Abstract

Phononic crystals (PCs) and metamaterials (MMs) can exhibit abnormal properties, even far beyond those found in nature, through artificial design of the topology or ordered structure of unit cells. This emerging class of materials has diverse application potentials in many fields. Recently, the concept of tunable PCs or MMs has been proposed to manipulate a variety of wave functions on demand. In this review, we survey recent developments in tunable and active PCs and MMs, including bandgap and bandgap engineering, anomalous behaviors of wave propagation, as well as tunable manipulation of waves based on different regulation mechanisms: tunable mechanical reconfiguration and materials with multifield coupling. We conclude by outlining future directions in the emerging field.

References

1.
Deymier
,
P. A.
,
2013
,
Acoustic Metamaterials and Phononic Crystals
,
Springer Science & Business Media
,
Heidelberg
.
2.
Laude
,
V.
,
2015
,
Phononic Crystals: Artificial Crystals for Sonic, Acoustic, and Elastic Waves
,
Walter de Gruyter GmbH & Co KG
,
Berlin
.
3.
Khelif
,
A.
, and
Adibi
,
A.
,
2016
,
Phononic Crystals: Fundamentals and Applications
,
Springer
,
Berlin, Germany
.
4.
Phani
,
A. S.
, and
Hussein
,
M. I.
,
2017
,
Dynamics of Lattice Materials
,
Wiley
,
New York
.
5.
Sigalas
,
M. M.
, and
Economou
,
E. N.
,
1992
, “
Elastic and Acoustic Wave Band Structure
,”
J. Sound Vib.
,
158
(
2
), pp.
377
382
.10.1016/0022-460X(92)90059-7
6.
Kushwaha
,
M. S.
,
Halevi
,
P.
,
Dobrzynski
,
L.
, and
Djafari-Rouhani
,
B.
,
1993
, “
Acoustic Band Structure of Periodic Elastic Composites
,”
Phys. Rev. Lett.
,
71
(
13
), pp.
2022
2025
.10.1103/PhysRevLett.71.2022
7.
Mead
,
D. M.
,
1996
, “
Wave Propagation in Continuous Periodic Structures: Research Contributions From Southampton, 1964–1995
,”
J. Sound Vib.
,
190
(
3
), pp.
495
524
.10.1006/jsvi.1996.0076
8.
Hussein
,
M. I.
,
Leamy
,
M. J.
, and
Ruzzene
,
M.
,
2014
, “
Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook
,”
ASME Appl. Mech. Rev.
,
66
(
4
), p.
040802
.10.1115/1.4026911
9.
Martinez-Sala
,
R.
,
Sancho
,
J.
,
Sanchez
,
J. V.
,
Gomez
,
V.
, and
Llinares
,
J.
,
1995
, “
Sound Attenuation by Sculpture
,”
Nature
,
378
, p.
241
.10.1038/378241a0
10.
Liu
,
Z.
,
Zhang
,
X.
,
Mao
,
Y.
,
Zhu
,
Y. Y.
,
Yang
,
Z.
,
Chan
,
C. T.
, and
Sheng
,
P.
,
2000
, “
Locally Resonant Sonic Materials
,”
Science
,
289
(
5485
), pp.
1734
1736
.10.1126/science.289.5485.1734
11.
Liu
,
Z.
,
Chan
,
C. T.
, and
Sheng
,
P.
,
2005
, “
Analytic Model of Phononic Crystals With Local Resonances
,”
Phys. Rev. B
,
71
(
1
), p.
014103
.10.1103/PhysRevB.71.014103
12.
Ma
,
G.
, and
Sheng
,
P.
,
2016
, “
Acoustic Metamaterials: From Local Resonances to Broad Horizons
,”
Sci. Adv.
,
2
(
2
), p.
e1501595
.10.1126/sciadv.1501595
13.
Lai
,
Y.
,
Wu
,
Y.
,
Sheng
,
P.
, and
Zhang
,
Z.-Q.
,
2011
, “
Hybrid Elastic Solids
,”
Nat. Mater.
,
10
(
8
), pp.
620
624
.10.1038/nmat3043
14.
Zhu
,
R.
,
Liu
,
X. N.
,
Hu
,
G. K.
,
Sun
,
C. T.
, and
Huang
,
G. L.
,
2014
, “
Negative Refraction of Elastic Waves at the Deep-Subwavelength Scale in a Single-Phase Metamaterial
,”
Nat. Commun.
,
5
(
1
), p.
5510
.10.1038/ncomms6510
15.
Oh
,
J. H.
,
Seung
,
H. M.
, and
Kim
,
Y. Y.
,
2014
, “
A Truly Hyperbolic Elastic Metamaterial Lens
,”
Appl. Phys. Lett.
,
104
(
7
), p.
073503
.10.1063/1.4865907
16.
Dong
,
H.-W.
,
Zhao
,
S.-D.
,
Wang
,
Y.-S.
, and
Zhang
,
C.
,
2018
, “
Broadband Single-Phase Hyperbolic Elastic Metamaterials for Super-Resolution Imaging
,”
Sci. Rep.
,
8
(
1
), p.
2247
.10.1038/s41598-018-20579-8
17.
Li
,
Y.
,
Liang
,
B.
,
Gu
,
Z.-M.
,
Zou
,
X.
, and
Cheng
,
J. C.
,
2013
, “
Reflected Wavefront Manipulation Based on Ultrathin Planar Acoustic Metasurfaces
,”
Sci. Rep.
,
3
(
1
), p.
2546
.10.1038/srep02546
18.
Zhao
,
J.
,
Li
,
B.
,
Chen
,
Z.
, and
Qiu
,
C.-W.
,
2013
, “
Manipulation Acoustic Wavefront by Inhomogeneous Impedance and Steerable Extraordinary Reflection
,”
Sci. Rep.
,
3
(
1
), p.
2537
.10.1038/srep02537
19.
Yu
,
N.
,
Genevet
,
P.
,
Kats
,
M. A.
,
Aieta
,
F.
,
Tetienne
,
J.-P.
,
Capasso
,
F.
, and
Gaburro
,
Z.
,
2011
, “
Light Propagation With Phase Discontinuities: Generalized Laws of Reflection and Refraction
,”
Science
,
334
(
6054
), pp.
333
337
.10.1126/science.1210713
20.
Xie
,
Y.
,
Wang
,
W.
,
Chen
,
H.
,
Konneker
,
A.
,
Popa
,
B.-I.
, and
Cummer
,
S. A.
,
2014
, “
Wavefront Modulation and Subwavelength Diffractive Acoustics With an Acoustic Metasurface
,”
Nat. Commun.
,
5
(
1
), p.
5553
.10.1038/ncomms6553
21.
Assouar
,
B.
,
Liang
,
B.
,
Wu
,
Y.
,
Li
,
Y.
,
Cheng
,
J.
, and
Jing
,
Y.
,
2018
, “
Acoustic Metasurfaces
,”
Nat. Rev. Mater.
,
3
(
12
), pp.
460
472
.10.1038/s41578-018-0061-4
22.
Fok
,
L.
,
Ambati
,
M.
, and
Zhang
,
X.
,
2008
, “
Acoustic Metamaterials
,”
MRS Bull.
,
33
(
10
), pp.
931
934
.10.1557/mrs2008.202
23.
Lu
,
M.-H.
,
Feng
,
L.
, and
Chen
,
Y.-F.
,
2009
, “
Phononic Crystals and Acoustic Metamaterials
,”
Mater. Today
,
12
(
12
), pp.
34
42
.10.1016/S1369-7021(09)70315-3
24.
Maldovan
,
M.
,
2013
, “
Sound and Heat Revolutions in Phononics
,”
Nature
,
503
(
7475
), pp.
209
217
.10.1038/nature12608
25.
García-Chocano
,
V. M.
,
Cabrera
,
S.
, and
Sánchez-Dehesa
,
J.
,
2012
, “
Broadband Sound Absorption by Lattices of Microperformated Cylindrical Shells
,”
Appl. Phys. Lett.
,
101
(
18
), p.
184101
.10.1063/1.4764560
26.
Assouar
,
B.
,
Senesi
,
M.
,
Oudich
,
M.
,
Ruzzene
,
M.
, and
Hou
,
Z.
,
2012
, “
Broadband Plate-Type Acoustic Metamaterial for Low-Frequency Sound Attenuation
,”
Appl. Phys. Lett.
,
101
, p.
173505
.10.1063/1.4764072
27.
Hussein
,
M. I.
,
Hulbert
,
G. M.
, and
Scott
,
R. A.
,
2007
, “
Dispersive Elastodynamics of 1D Banded Materials and Structures: Design
,”
J. Sound Vib.
,
307
(
3–5
), pp.
865
893
.10.1016/j.jsv.2007.07.021
28.
Pennec
,
Y.
,
Djafari-Rouhani
,
B.
