Considerable interest has been devoted to the development of various classes of acoustic metamaterials. Acoustic metamaterials are those structurally engineered materials that are composed of periodic cells designed in such a fashion to yield specific material properties (density and bulk modulus) that would affect the wave propagation pattern within in a specific way. All the currently exerted efforts are focused on studying passive metamaterials with fixed material properties. In this paper, the emphasis is placed on the development of a new class of composite one-dimensional acoustic metamaterials with effective densities that are programmed to vary according to any prescribed patterns along the volume of the metamaterial. The theoretical analysis of this class of multilayered composite active acoustic metamaterials (CAAMM) is presented and the theoretical predictions are determined for an array of fluid cavities separated by piezoelectric boundaries. These smart self-sensing and actuating boundaries are used to modulate the overall stiffness of the metamaterial periodic cell and in turn its dynamic density through direct acoustic pressure feedback. The interaction between the neighboring layers of the composite metamaterial is modeled using a lumped-parameter approach. One-dimensional wave propagation as well as long wavelength assumptions are adapted in the current analysis. Numerical examples are presented to demonstrate the performance characteristics of the proposed CAAMM and its potential for generating prescribed spatial and spectral patterns of density variation. The CAAMM presents a viable approach to the development of effective acoustic cloaks that can be used for treating critical objects in order to render them acoustically invisible.

References

References
1.
Lapine
,
M.
,
2007
, “
The Age of Metamaterials
,”
Metamaterials
,
1
,
pp.
1
.10.1016/j.metmat.2007.02.006
2.
Shamonina
,
E.
, and
Solymar
,
L.
,
2007
, “
Metamaterials: How the Subject Started
,”
Metamaterials
,
1
,
pp.
12
18
.10.1016/j.metmat.2007.02.001
3.
Guenneau
,
S.
,
Movchan
,
A.
,
Pétursson
,
G.
, and
Ramakrishna
,
S.
,
2007
, “
Acoustic Metamaterials for Sound Focusing and Confinement
,”
New J. Phys.
,
9
,
p.
399
.10.1088/1367-2630/9/11/399
4.
Torrent
,
D.
, and
Sanchez-Dehesa
,
J.
,
2007
, “
Acoustic Metamaterials for New Two-Dimensional Sonic Devices
,”
New J. Phys.
,
9
,
p.
323
.10.1088/1367-2630/9/9/323
5.
Torrent
,
D.
, and
Sanchez-Dehesa
,
J.
,
2008
, “
Anisotropic Mass Density by Two-Dimensional Acoustic Metamaterials
,”
New J. Phys.
,
10
,
p.
023004
. 10.1088/1367-2630/10/2/023004
6.
Cervera
,
F.
,
Sanchis
,
L.
,
Pérez
,
J. S.
,
Sala
,
R.
,
Rubio
,
C.
, and
Meseguer
,
F.
,
2001
, “
Refractive Acoustic Devices for Airborne Sound
,”
Phys. Rev. Lett.
,
88
(
2
), p.
023902
.10.1103/PhysRevLett.88.023902
7.
Krokhin
,
A. A.
,
Arriaga
,
J.
, and
Gumen
,
L. N.
,
2003
, “
Speed of Sound in Periodic Elastic Composites
,”
Phys. Rev. Lett.
,
91
(
26
), p.
264302
.10.1103/PhysRevLett.91.264302
8.
Torrent
,
D.
,
Sanchez-Dehesa
,
J.
, and
Cervera
,
F.
,
2007
, “
Evidence of Two-Dimensional Magic Clusters in the Scattering of Sound
,”
Phys. Rev. B
,
75
, p.
241404
.10.1103/PhysRevB.75.241404
9.
Farhat
,
M.
,
Enoch
,
S.
,
Guenneau
,
S.
, and
Movchan
,
A. B.
,
2008
, “
Broadband Cylindrical Acoustic Cloak for Linear Surface Waves in a Fluid
,”
Phys. Rev. Lett.
,
101
, p.
134501
.10.1103/PhysRevLett.101.134501
10.
Chan
,
C. T.
,
Jensen
,
L. I.
, and
Fung
,
K. H.
,
2006
, “
On Extending the Concept of Double Negativity to Acoustic Waves
,”
J. Zhejiang Univ. Sci. A
,
7
(
1
),
pp.
24
28
.10.1631/jzus.2006.A0024
11.
Milton
,
G. W.
, and
Willis
,
J. R.
,
2006
, “
On Modifications of Newton's Second Law and Linear Continuum Elastodynamics
,”
Proc. R. Soc
.,
London, Ser. A
,
463
,
pp.
855
880
. 10.1098/rspa.2006.1795
12.
Yao
,
S.
,
Zhou
,
X.
, and
Hu
,
G.
,
2008
, “
Experimental Study on Negative Effective Mass in a 1D Mass–Spring System
,”
New J. Phys.
,
10
, p.
043020
.10.1088/1367-2630/10/4/043020
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
,
pp.
610
617
.10.1016/j.ijengsci.2008.12.007
14.
Pendry
,
J. B.
,
2000
, “
Negative Refraction Makes a Perfect Lens
,”
Phys. Rev. Lett.
