011, “
A Holey-Structured Metamaterial for Acoustic Deep-Subwavelength Imaging
,”
Nature Phys.
,
7
, p.
52
.
20.
Li
,
J.
,
Fok
,
L.
,
Yin
,
X. B.
,
Bartal
,
G.
, and
Zhang
,
X.
, 2009, “
Experimental Demonstration of an Acoustic Magnifying Hyperlens
,”
Nature Mater.
,
8
, p.
931
.
21.
Baz
,
Amr. M.
, 2010, “
An Active Acoustic Metamaterial With Tunable Effective Density
,”
ASME J. Vibr. Acoust.
,
132
, p.
041011
.
22.
Wang
,
G.
,
Yu
,
D. L.
,
Wen
,
J. H.
,
Liu
,
Y. Z.
, and
Wen
,
X. S.
, 2004, “
One-Dimensional Phononic Crystals with Locally Resonant Structures
,”
Phys. Lett. A
,
327
, p.
512
.
23.
Zhao
,
D.
,
Wang
,
W.
,
Liu
,
Z.
,
Shi
,
J.
, and
Wen
,
W.
, 2007, “
Peculiar Transmission Property of Acoustic Waves in a One-Dimensional Layered Phononic Crystal
,”
Physica B
,
390
, pp.
159
166
.
24.
Nemat-Nasser
,
S.
, and
Willis
,
J. R.
, 2011, “
Homogenization of Periodic Elastic Composites and Locally Resonant Sonic Materials
,”
Phys. Rev. B
,
83
, p.
104103
.
25.
Manzanares-Martínez
,
B.
,
Sánchez-Dehesa
,
J.
,
Håkansson
,
A.
,
Cervera
,
F.
, and
Ramos-Mendieta
,
F.
, 2004, “
Experimental Evidence of Omnidirectional Elastic Bandgap in Finite One-dimensional Phononic Systems
,”
Appl. Phys. Lett.
,
85
, p.
154
.
26.
Day
,
N. A.
,
Zhu
,
C.
, and
Kinra
,
V. K.
, 1994, “
A Study of Dispersive Waves Propagation in Periodic Layered Composites
,”
Rev. Prog. Quant. Nondestruct. Eval.
,
13
, pp.
243
250
.
27.
Cao
,
W. W.
and
Qi
,
W. K.
, 1995, “
Plane-Wave Propagation in Finite 2-2-Composites
,”
J. Appl. Phys.
,
78
(
7
), pp.
4627
4632
.
28.
Hussein
,
M. I.
,
Hulbert
,
G. M.
, and
Scott
,
R. A.
, 2006, “
Dispersive Elastodynamics of 1D Banded Materials and Structures: Analysis
,”
J. Sound Vib.
,
289
(
4-5
), pp.
779
806
.
29.
Milton
,
G. W.
, 2002,
The Theory of Composites
,
Cambridge University Press
,
Cambridge
.
30.
Schoenberg
,
M.
and
Sen
,
P. N.
, 1983, “
Properties of a Periodically Stratified Acoustic Half-space and Its Relation to a Biot Fluid
,”
J. Acoust. Soc. Am.
,
73
, pp.
61
67
.
31.
Cheng
,
Y.
,
Yang
,
F.
,
Xu
,
J. Y.
, and
Liu
,
X. J.
, 2008, “
A Multilayer Structured Acoustic Cloak with Homogeneous Isotropic Materials
,”
Appl. Phys. Lett.
,
92
, p.
151913
.
32.
Torrent
,
D.
and
Sánchez-Dehesa
,
J.
, 2010, “
Anisotropic Mass Density by Radially Periodic Fluid Structures
,”
Phys. Rev. Lett.
,
105
, p.
174301
.
33.
Wu
,
Y.
,
Yun
,
L.
, and
Zhang
,
Z. Q.
, 2007, “
Effective Medium Theory for Elastic Metamaterials in Two Dimensions
,”
Phys. Rev. B
,
76
, p.
205313
.
34.
Zhou
,
X. M.
and
Hu
,
G. K.
, 2009, “
Analytic Model of Elastic Metamaterials with Local Resonances
,”
Phys. Rev. B
,
79
, p.
195109
.
35.
Smith
,
D. R.
,
Schultz
,
S.
,
Markos
,
P.
, and
Soukoulis
,
C. M.
, 2002, “
Determination of Effective Permittivity and Permeability of Metamaterials from Reflection and Transmission Coefficients
,”
Phys. Rev. B
,
65
, p.
195104
.
36.
Chen
,
X. D.
,
Grzegorczyk
,
T. M.
,
Wu
,
B. I.
,
Pacheco
,
J.
, and
Kong
,
J. A.
, 2004, “
Robust Method to Retrieve the Constitute Effective Parameters of Metamaterials
,”
Phys. Rev. E
,
70
, p.
016608
.
37.
Fokin
,
V.
,
Ambati
,
M.
,
Sun
,
C.
, and
Zhang
,
X.
, 2007, “
Method for Retrieving Effective Properties of Locally Resonant Acoustic Metamaterials
,”
Phys. Rev. B
,
76
, p.
144302
.
38.
Popa
,
B.
and
Cummer
,
S. A.
, 2009, “
Design and Characterization of Broadband Acoustic Composite Metamaterials
,”
Phys. Rev. B
,
80
, p.
174303
.
39.
Brekhovskikh
,
L.
, 1980,
Waves in Layered Media
,
Academic
,
New York
.
40.
Martin
,
P. A.
,
Maurel
,
A.
, and
Parnell
,
W. J.
, 2010, “
Estimating the Dynamic Effective Mass Density of Random Composites
,”
J. Acoust. Soc. Am.
,
128
, pp.
571
577
.
41.
Berryman
,
J. G.
, 1980, “
Long -Wavelength Propagation in Composite Elastic Media—I. Spherical Inclusions
,”
J. Acoust. Soc. Am.
,
68
, pp.
1809
1819
.
42.
Berryman
,
J. G.
, 1980, “
Long -Wavelength Propagation in Composite Elastic Media—II. Ellipsoidal Inclusions
,”
J. Acoust. Soc. Am.
,
68
, pp.
1820
1831
.
43.
Mei
,
J.
,
Liu
,
Z. Y.
,
Wen
,
W. J.
, and
Sheng
,
P.
, 2006, “
Effective Mass Density of Fluid-Solid Composites
,”
Phys. Rev. Lett.
,
96
, p.
024301
.
44.
Torrent
,
D.
and
Sánchez-Dehesa
,
J.
, 2006, “
Effective Parameters of Clusters of Cylinders Embedded in a Nonviscous Fluid or Gas
,”
Phys. Rev. B
,
74
, p.
224305
.
45.
Huang
,
H. H.
and
Sun
,
C. T.
, 2009, “
Wave Attenuation Mechanism in an Acoustic Metamaterial with Negative Effective Mass Density
,”
New J. Phys.
,
11
, p.
013003
.
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