,
Vasseur
,
J. O.
,
Larabi
,
H.
,
Khelif
,
A.
,
Choujaa
,
A.
,
Benchabane
,
S.
, and
Laude
,
V.
,
2005
, “
Acoustic Channel Drop Tunneling in a Phononic Crystal
,”
Appl. Phys. Lett.
,
87
(
26
), p.
261912
.10.1063/1.2158019
29.
Benchabane
,
S.
,
Khelif
,
A.
,
Choujaa
,
A.
,
Djafari-Rouhani
,
B.
, and
Laude
,
V.
,
2005
, “
Interaction of Waveguide and Localized Modes in a Phononic Crystal
,”
EPL (Europhys. Lett.)
,
71
(
4
), pp.
570
575
.10.1209/epl/i2005-10131-2
30.
Zhu
,
H.
, and
Semperlotti
,
F.
,
2014
, “
A Passively Tunable Acoustic Metamaterial Lens for Selective Ultrasonic Excitation
,”
J. Appl. Phys.
,
116
(
9
), p.
094901
.10.1063/1.4894279
31.
Pennec
,
Y.
,
Djafari-Rouhani
,
B.
,
Vasseur
,
J. O.
,
Khelif
,
A.
, and
Deymier
,
P. A.
,
2004
, “
Tunable Filtering and Demultiplexing in Phononic Crystals With Hollow Cylinders
,”
Phys. Rev. E.
,
69
(
4
), p.
046608
.10.1103/PhysRevE.69.046608
32.
Tamura
,
S.
,
Hurley
,
D. C.
, and
Wolfe
,
J. P.
,
1988
, “
Acoustic-Phonon Propagation in Superlattices
,”
Phys. Rev. B
,
38
(
2
), pp.
1427
1449
.10.1103/PhysRevB.38.1427
33.
Wang
,
Y.-F.
,
Maznev
,
A. A.
, and
Laude
,
V.
,
2016
, “
Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model
,”
Crystals
,
6
(
5
), p.
52
.10.3390/cryst6050052
34.
Yilmaz
,
C.
,
Hulbert
,
G. M.
, and
Kikuchi
,
N.
,
2007
, “
Phononic Band Gaps Induced by Inertial Amplification in Periodic Media
,”
Phys. Rev. B
,
76
(
5
), p.
054309
.10.1103/PhysRevB.76.054309
35.
Acar
,
G.
, and
Yilmaz
,
C.
,
2013
, “
Experimental and Numerical Evidence for the Existence of Wide and Deep Phononic Gaps Induced by Inertial Amplification in Two-Dimensional Solid Structures
,”
J. Sound Vib.
,
332
(
24
), pp.
6389
6404
.10.1016/j.jsv.2013.06.022
36.
Frandsen
,
N. M. M.
,
Bilal
,
O. R.
,
Jensen
,
J. S.
, and
Hussein
,
M. I.
,
2016
, “
Inertial Amplification of Continuous Structures: Large Band Gaps From Small Masses
,”
J. Appl. Phys.
,
119
(
12
), p.
124902
.10.1063/1.4944429
37.
Hussein
,
M. I.
, and
Frazier
,
M. J.
,
2010
, “
Band Structure of Phononic Crystals With General Damping
,”
J. Appl. Phys.
,
108
(
9
), p.
093506
.10.1063/1.3498806
38.
Farzbod
,
F.
, and
Leamy
,
M. J.
,
2011
, “
Analysis of Bloch's Method and the Propagation Technique in Periodic Structures
,”
ASME J. Vib. Acoust.
,
133
(
3
), p.
031010
.10.1115/1.4003202
39.
Deng
,
B.
,
Wang
,
P.
,
He
,
Q.
,
Tournat
,
V.
, and
Bertoldi
,
K.
,
2018
, “
Metamaterials With Amplitude Gaps for Elastic Solitons
,”
Nat. Commun.
,
9
(
1
), p.
3410
.10.1038/s41467-018-05908-9
40.
Zhou
,
X.-Z.
,
Wang
,
Y.-S.
, and
Zhang
,
C.
,
2009
, “
Effects of Material Parameters on Elastic Band Gaps of Two-Dimensional Solid Phononic Crystals
,”
J. Appl. Phys.
,
106
(
1
), p.
014903
.10.1063/1.3159644
41.
Su
,
X.-X.
,
Wang
,
Y.-F.
, and
Wang
,
Y.-S.
,
2012
, “
Effects of Poisson's Ratio on the Band Gaps and Defect States in Two-Dimensional Vacuum/Solid Porous Phononic Crystals
,”
Ultrasonics
,
52
(
2
), pp.
255
265
.10.1016/j.ultras.2011.08.010
42.
Ma
,
T.-X.
,
Su
,
X.-X.
,
Wang
,
Y.-S.
, and
Wang
,
Y.-F.
,
2013
, “
Effects of Material Parameters on Elastic Band Gaps of Three-Dimensional Solid Phononic Crystals
,”
Phys. Scr.
,
87
(
5
), p.
055604
.10.1088/0031-8949/87/05/055604
43.
Lin
,
S.-C. S.
, and
Huang
,
T. J.
,
2011
, “
Tunable Phononic Crystals With Anisotropic Inclusions
,”
Phys. Rev. B
,
83
(
17
), p.
174303
.10.1103/PhysRevB.83.174303
44.
Moiseyenko
,
R. P.
, and
Laude
,
V.
,
2011
, “
Material Loss Influence on the Complex Band Structure and Group Velocity in Phononic Crystals
,”
Phys. Rev. B
,
83
(
6
), p.
064301
.10.1103/PhysRevB.83.064301
45.
Wang
,
Y.-F.
,
Wang
,
Y.-S.
, and
Laude
,
V.
,
2015
, “
Wave Propagation in Two-Dimensional Viscoelastic Metamaterials
,”
Phys. Rev. B
,
92
(
10
), p.
104110
.10.1103/PhysRevB.92.104110
46.
Frazier
,
M. J.
, and
Hussein
,
M. I.
,
2015
, “
Viscous-to-Viscoelastic Transition in Phononic Crystal and Metamaterial Band Structures
,”
J. Acoust. Soc. Am.
,
138
(
5
), pp.
3169
3180
.10.1121/1.4934845
47.
Frazier
,
M. J.
, and
Hussein
,
M. I.
,
2016
, “
Generalized Bloch's Theorem for Viscous Metamaterials: Dispersion and Effective Properties Based on Frequencies and Wavenumbers That Are Simultaneously Complex
,”
C. R. Phys.
,
17
(
5
), pp.
565
577
.10.1016/j.crhy.2016.02.009
48.
Wang
,
Y.-F.
,
Wang
,
Y.-S.
, and
Zhang
,
C.
,
2016
, “
Two-Dimensional Locally Resonant Elastic Metamaterials With Chiral Comb-Like Interlayers: Bandgap and Simultaneously Double Negative Properties
,”
J. Acoust. Soc. Am.
,
139
(
6
), pp.
3311
3319
.10.1121/1.4950766
49.
Li
,
F.-M.
,
Wang
,
Y.-Z.
,
Fang
,
B.
, and
Wang
,
Y.-S.
,
2007
, “
Propagation and Localization of Two-Dimensional in-Plane Elastic Waves in Randomly Disordered Layered Piezoelectric Phononic Crystals
,”
Int. J. Solids Struct.
,
44
(
22–23
), pp.
7444
7456
.10.1016/j.ijsolstr.2007.04.021
50.
Wang
,
Y.-Z.
,
Li
,
F.-M.
,
Huang
,
W.-H.
,
Jiang
,
X.
,
Wang
,
Y.-S.
, and
Kishimoto
,
K.
,
2008
, “
Wave Band Gaps in Two-Dimensional Piezoelectric/Piezomagnetic Phononic Crystals
,”
Int. J. Solids Struct.
,
45
(
14–15
), pp.
4203
4210
.10.1016/j.ijsolstr.2008.03.001
51.
Wang
,
Y.-Z.
,
Li
,
F.-M.
,
Huang
,
W.-H.
, and
Wang
,
Y.-S.
,
2007
, “
Effects of Inclusion Shapes on the Band Gaps in Two-Dimensional Piezoelectric Phononic Crystals
,”
J. Phys.: Condens. Matter
,
19
, p.
496204
.10.1088/0953-8984/19/49/496204
52.
Wang
,
Y.-Z.
,
Li
,
F.-M.
,
Huang
,
W.-H.
, and
Wang
,
Y.-S.
,
2008
, “
The Propagation and Localization of Rayleigh Waves in Disordered Piezoelectric Phononic Crystals
,”
J. Mech. Phys. Solids
,
56
(
4
), pp.
1578
1590
.10.1016/j.jmps.2007.07.014
53.
Wang
,
Y.-Z.
,
Li
,
F.-M.
,
Kishimoto
,
K.