,
85
(
18
),
pp.
3966
3969
.10.1103/PhysRevLett.85.3966
15.
Berryman
,
J. G.
,
2006
, “
Effective Medium Theories for Multicomponent Poroelastic Composites
,”
J. Eng. Mech.
,
132
(
5
),
pp.
519
531
.10.1061/(ASCE)0733-9399(2006)132:5(519)
16.
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
,
pp.
4464
4469
.10.1016/j.physleta.2009.10.013
17.
Lee
,
S. H.
,
Park
,
C. M.
,
Seo
,
Y. M.
,
Wang
,
Z. G.
, and
Kim
,
C. K.
,
2009
, “
Reverse Doppler Effect of Sound
,”
e-print arXiv:cond-mat/0901.2772v2
.
18.
Photiadis
,
D.
,
1991
, “
The Effect of Wall Elasticity on the Properties of a Helmholtz Resonator
,”
J. Acoust. Soc. Am.
,
90
(
2
),
pp.
1188
1190
.10.1121/1.402026
19.
Huang
,
L.
,
1999
, “
A Theoretical Study of Duct Noise Control by Flexible Panels
,”
J. Acoust. Soc. Am.
,
106
(
4
),
pp.
1801
1809
.10.1121/1.427930
20.
Huang
,
L.
,
Choy
,
Y.
,
So
,
R. M. C.
, and
Chong
,
T.
,
2000
, “
Experimental Study of Sound Propagation in a Flexible Panel
,”
J. Acoust. Soc. Am.
,
108
(
2
),
pp.
624
631
.10.1121/1.429594
21.
Huang
,
L.
,
2002
, “
Modal Analysis of a Drum-Like Silencer
,”
J. Acoust. Soc. Am.
,
112
(
5
),
pp.
2014
2025
.10.1121/1.1508778
22.
Choia
,
S.
, and
Kim
,
Y.
,
2002
, “
Sound-Wave Propagation in a Membrane–Duct (L)
,”
J. Acoust. Soc. Am.
,
112
(
5
),
pp.
1749
1752
.10.1121/1.1509761
23.
Chiu
,
Y. H.
,
Cheng
,
L.
, and
Huang
,
L.
,
2006
, “
Drum-Like Silencers Using Magnetic Forces in a Pressurized Cavity
,”
J. Sound Vib.
,
297
,
pp.
895
915
.10.1016/j.jsv.2006.05.006
24.
Torrent
,
D.
,
Hakansson
,
A.
,
Cervera
,
F.
, and
Sanchez-Dehesa
,
J.
,
2006
, “
Homogenization of Two-Dimensional Clusters of Rigid Rods in Air
,”
Phys. Rev. Lett.
,
95
, p.
204302
.10.1103/PhysRevLett.96.204302
25.
Hubbard
,
G. C.
,
1931
, “
The Acoustic Resonator Interferometer: I. The Acoustic System and Its Equivalent Electric Network
,”
Phys. Rev.
,
38
,
pp.
1011
1019
.10.1103/PhysRev.38.1011
26.
Prasad
,
S.
,
Gallas
,
Q.
,
Horowitz
,
S.
,
Homeijer
,
B.
,
Sankar
,
B. V.
,
Cattafesta
,
L. N.
, and
Sheplak
,
M.
,
2006
, “
Analytical Electroacoustic Model of a Piezoelectric Composite Circular Plate
,“
AIAA J.
,
44
(
10
),
pp.
2311
2318
.10.2514/1.19855
27.
Blauert
,
J.
, and
Xiang
,
N.
,
2009
,
Acoustics for Engineers
,
2nd ed.
,
Springer
,
Berlin
.
28.
Kinsler
,
L.
,
Frey
,
A.
,
Coppens
,
A.
, and
Sanders
,
J.
,
2000
,
Fundamentals of Acoustics
,
4th ed.
,
John Wiley & Sons, Inc.
,
New York - London
.
29.
Li
,
J.
, and
Chan
,
C. T.
,
2004
, “
Double-Negative Acoustic Metamaterial
,”
Phys. Rev. E
,
70
, p.
055602
.10.1103/PhysRevE.70.055602
30.
Mei
,
J.
,
Liu
,
Z.
,
Wen
,
W.
, and
Sheng
,
P.
,
2006
, “
Effective Mass Density of Fluid-Solid Composites
,”
Phys. Rev. Lett.
,
96
, p.
024301
.10.1103/PhysRevLett.96.024301
31.
Fang
,
N.
,
Xi
,
D.
,
Xu
,
J.
,
Ambati
,
M.
,
Srituravanich
,
W.
,
Sun
,
C.
, and
Zhang
,
X.
,
2006
, “
Ultrasonic Metamaterials With Negative Modulus
,”
Nature Mater.
,
5
,
pp.
452
456
.10.1038/nmat1644
32.
Baz
,
A.
,
2009
, “
The Structure of an Active Acoustic Metamaterial With Tunable Effective Density
,”
New J. Phys.
,
11
, p.
123010
.10.1088/1367-2630/11/12/123010
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