,
Wang
,
Y.-S.
, and
Huang
,
W.-H.
,
2009
, “
Elastic Wave Band Gaps in Magnetoelectroelastic Phononic Crystals
,”
Wave Motion
,
46
(
1
), pp.
47
56
.10.1016/j.wavemoti.2008.08.001
54.
Wang
,
Y.-Z.
,
Li
,
F.-M.
,
Kishimoto
,
K.
,
Wang
,
Y.-S.
, and
Huang
,
W.-H.
,
2009
, “
Wave Band Gaps in Three-Dimensional Periodic Piezoelectric Structures
,”
Mech. Res. Commun.
,
36
(
4
), pp.
461
468
.10.1016/j.mechrescom.2009.01.003
55.
Wang
,
Y.-Z.
,
Li
,
F.-M.
, and
Wang
,
Y.-S.
,
2016
, “
Influences of Active Control on Elastic Wave Propagation in a Weakly Nonlinear Phononic Crystal With a Monoatomic Lattice Chain
,”
Int. J. Mech. Sci.
,
106
, pp.
357
362
.10.1016/j.ijmecsci.2015.12.004
56.
Wang
,
Y.-F.
, and
Wang
,
Y.-S.
,
2013
, “
Complete Bandgap in Three-Dimensional Holey Phononic Crystals With Resonators
,”
ASME J. Vib. Acoust.
,
135
(
4
), p.
041009
.10.1115/1.4023823
57.
Wang
,
Y.-F.
, and
Wang
,
Y.-S.
,
2013
, “
Complete Bandgaps in Two-Dimensional Phononic Crystal Slabs With Resonators
,”
J. Appl. Phys.
,
114
(
4
), p.
043509
.10.1063/1.4816273
58.
Wang
,
Y.-F.
, and
Wang
,
Y.-S.
,
2013
, “
Multiple Wide Complete Bandgaps of Two-Dimensional Phononic Crystal Slabs With Cross-Like Holes
,”
J. Sound Vib.
,
332
(
8
), pp.
2019
2037
.10.1016/j.jsv.2012.11.031
59.
Wang
,
Y.-F.
,
Wang
,
Y.-S.
, and
Su
,
X.-X.
,
2011
, “
Large Bandgaps of Two-Dimensional Phononic Crystals With Cross-Like Holes
,”
J. Appl. Phys.
,
110
(
11
), p.
113520
.10.1063/1.3665205
60.
Zhen
,
N.
,
Wang
,
Y.-S.
, and
Zhang
,
C.
,
2012
, “
Surface/Interface Effect on Band Structures of Nanosized Phononic Crystals
,”
Mech. Res. Commun.
,
46
, pp.
81
89
.10.1016/j.mechrescom.2012.09.002
61.
Zhen
,
N.
,
Wang
,
Y.-S.
, and
Zhang
,
C.
,
2013
, “
Bandgap Calculation of in-Plane Waves in Nanoscale Phononic Crystals Taking Account of Surface/Interface Effects
,”
Phys. E
,
54
, pp.
125
132
.10.1016/j.physe.2013.06.012
62.
Kushwaha
,
M. S.
, and
Halevi
,
P.
,
1994
, “
Band-Gap Engineering in Periodic Elastic Composites
,”
Appl. Phys. Lett.
,
64
(
9
), pp.
1085
1087
.10.1063/1.110940
63.
Sigmund
,
O.
, and
Jensen
,
J.
,
2003
, “
S. Systematic Design of Phononic Band–Gap Materials and Structures by Topology Optimization
,”
Philos. Trans. R. Soc. London A: Math., Phys. Eng. Sci.
,
361
(
1806
), pp.
1001
1019
.10.1098/rsta.2003.1177
64.
Bilal
,
O. R.
, and
Hussein
,
M. I.
,
2011
, “
Ultrawide Phononic Band Gap for Combined in-Plane and Out-of-Plane Waves
,”
Phys. Rev. E
,
84
(
6
), p.
065701
.10.1103/PhysRevE.84.065701
65.
Dong
,
H.-W.
,
Su
,
X.-X.
,
Wang
,
Y.-S.
, and
Zhang
,
C.
,
2014
, “
Topological Optimization of Two-Dimensional Phononic Crystals Based on the Finite Element Method and Genetic Algorithm
,”
Struct. Multidiscip. Optim.
,
50
(
4
), pp.
593
604
.10.1007/s00158-014-1070-6
66.
Dong
,
H.-W.
,
Su
,
X.-X.
, and
Wang
,
Y.-S.
,
2014
, “
Multi-Objective Optimization of Two-Dimensional Porous Phononic Crystals
,”
J. Phys. D: Appl. Phys.
,
47
(
15
), p.
155301
.10.1088/0022-3727/47/15/155301
67.
Dong
,
H.-W.
,
Su
,
X.-X.
,
Wang
,
Y.-S.
, and
Zhang
,
C.
,
2014
, “
Topology Optimization of Two-Dimensional Asymmetrical Phononic Crystals
,”
Phys. Lett. A
,
378
(
4
), pp.
434
441
.10.1016/j.physleta.2013.12.003
68.
Dong
,
H.-W.
,
Wang
,
Y.-S.
,
Wang
,
Y.-F.
, and
Zhang
,
C.
,
2015
, “
Reducing Symmetry in Topology Optimization of Two-Dimensional Porous Phononic Crystals
,”
AIP Adv.
,
5
(
11
), p.
117149
.10.1063/1.4936640
69.
Lu
,
Y.
,
Yang
,
Y.
,
Guest
,
J. K.
, and
Srivastava
,
A.
,
2017
, “
3D Phononic Crystals With Ultra-Wide Band Gaps
,”
Sci. Rep.
,
7
(
1
), p.
43407
.10.1038/srep43407
70.
Hussein
,
M. I.
, and
Frazier
,
M. J.
,
2013
, “
An Emergent Phenomenon in Dissipative Metamaterials
,”
J. Sound Vib.
,
332
(
20
), pp.
4767
4774
.10.1016/j.jsv.2013.04.041
71.
Depauw
,
D.
,
Al Ba'ba'a
,
H.
, and
Nouh
,
M.
,
2018
, “
Metadamping and Energy Dissipation Enhancement Via Hybrid Phononic Resonators
,”
Extreme Mech. Lett.
,
18
, pp.
36
44
.10.1016/j.eml.2017.11.002
72.
Bacquet
,
C. L.
,
Al Ba'ba'aa
,
H.
,
Frazier
,
M. J.
,
Nouh
,
M.
,
Hussein
,
M. I.
, and
Metadamping
,
2018
, “
Dissipation Emergence in Elastic Metamaterials
,”
Adv. Appl. Mech.
,
51
, pp.
115
164
.10.1016/bs.aams.2018.09.001
73.
Espinosa
,
V.
,
Sánchez-Morcillo
,
V. J.
,
Staliunas
,
K.
,
Pérez-Arjona
,
I.
, and
Redondo
,
J.
,
2007
, “
Subdiffractive Propagation of Ultrasound in Sonic Crystals
,”
Phys. Rev. B
,
76
(
14
), p.
140302
.10.1103/PhysRevB.76.140302
74.
Wen
,
J.
,
Yu
,
D.
,
Cai
,
L.
, and
Wen
,
X.
,
2009
, “
Acoustic Directional Radiation Operating at the Pass Band Frequency in Two-Dimensional Phononic Crystals
,”
J. Phys. D: Appl. Phys.
,
42
(
11
), p.
115417
.10.1088/0022-3727/42/11/115417
75.
Morvan
,
B.
,
Tinel
,
A.
,
Vasseur
,
J. O.
,
Sainidou
,
R.
,
Rembert
,
P.
,
Hladky-Hennion
,
A. C.
,
Swinteck
,
N.
, and
Deymier
,
P. A.
,
2014
, “
Ultra-Directional Source of Longitudinal Acoustic Waves Based on a Two-Dimensional Solid/Solid Phononic Crystal
,”
J. Appl. Phys.
,
116
(
21
), p.
214901
.10.1063/1.4903076
76.
Wang
,
Y.-F.
,
Wang
,
Y.-S.
, and
Zhang
,
C.
,
2014
, “
Bandgaps and Directional Propagation of Elastic Waves in 2d Square Zigzag Lattice Structures
,”
J. Phys. D: Appl. Phys.
,
47
(
48
), p.
485102
.10.1088/0022-3727/47/48/485102
77.
Andreassen
,
E.
,
Manktelow
,
K.
, and
Ruzzene
,
M.
,
2015
, “
Directional Bending Wave Propagation in Periodically Perforated Plates
,”
J. Sound Vib.
,
335
, pp.
187
203
.10.1016/j.jsv.2014.09.035
78.
Shi
,
J.
,
Lin
,
S.-C. S.
, and
Huang
,
T. J.
,
2008
, “
Wide-Band Acoustic Collimating by Phononic Crystal Composites
,”
Appl. Phys. Lett.
,
92
(
11
), p.
111901
.10.1063/1.2895019
79.
Chen
,
L. S.
,
Kuo
,
C. H.
, and
Ye
,
Z.
,
2004
, “
Acoustic Imaging and Collimating by Slabs of Sonic Crystals Made From Arrays of Rigid Cylinders in Air
,”
Appl. Phys. Lett.
,
85
(
6
), pp.
1072
1074
.10.1063/1.1781351
80.
Qiu
,
C.
, and
Liu
,
Z.
,
2006
, “
Acoustic Directional Radiation and Enhancement Caused by Band-Edge States of Two-Dimensional Phononic Crystals
,”
Appl. Phys. Lett.
,
89
(
6
), p.
063106
.10.1063/1.2335975
81.
Liu
,
W.
, and
Su
,
X.
,
2010
, “
Collimation and Enhancement of Elastic Transverse Waves in Two-Dimensional Solid Phononic Crystals
,”
Phys. Lett. A
,
374
(
29
), pp.
2968
2971
.10.1016/j.physleta.2010.05.016
82.
Wu
,
T.-T.
,
Hsu
,
C.-H.
, and
Sun
,
J.-H.
,
2006
, “
Design of a Highly Magnified Directional Acoustic Source Based on the Resonant Cavity of Two-Dimensional Phononic Crystals
,”
Appl. Phys. Lett.
,
89
(
17
), p.
171912
.10.1063/1.2370382
83.
Ke
,
M.
,
Liu
,
Z.
,
Pang
,
P.
,
Qiu
,
C.
,
Zhao
,
D.
,
Peng
,
S.
,
Shi
,
J.
, and
Wen
,
W.
,
2007
, “
Experimental Demonstration of Directional Acoustic Radiation Based on Two-Dimensional Phononic Crystal Band Edge States
,”
Appl. Phys. Lett.
,
90
(
8
), p.
083509
.10.1063/1.2696621
84.
Ke
,
M.
,
Liu
,
Z.
,
Pang
,
P.
,
Wang
,
W.
,
Cheng
,
Z.
,
Shi
,
J.
,
Zhao
,
X.
, and
Wen
,
W.
,
2006
, “
Highly Directional Acoustic Wave Radiation Based on Asymmetrical Two-Dimensional Phononic Crystal Resonant Cavity
,”
Appl. Phys. Lett.
,
88
(
26
), p.
263505
.10.1063/1.2217923
85.
Christensen
,
J.
,
Fernandez-Dominguez
,
A. I.
,
Leon-Perez
,
F. D.
,
Martin-Moreno
,
L.
, and
Garcia-Vidal
,
F. J.
,
2007
, “
Collimation of Sound Assisted by Acoustic Surface Waves
,”
Nat. Phys.
,
3
(
12
), pp.
851
852
.10.1038/nphys774
86.
Ke
,
M.
,
Liu
,
Z.
,
Qiu
,
C.
,
Wang
,
W.
,
Shi
,
J.
,
Wen
,
W.
, and
Sheng
,
P.
,
2005
, “
Negative-Refraction Imaging With Two-Dimensional Phononic Crystals
,”
Phys. Rev. B
,
72
(
6
), p.
064306
.10.1103/PhysRevB.72.064306
87.
Li
,
J.
,
Fung
,
K. H.
,
Liu
,
Z. Y.
,
Sheng
,
P.
, and
Chan
,
C. T.
,
2007
, “
Generalizing the Concept of Negative Medium to Acoustic Waves
,”
Physics of Negative Refraction and Negative Index Materials
,
C. M.
Krowne
and
Y.
Zhang
, eds.,
Springer
,
Berlin, Germany
.
88.
Hu
,
X.
,
Shen
,
Y.
,
Liu
,
X.
,
Fu
,
R.
, and
Zi
,
J.
,
2004
, “
Superlensing Effect in Liquid Surface Waves
,”
Phys. Rev. E
,
69
(
3
), p.
030201
.10.1103/PhysRevE.69.030201
89.
Lu
,
M.-H.
,
Zhang
,
C.
,
Feng
,
L.
,
Zhao
,
J.
,
Chen
,
Y.-F.
,
Mao
,
Y.-W.
,
Zi
,
J.
,
Zhu
,
Y.-Y.
,
Zhu
,
S.-N.
, and
Ming
,
N.-B.
,
2007
, “
Negative Birefraction of Acoustic Waves in a Sonic Crystal
,”
Nat. Mater.
,
6
(
10
), pp.
744
748
.10.1038/nmat1987
90.
Zhao
,
S. D.
, and
Wang
,
Y. S.
,
2016
, “
Negative Refraction and Imaging of Acoustic Waves in a Two-Dimensional Square Chiral Lattice Structure
,”
C. R. Phys.
,
17
(
5
), pp.
533
542
.10.1016/j.crhy.2016.02.003
91.
Hladky-Hennion
,
A. C.
,
Vasseur
,
J. O.
,
Haw
,
G.
,
Croënne
,
C.
,
Haumesser
,
L.
, and
Norris
,
A. N.
,
2013
, “
Negative Refraction of Acoustic Waves Using a Foam-Like Metallic Structure
,”
Appl. Phys. Lett.
,
102
(
14
), p.
144103
.10.1063/1.4801642
92.
Sukhovich
,
A.
,
Jing
,
L.
, and
Page
,
J. H.
,
2008
, “
Negative Refraction and Focusing of Ultrasound in Two-Dimensional Phononic Crystals
,”
Phys. Rev. B
,
77
(
1
), p.
014301
.10.1103/PhysRevB.77.014301
93.
Feng
,
L.
,
Liu
,
X.-P.
,
Lu
,
M.-H.
,
Chen
,
Y.-B.
,
Chen
,
Y.-F.
,
Mao
,
Y.-W.
,
Zi
,
J.
,
Zhu
,
Y.-Y.
,
Zhu
,
S.-N.
, and
Ming
,
N.-B.
,
2006
, “
Acoustic Backward-Wave Negative Refractions in the Second Band of a Sonic Crystal
,”
Phys. Rev. Lett.
,
96
(
1
), p.
014301
.10.1103/PhysRevLett.96.014301
94.
Li
,
J.
,
Liu
,
Z.
, and
Qiu
,
C.
,
2008
, “
Negative Refraction Imaging of Solid Acoustic Waves by Two-Dimensional Three-Component Phononic Crystal
,”
Phys. Lett. A
,
372
(
21
), pp.
3861
3867
.10.1016/j.physleta.2008.02.043
95.
Croënne
,
C.
,
Manga
,
E. D.
,
Morvan
,
B.
,
Tinel
,
A.
,
Dubus
,
B.
,
Vasseur
,
J.
, and
Hladky-Hennion
,
A. C.
,
2011
, “
Negative Refraction of Longitudinal Waves in a Two-Dimensional Solid-Solid Phononic Crystal
,”
Phys. Rev. B
,
83
(
5
), p.
054301
.10.1103/PhysRevB.83.054301
96.
Morvan
,
B.
,
Tinel
,
A.
,
Hladky-Hennion
,
A. C.
,
Vasseur
,
J.
, and
Dubus
,
B.
,
2010
, “
Experimental Demonstration of the Negative Refraction of a Transverse Elastic Wave in a Two-Dimensional Solid Phononic Crystal
,”
Appl. Phys. Lett.
,
96
(
10
), p.
101905
.10.1063/1.3302456
97.
Lee
,
M. K.
,
Ma
,
P. S.
,
Lee
,
I. K.
,
Kim
,
H. W.
, and
Kim
,
Y. Y.
,
2011
, “
Negative Refraction Experiments With Guided Shear-Horizontal Waves in Thin Phononic Crystal Plates
,”
Appl. Phys. Lett.
,
98
(
1
), p.
011909
.10.1063/1.3533641
98.
Pierre
,
J.
,
Boyko
,
O.
,
Belliard
,
L.
,
Vasseur
,
J. O.
, and
Bonello
,
B.
,
2010
, “
Negative Refraction of Zero Order Flexural Lamb Waves Through a Two-Dimensional Phononic Crystal
,”
Appl. Phys. Lett.
,
97
(
12
), p.
121919
.10.1063/1.3491290
99.
Gerardin
,
B.
,
Laurent
,
J.
,
Prada
,
C.
, and
Aubry
,
A.
,
2016
, “
Negative Reflection of Lamb Waves at a Free Edge: Tunable Focusing and Mimicking Phase Conjugation
,”
J. Acoust. Soc. Am.
,
140
, p.
591
.10.1121/1.4959024
100.
Liu
,
X. N.
,
Hu
,
G. K.
,
Huang
,
G. L.
, and
Sun
,
C. T.
,
2011
, “
An Elastic Metamaterial With Simultaneously Negative Mass Density and Bulk Modulus
,”
Appl. Phys. Lett.
,
98
(
25
), p.
251907
.10.1063/1.3597651
101.
Wu
,
Y.
,
Lai
,
Y.
, and
Zhang
,
Z.-Q.
,
2011
, “
Elastic Metamaterials With Simultaneously Negative Effective Shear Modulus and Mass Density
,”
Phys. Rev. Lett.
,
107
(
10
), p.
105506
.10.1103/PhysRevLett.107.105506
102.
Dong
,
H.-W.
,
Zhao
,
S.-D.
,
Wang
,
Y.-S.
, and
Zhang
,
C.
,
2017
, “
Topology Optimization of Anisotropic Broadband Double-Negative Elastic Metamaterials
,”
J. Mech. Phys. Solids
,
105
, pp.
54
80
.10.1016/j.jmps.2017.04.009
103.
Deng
,
K.
,
Ding
,
Y.
,
He
,
Z.
,
Zhao
,
H.
,
Shi
,
J.
, and
Liu
,
Z.
,
2009
, “
Theoretical Study of Subwavelength Imaging by Acoustic Metamaterial Slabs
,”
J. Appl. Phys.
,
105
(
12
), p.
124909
.10.1063/1.3153976
104.
Zhang
,
X.
, and
Liu
,
Z.
,
2004
, “
Negative Refraction of Acoustic Waves in Two-Dimensional Phononic Crystals
,”
Appl. Phys. Lett.
,
85
(
2
), pp.
341
343
.10.1063/1.1772854
105.
Feng
,
L.
,
Liu
,
X.-P.
,
Chen
,
Y.-B.
,
Huang
,
Z.-P.
,
Mao
,
Y.-W.
,
Chen
,
Y.-F.
,
Zi
,
J.
, and
Zhu
,
Y.-Y.
,
2005
, “
Negative Refraction of Acoustic Waves in Two-Dimensional Sonic Crystals
,”
Phys. Rev. B
,
72
(
3
), p.
033108
.10.1103/PhysRevB.72.033108
106.
Li
,
J.
,
Liu
,
Z.
, and
Qiu
,
C.
,
2006
, “
Negative Refraction Imaging of Acoustic Waves by a Two-Dimensional Three-Component Phononic Crystal
,”
Phys. Rev. B
,
73
(
5
), p.
054302
.10.1103/PhysRevB.73.054302
107.
Christensen
,
J.
, and
De Abajo
,
F. J. G.
,
2012
, “
Anisotropic Metamaterials for Full Control of Acoustic Waves
,”
Phys. Rev. Lett.
,
108
(
12
), p.
124301
.10.1103/PhysRevLett.108.124301
108.
García-Chocano
,
V. M.
,
Christensen
,
J.
, and
Sánchez-Dehesa
,
J.
,
2014
, “
Negative Refraction and Energy Funneling by Hyperbolic Materials: An Experimental Demonstration in Acoustics
,”
Phys. Rev. Lett.
,
112
(
14
), p.
144301
.10.1103/PhysRevLett.112.144301
109.
Feng
,
L.
,
Liu
,
X.-P.
,
Lu
,
M.-H.
,
Chen
,
Y.-B.
,
Chen
,
Y.-F.
,
Mao
,
Y.-W.
,
Zi
,
J.
,
Zhu
,
Y.-Y.
,
Zhu
,
S.-N.
, and
Ming
,
N.-B.
,
2006
, “
Refraction Control of Acoustic Waves in a Square-Rod-Constructed Tunable Sonic Crystal
,”
Phys. Rev. B
,
73
(
19
), p.
193101
.10.1103/PhysRevB.73.193101
110.
Yang
,
S. X.
,
Page
,
J. H.
,
Liu
,
Z. Y.
,
Cowan
,
M. L.
,
Chan
,
C. T.
, and
Sheng
,
P.
,
2004
, “
Focusing of Sound in a 3D Phononic Crystal
,”
Phys. Rev. Lett.
,
93
(
2
), p.
024301
.10.1103/PhysRevLett.93.024301
111.
Lin
,
S.-C. S.
,
Huang
,
T. J.
,
Sun
,
J.-H.
, and
Wu
,
T.-T.
,
2009
, “
Gradient-Index Phononic Crystals
,”
Phys. Rev. B
,
79
(
9
), p.
094302
.10.1103/PhysRevB.79.094302
112.
Peng
,
S.
,
He
,
Z.
,
Jia
,
H.
,
Zhang
,
A.
,
Qiu
,
C.
,
Ke
,
M.
, and
Liu
,
Z.
,
2010
, “
Acoustic Far-Field Focusing Effect for Two-Dimensional Graded Negative Refractive-Index Sonic Crystals
,”
Appl. Phys. Lett.
,
96
(
26
), p.
263502
.10.1063/1.3457447
113.
Zhao
,
S.-D.
,
Wang
,
Y.-S.
, and
Zhang
,
C.
,
2017
, “
High-Transmission Acoustic Self-Focusing and Directional Cloaking in a Graded Perforated Metal Slab
,”
Sci. Rep.
,
7
(
1
), p.
4368
.10.1038/s41598-017-04512-z
114.
Craster
,
R. V.
, and
Guenneau
,
S.
,
2012
,
Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking
,
Springer Science & Business Media
,
Dordrecht
.
115.
Norris
,
A. N.
,
2008
, “
Acoustic Cloaking Theory
,”
Proc. R. Soc. A
,
464
(
2097
), pp.
2411
2434
.10.1098/rspa.2008.0076
116.
Zhang
,
S.
,
Xia
,
C.
, and
Fang
,
N.
,
2011
, “
Broadband Acoustic Cloak for Ultrasound Waves
,”
Phys. Rev. Lett.
,
106
(
2
), p.
024301
.10.1103/PhysRevLett.106.024301
117.
Zigoneanu
,
L.
,
Popa
,
B.-I.
, and
Cummer
,
S. A.
,
2014
, “
Three-Dimensional Broadband Omnidirectional Acoustic Ground Cloak
,”
Nat. Mater.
,
13
(
4
), pp.
352
355
.10.1038/nmat3901
118.
Milton
,
G. W.
,
Briane
,
M.
, and
Willis
,
J. R.
,
2006
, “
On Cloaking for Elasticity and Physical Equations With a Transformation Invariant Form
,”
New J. Phys.
,
8
(
10
), pp.
248
248
.10.1088/1367-2630/8/10/248
119.
Gracia-Salgado
,
R.
,
García-Chocano
,
V. M.
,
Torrent
,
D.
, and
Sanchez-Dehesa
,
J. V.
,
2013
, “
Negative Mass Density and Rho-Near-Zero Quasi-Teo-Dimensional Metamaterials: Design and Applications
,”
Phys. Rev. B
,
88
(
22
), p.
224305
.10.1103/PhysRevB.88.224305
120.
Zheng
,
L.-Y.
,
Wu
,
Y.
,
Ni
,
X.
,
Chen
,
Z.-G.
,
Lu
,
M.-H.
, and
Chen
,
Y.-F.
,
2014
, “
Acoustic Cloaking by a Near-Zero-Index Phononic Crystal
,”
Appl. Phys. Lett.
,
104
(
16
), p.
161904
.10.1063/1.4873354
121.
Chen
,
Y.
,
Zheng
,
M.
,
Liu
,
X.
,
Bi
,
Y.
,
Sun
,
Z.
,
Xiang
,
P.
,
Yang
,
J.
, and
Hu
,
G.
,
2017
, “
Broadband Solid Cloak for Underwater Acoustics
,”
Phys. Rev. B
,
95
(
18
), p.
180104
.10.1103/PhysRevB.95.180104
122.
Zhu
,
W.
,
Fing
,
C.
, and
Zhao
,
X.
,
2010
, “
A Numerical Method for Designing Acoustic Cloak With Homogeneous Metamaterials
,”
Appl. Phys. Lett.
,
97
(
13
), p.
131902
.10.1063/1.3492851
123.
Popa
,
B.-I.
, and
Cummer
,
S. A.
,
2011
, “
Homogeneous and Compact Acoustic Ground Cloaks
,”
Phys. Rev. B
,
83
(
22
), p.
224304
.10.1103/PhysRevB.83.224304
124.
Popa
,
B.-I.
,
Zigoneanu
,
L.
, and
Cummer
,
S. A.
,
2011
, “
Experimental Acoustic Ground Cloak in Air
,”
Phys. Rev. Lett.
,
106
(
25
), p.
253901
.10.1103/PhysRevLett.106.253901
125.
Bi
,
Y.
,
Jia
,
H.
,
Sun
,
Z.
,
Yang
,
Y.
,
Zhao
,
H.
, and
Yang
,
J.
,
2018
, “
Experimental Demonstration of Three-Dimensional Broadband Underwater Acoustic Carpet Cloak
,”
Appl. Phys. Lett.
,
112
(
22
), p.
223502
.10.1063/1.5026199
126.
Vasić
,
B.
, and
Gajić
,
R.
,
2011
, “
Self-Focusing Media Using Graded Photonic Crystals: Focusing, Fourier Transforming and Imaging, Directive Emission, and Directional Cloaking
,”
J. Appl. Phys.
,
110
(
5
), p.
053103
.10.1063/1.3630116
127.
Parnell
,
W. J.
,
Norris
,
A. N.
, and
Shearer
,
T.
,
2012
, “
Employing Pre-Stress to Generate Finite Cloaks for Antiplane Elastic Waves
,”
Appl. Phys. Lett.
,
100
(
17
), p.
171907
.10.1063/1.4704566
128.
Norris
,
A. N.
, and
Parnell
,
W. J.
,
2012
, “
Hyperelastic Cloaking Theory: Transformation Elasticity With Pre-Stressed Solids
,”
Proc. R. Soc. A
,
468
(
2146
), pp.
2881
2903
.10.1098/rspa.2012.0123
129.
Darabi
,
A.
,
Zareei
,
A.
,
Alam
,
M. R.
, and
Leamy
,
M. J.
,
2018
, “
Experimental Demonstration of an Ultrabroadband Nonlinear Cloak for Flexural Waves
,”
Phys. Rev. Lett.
,
121
(
17
), p.
174301
.10.1103/PhysRevLett.121.174301
130.
Liang
,
B.
,
Yuan
,
B.
, and
Cheng
,
J.-C.
,
2009
, “
Acoustic Diode: Rectification of Acoustic Energy Flux in One-Dimensional Systems
,”
Phys. Rev. Lett.
,
103
(
10
), p.
104301
.10.1103/PhysRevLett.103.104301
131.
Liang
,
B.
,
Guo
,
X. S.
,
Tu
,
J.
,
Zhang
,
D.
, and
Cheng
,
J. C.
,
2010
, “
An Acoustic Rectifier
,”
Nat. Mater.
,
9
(
12
), pp.
989
992
.10.1038/nmat2881
132.
Fleury
,
R.
,
Sounas
,
D. L.
,
Sieck
,
C. F.
,
Haberman
,
M. R.
, and
Alu
,
A.
,
2014
, “
Sound Isolation and Giant Linear Nonreciprocity in a Compact Acoustic Circulator
,”
Science
,
343
(
6170
), pp.
516
519
.10.1126/science.1246957
133.
Nassar
,
H.
,
Xu
,
X. C.
,
Norris
,
A. N.
, and
Huang
,
G. L.
,
2017
, “
Modulated Phononic Crystals: Non-Reciprocal Wave Propagation and Willis Materials
,”
J. Mech. Phys. Solids
,
101
, pp.
10
29
.10.1016/j.jmps.2017.01.010
134.
Swinteck
,
N.
,
Matsuo
,
S.
,
Runge
,
K.
,
Vasseur
,
J.
,
Lucas
,
P.
, and
Deymier
,
P. A.
,
2015
, “
Bulk Elastic Waves With Unidirectional Backscattering-Immune Topological States in a Time-Dependent Superlattice
,”
J. Appl. Phys.
,
118
(
6
), p.
063103
.10.1063/1.4928619
135.
Trainiti
,
G.
, and
Ruzzene
,
M.
,
2016
, “
Non-Reciprocal Elastic Wave Propagation in Spatiotemporal Periodic Structures
,”
New J. Phys.
,
18
(
8
), p.
083047
.10.1088/1367-2630/18/8/083047
136.
Yu
,
Z.
, and
Fan
,
S. H.
,
2009
, “
Complete Optical Isolation Created by Indirect Interband Photonic Transitions
,”
Nat. Photonics
,
3
(
2
), pp.
91
94
.10.1038/nphoton.2008.273
137.
Zanjani
,
M. B.
,
Davoyan
,
A. R.
,
Mahmoud
,
A. M.
,
Engheta
,
N.
, and
Lukes
,
J. R.
,
2014
, “
One-Way Phonon Isolation in Acoustic Waveguides
,”
Appl. Phys. Lett.
,
104
(
8
), p.
081905
.10.1063/1.4866590
138.
Mousavi
,
S. H.
,
Khanikaev
,
A. B.
, and
Wang
,
Z.
,
2015
, “
Topologically Protected Elastic Waves in Phononic Metamaterials
,”
Nat. Commun.
,
6
(
1
), p.
8682
.10.1038/ncomms9682
139.
Li
,
Z. N.
,
Wang
,
Y. Z.
, and
Wang
,
Y. S.
,
2018
, “
Nonreciprocal Phenomenon in Nonlinear Elastic Wave Metamaterials With Continuous Properties
,”
Int. J. Solids Struct.
,
150
, pp.
125
134
.10.1016/j.ijsolstr.2018.06.008
140.
Li
,
X.-F.
,
Ni
,
X.
,
Feng
,
L.
,
Lu
,
M.-H.
,
He
,
C.
, and
Chen
,
Y.-F.
,
2011
, “
Tunable Unidirectional Sound Propagation Through a Sonic-Crystal-Based Acoustic Diode
,”
Phys. Rev. Lett.
,
106
(
8
), p.
084301
.10.1103/PhysRevLett.106.084301
141.
Chen
,
Y. Y.
,
Li
,
T. T.
,
Scarpa
,
F.
, and
Wang
,
L. F.
,
2017
, “
Lattice Metamaterials With Mechanically Tunable Poisson's Ratio for Vibration Control
,”
Phys. Rev. Appl.
,
7
(
2
), p.
024012
.10.1103/PhysRevApplied.7.024012
142.
Walker
,
E.
,
Neogi
,
A.
,
Bozhko
,
A.
,
Zubov
,
Y.
,
Arriaga
,
J.
,
Heo
,
H.
,
Ju
,
J.
, and
Krokhin
,
A. A.
,
2018
, “
Nonreciprocal Linear Transmission of Sound in a Viscous Environment With Broken p Symmetry
,”
Phys. Rev. Lett.
,
120
(
20
), p.
204501
.10.1103/PhysRevLett.120.204501
143.
Deymier
,
P. A.
,
Gole
,
V.
,
Lucas
,
P.
,
Vasseur
,
J. O.
, and
Runge
,
K.
,
2017
, “
Tailoring Phonon Band Structures With Broken Symmetry by Shaping Spatiotemporal Modulations of Stiffness in a One-Dimensional Elastic Waveguide
,”
Phys. Rev. B
,
96
(
6
), p.
064304
.10.1103/PhysRevB.96.064304
144.
Wright
,
D. W.
, and
Cobbold
,
R. S. C.
,
2010
, “
Two-Dimensional Phononic Crystals With Time-Varying Properties: A Multiple Scattering Analysis
,”
Smart Mater. Struct.
,
19
(
4
), p.
045006
.10.1088/0964-1726/19/4/045006
145.
Wright
,
D. W.
, and
Cobbold
,
R. S. C.
,
2009
, “
Acoustic Wave Transmission in Time-Varying Phononic Crystals
,”
Smart Mater. Struct.
,
18
(
1
), p.
015008
.10.1088/0964-1726/18/1/015008
146.
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
(
11
), pp.
7387
7392
.10.1103/PhysRevB.62.7387
147.
Cebrecos
,
A.
,
Krattiger
,
D.
,
Sánchez-Morcillo
,
V. J.
,
Romero-García
,
V.
, and
Hussein
,
M. I.
,
2019
, “
The Finite-Element Time-Domain Method for Elastic Band-Structure Calculations
,”
Comput. Phys. Commun.
,
238
, pp.
77
87
.10.1016/j.cpc.2018.12.016
148.
Sounas
,
D. L.
, and
Alu
,
A.
,
2017
, “
Non-Reciprocal Photonics Based on Time Modulation
,”
Nat. Photonics
,
11
(
12
), pp.
774
783
.10.1038/s41566-017-0051-x
149.
Peano
,
V.
,
Brendel
,
C.
,
Schmidt
,
M.
, and
Marquardt
,
F.
,
2015
, “
Topological Phases of Sound and Light
,”
Phys. Rev. X
,
5
(
3
), p.
031011
.10.1103/PhysRevX.5.031011
150.
Yang
,
Z.
,
Gao
,
F.
,
Shi
,
X.
,
Lin
,
X.
,
Gao
,
Z.
,
Chong
,
Y. D.
, and
Zhang
,
B.
,
2015
, “
Topological Acoustics
,”
Phys. Rev. Lett.
,
114
(
11
), p.
114301
.10.1103/PhysRevLett.114.114301
151.
Huber
,
S. D.
,
2016
, “
Topological Mechanics
,”
Nat. Phys.
,
12
(
7
), pp.
621
623
.10.1038/nphys3801
152.
Deymier
,
P. A.
,
Runge
,
K.
,
Swinteck
,
N.
, and
Muralidharan
,
K.
,
2015
, “
Torsional Topology and Fermion-Like Behavior of Elastic Waves in Phononic Structures
,”
C. R. Acad. Sci. Méc.
,
343
(
12
), pp.
700
711
.10.1016/j.crme.2015.07.003
153.
Xiao
,
M.
,
Ma
,
G.
,
Yang
,
Z.
,
Sheng
,
P.
,
Zhang
,
Z. Q.
, and
Chan
,
C. T.
,
2015
, “
Geometric Phase and Band Inversion in Periodic Acoustic Systems
,”
Nat. Phys.
,
11
(
3
), pp.
240
244
.10.1038/nphys3228
154.
Huang
,
H.
,
Chen
,
J.
, and
Huo
,
S.
,
2017
, “
Simultaneous Topological Bragg and Locally Resonant Edge Modes of Shear Horizontal Guided Wave in One-Dimensional Structure
,”
J. Phys. D: Appl. Phys.
,
50
(
27
), p.
275102
.10.1088/1361-6463/aa7619
155.
Fleury
,
R.
,
Khanikaev
,
A. B.
, and
Alu
,
A.
,
2016
, “
Floquet Topological Insulators for Sound
,”
Nat. Commun.
,
7
(
1
), p.
11744
.10.1038/ncomms11744
156.
Wang
,
P.
,
Lu
,
L.
, and
Bertoldi
,
K.
,
2015
, “
Topological Phononic Crystals With One-Way Elastic Edge Waves
,”
Phys. Rev. Lett.
,
115
(
10
), p.
104302
.10.1103/PhysRevLett.115.104302
157.
Nash
,
L. M.
,
Kleckner
,
D.
,
Read
,
A.
,
Vitelli
,
V.
,
Turner
,
A. M.
, and
Irvine
,
W. T. M.
,
2015
, “
Topological Mechanics of Gyroscopic Metamaterials
,”
Proc. Natl. Acad. Sci.
,
112
(
47
), pp.
14495
14500
.10.1073/pnas.1507413112
158.
Hasan
,
M. Z.
, and
Kane
,
C. L.
,
2010
, “
Colloquium: Topological Insulators
,”
Rev. Mod. Phys.
,
82
(
4
), pp.
3045
3067
.10.1103/RevModPhys.82.3045
159.
Peng
,
Y. G.
,
Qin
,
C. Z.
,
Zhao
,
D. G.
,
Shen
,
Y. X.
,
Xu
,
X. Y.
,
Bao
,
M.
,
Jia
,
H.
, and
Zhu
,
X. F.
,
2016
, “
Experimental Demonstration of Anomalous Floquet Topological Insulator for Sound
,”
Nat. Commun.
,
7
(
1
), p.
13368
.10.1038/ncomms13368
160.
He
,
C.
,
Ni
,
X.
,
Ge
,
H.
,
Sun
,
X. C.
,
Chen
,
Y. B.
,
Lu
,
M. H.
,
Liu
,
X. P.
, and
Chen
,
Y. F.
,
2016
, “
Acoustic Topological Insulator and Robust One-Way Sound Transport
,”
Nat. Phys.
,
12
(
12
), pp.
1124
1129
.10.1038/nphys3867
161.
Deng
,
Y.
,
Ge
,
H.
,
Tian
,
Y.
,
Lu
,
M. H.
, and
Jing
,
Y.
,
2017
, “
Observation of Zone Folding Induced Acoustic Topological Insulators and the Role of Spin-Mixing Defects
,”
Phys. Rev. B
,
96
(
18
), p.
184305
.10.1103/PhysRevB.96.184305
162.
Pal
,
R. K.
, and
Ruzzene
,
M.
,
2017
, “
Edge Waves in Plates With Resonators: An Elastic Analogue of the Quantum Valley Hall Effect
,”
New J. Phys.
,
19
(
2
), p.
025001
.10.1088/1367-2630/aa56a2
163.
Chen
,
J. J.
,
Huo
,
S. Y.
,
Geng
,
Z. G.
,
Huang
,
H. B.
, and
Zhu
,
X. F.
,
2017
, “
Topological Valley Transport of Plate-Mode Waves in a Homogenous Thin Plate With Periodic Stubbed Surface
,”
AIP Adv.
,
7
(
11
), p.
115215
.10.1063/1.5006010
164.
Huo
,
S. Y.
,
Chen
,
J. J.
,
Huang
,
H. B.
, and
Huang
,
G. L.
,
2017
, “
Simultaneous Multi-Band Valley-Protected Topological Edge States of Shear Vertical Wave in Two-Dimensional Phononic Crystals With Veins
,”
Sci. Rep.
,
7
(
1
), p.
10335
.10.1038/s41598-017-10857-2
165.
Wang
,
J.
, and
Mei
,
J.
,
2018
, “
Topological Valley-Chiral Edge States of Lamb Waves in Elastic Thin Plates
,”
Appl. Phys. Express
,
11
(
5
), p.
057302
.10.7567/APEX.11.057302
166.
Yang
,
Y.
,
Yang
,
Z.
, and
Zhang
,
B.
,
2018
, “
Acoustic Valley Edge States in a Graphene-Like Resonator System
,”
J. Appl. Phys.
,
123
(
9
), p.
091713
.10.1063/1.5009626
167.
Wang
,
J.
,
Huang
,
Y.
, and
Chen
,
W.
,
2020
, “
Tailoring Edge and Interface States in Topological Metastructures Exhibiting the Acoustic Valley Hall Effect
,”
Sci. China: Phys., Mech. Astron.
,
63
, p.
224611
.10.1007/s11433-019-9601-6
168.
Zhang
,
Z.
,
Tian
,
Y.
,
Cheng
,
Y.
,
Wei
,
Q.
,
Liu
,
X.
, and
Christensen
,
J.
,
2018
, “
Topological Acoustic Delay Line
,”
Phys. Rev. Appl.
,
9
(
3
), p.
034032
.10.1103/PhysRevApplied.9.034032
169.
Zhang
,
X. J.
,
Xiao
,
M.
,
Cheng
,
Y.
,
Lu
,
M. H.
, and
Christensen
,
J.
,
2018
, “
Topological Sound
,”
Commun. Phys.
,
1
(
1
), p.
97
.10.1038/s42005-018-0094-4
170.
Ma
,
G. C.
,
Xiao
,
M.
, and
Chan
,
C. T.
,
2019
, “
Topological Phases in Acoustic and Mechanical Systems
,”
Nat. Rev. Phys.
,
1
(
4
), pp.
281
294
.10.1038/s42254-019-0030-x
171.
Huang
,
T.-Y.
,
Shen
,
C.
, and
Jing
,
Y.
,
2016
, “
Membrane- and Plate-Type Acoustic Metamaterials
,”
J. Acoust. Soc. Am.
,
139
(
6
), pp.
3240
3250
.10.1121/1.4950751
172.
Faure
,
C.
,
Richoux
,
O.
,
Félix
,
S.
, and
Pagneux
,
V.
,
2016
, “
Experiments on Metasurface Carpet Cloaking for Audible Acoustics
,”
Appl. Phys. Lett.
,
108
(
6
), p.
064103
.10.1063/1.4941810
173.
Esfahlani
,
H.
,
Karkar
,
S.
,
Lissek
,
H.
, and
Mosig
,
J. R.
,
2016
, “
Acoustic Carpet Cloak Based on an Ultrathin Metasurface
,”
Phys. Rev. B
,
94
(
1
), p.
014302
.10.1103/PhysRevB.94.014302
174.
Zhu
,
Y.-F.
,
Zou
,
X.-Y.
,
Li
,
R.-Q.
,
Jiang
,
X.
,
Tu
,
J.
,
Liang
,
B.
, and
Cheng
,
J.-C.
,
2015
, “
Dispersionless Manipulation of Reflected Acoustic Wavefront by Subwavelength Corrugated Surface
,”
Sci. Rep.
,
5
(
1
), p.
10966
.10.1038/srep10966
175.
Li
,
Y.
,
Jiang
,
X.
,
Li
,
R.-Q.
,
Liang
,
B.
,
Zou
,
X.-Y.
,
Yin
,
L.-L.
, and
Cheng
,
J.-C.
,
2014
, “
Experimental Realization of Full Control of Reflected Waves With Subwavelength Acoustic Metasurfaces
,”
Phys. Rev. Appl.
,
2
(
6
), p.
064002
.10.1103/PhysRevApplied.2.064002
176.
Li
,
Y.
,
Shen
,
C.
,
Xie
,
Y.
,
Li
,
J.
,
Wang
,
W.
,
Cummer
,
S. A.
, and
Jing
,
Y.
,
2017
, “
Tunable Asymmetric Transmission Via Lossy Acoustic Metasurfaces
,”
Phys. Rev. Lett.
,
119
(
3
), p.
035501
.10.1103/PhysRevLett.119.035501
177.
Qi
,
S.
,
Li
,
Y.
, and
Assouar
,
B.
,
2017
, “
Acoustic Focusing and Energy Confinement Based on Multilateral Metasurfaces
,”
Phys. Rev. Appl.
,
7
(
5
), p.
054006
.10.1103/PhysRevApplied.7.054006
178.
Zhu
,
X.
,
Li
,
K.
,
Zhang
,
P.
,
Zhu
,
J.
,
Zhang
,
J.
,
Tian
,
C.
, and
Liu
,
S.
,
2016
, “
Implementation of Dispersion-Free Slow Acoustic Wave Propagation and Phase Engineering With Helical-Structured Metamaterials
,”
Nat. Commun.
,
7
(
1
), p.
11731
.10.1038/ncomms11731
179.
Zhu
,
Y.
,
Fan
,
X.
,
Liang
,
B.
,
Cheng
,
J.
, and
Jing
,
Y.
,
2017
, “
Ultrathin Acoustic Metasurface-Based Schroeder Diffuser
,”
Phys. Rev. X
,
7
(
2
), p.
021034
.10.1103/PhysRevX.7.021034
180.
Ding
,
C.
,
Chen
,
H.
,
Zhai
,
S.
,
Liu
,
S.
, and
Zhao
,
X.
,
2015
, “
The Anomalous Manipulation of Acoustic Waves Based on Planar Metasurface With Split Hollow Sphere
,”
J. Phys. D: Appl. Phys.
,
48
(
4
), p.
045303
.10.1088/0022-3727/48/4/045303
181.
Lee
,
H.
,
Lee
,
J. K.
,
Seung
,
H. M.
, and
Kim
,
Y. Y.
,
2018
, “
Mass-Stiffness Substructuring of an Elastic Metasurface for Full Transmission Beam Steering
,”
J. Mech. Phys. Solids
,
112
, pp.
577
593
.10.1016/j.jmps.2017.11.025
182.
Su
,
X.
,
Lu
,
Z.
, and
Norris
,
A. N.
,
2018
, “
Elastic Metasurfaces for Splitting SV- and p-Waves in Elastic Solids
,”
J. Appl. Phys.
,
123
(
9
), p.
091701
.10.1063/1.5007731
183.
Zhu
,
H.
, and
Semperlotti
,
F.
,
2016
, “
Anomalous Refraction of Acoustic Guided Waves in Solids With Geometrically Tapered Metasurfaces
,”
Phys. Rev. Lett.
,
117
(
3
), p.
034302
.10.1103/PhysRevLett.117.034302
184.
Liu
,
Y.
,
Liang
,
Z.
,
Liu
,
F.
,
Diba
,
O.
,
Lamb
,
A.
, and
Li
,
J.
,
2017
, “
Source Illusion Devices for Flexural Lamb Waves Using Elastic Metasurfaces
,”
Phys. Rev. Lett.
,
119
(
3
), p.
034301
.10.1103/PhysRevLett.119.034301
185.
Yang
,
Z.
,
Mei
,
J.
,
Yang
,
M.
,
Chan
,
N. H.
, and
Sheng
,
P.
,
2008
, “
Membrane-Type Acoustic Metamaterial With Negative Dynamic Mass
,”
Phys. Rev. Lett.
,
101
(
20
), p.
204301
.10.1103/PhysRevLett.101.204301
186.
Mei
,
J.
,
Ma
,
G.
,
Yang
,
M.
,
Yang
,
Z.
,
Wen
,
W.
, and
Sheng
,
P.
,
2012
, “
Dark Acoustic Metamaterials as Super Absorbers for Low-Frequency Sound
,”
Nat. Commun.
,
3
(
1
), p.
756
.10.1038/ncomms1758
187.
Yang
,
Z.
,
Dai
,
H. M.
,
Chan
,
N. H.
,
Ma
,
G. C.
, and
Sheng
,
P.
,
2010
, “
Acoustic Metamaterial Panels for Sound Attenuation in the 50–1000 Hz Regime
,”
Appl. Phys. Lett.
,
96
(
4
), p.
041906
.10.1063/1.3299007
188.
Ma
,
G.
,
Yang
,
M.
,
Yang
,
Z.
, and
Sheng
,
P.
,
2013
, “
Low-Frequency Narrow-Band Acoustic Filter With Large Orifice
,”
Appl. Phys. Lett.
,
103
(
1
), p.
011903
.10.1063/1.4812974
189.
Ma
,
G.
,
Yang
,
M.
,
Xiao
,
S.
,
Yang
,
Z.
, and
Sheng
,
P.
,
2014
, “
Acoustic Metasurface With Hybrid Resonances
,”
Nat. Mater.
,
13
(
9
), pp.
873
878
.10.1038/nmat3994
190.
Fan
,
L.
,
Chen
,
Z.
,
Zhang
,
S.-Y.
,
Ding
,
J.
,
Li
,
X.-J.
, and
Zhang
,
H.
,
2015
, “
An Acoustic Metamaterial Composed of Multi-Layer Membrane-Coated Perforated Plates for Low-Frequency Sound Insulation
,”
Appl. Phys. Lett.
,
106
(
15
), p.
151908
.10.1063/1.4918374
191.
Ma
,
F.
,
Wu
,
J. H.
, and
Huang
,
M.
,
2015
, “
One-Dimensional Rigid Film Acoustic Metamaterials
,”
J. Phys. D: Appl. Phys.
,
48
(
46
), p.
465305
.10.1088/0022-3727/48/46/465305
192.
Oh
,
J. H.
,
Lee
,
I. K.
,
Ma
,
P. S.
, and
Kim
,
Y. Y.
,
2011
, “
Active Wave-Guiding of Piezoelectric Phononic Crystals
,”
Appl. Phys. Lett.
,
99
(
8
), p.
083505
.10.1063/1.3630231
193.
Vasseur
,
J. O.
,
Matar
,
O. B.
,
Robillard
,
J. F.
,
Hladky-Hennion
,
A. C.
, and
Deymier
,
P. A.
,
2011
, “
Band Structures Tunability of Bulk 2D Phononic Crystals Made of Magneto-Elastic Materials
,”
AIP Adv.
,
1
(
4
), p.
041904
.10.1063/1.3676172
194.
Popa
,
B.-I.
, and
Cummer
,
S. A.
,
2014
, “
Non-Reciprocal and Highly Nonlinear Active Acoustic Metamaterials
,”
Nat. Commun.
,
5
(
1
), p.
3398
.10.1038/ncomms4398
195.
Pichard
,
H.
,
Richoux
,
O.
, and
Groby
,
J. P.
,
2012
, “
Experimental Demonstrations in Audible Frequency Range of Band Gap Tunability and Negative Refraction in Two-Dimensional Sonic Crystal
,”
J. Acoust. Soc. Am.
,
132
(
4
), pp.
2816
2822
.10.1121/1.4744974
196.
Goffaux
,
C.
, and
Vigneron
,
J. P.
,
2001
, “
Theoretical Study of a Tunable Phononic Band Gap System
,”
Phys. Rev. B
,
64
(
7
), p.
075118
.10.1103/PhysRevB.64.075118
197.
Kaya
,
O. A.
,
Cicek
,
A.
,
Salman
,
A.
, and
Ulug
,
B.
,
2014
, “
Acoustic Mach–Zehnder Interferometer Utilizing Self-Collimated Beams in a Two-Dimensional Phononic Crystal
,”
Sens. Actuators, B
,
203
, pp.
197
203
.10.1016/j.snb.2014.06.097
198.
Xu
,
S.
,
Qiu
,
C.
,
Ke
,
M.
, and
Liu
,
Z.
,
2014
, “
Tunable Enhancement of the Acoustic Radiation Pressure Acting on a Rigid Wall Via Attaching a Metamaterial Slab
,”
EPL (Europhys. Lett.)
,
105
(
6
), p.
64004
.10.1209/0295-5075/105/64004
199.
Liu
,
F.
,
Cai
,
F.
,
Ding
,
Y.
, and
Liu
,
Z.
,
2008
, “
Tunable Transmission Spectra of Acoustic Waves Through Double Phononic Crystal Slabs
,”
Appl. Phys. Lett.
,
92
(
10
), p.
103504
.10.1063/1.2896146
200.
Hussein
,
M. I.
,
Biringen
,
S.
,
Bilal
,
O. R.
, and
Kucala
,
A.
,
2015
, “
Flow Stabilization by Subsurface Phonons
,”
Proc. R. Soc. A
,
471
(
2177
), p.
2014928
.10.1098/rspa.2014.0928
201.
Hao
,
L.-M.
,
Ding
,
C.-L.
, and
Zhao
,
X.-P.
,
2012
, “
Tunable Acoustic Metamaterial With Negative Modulus
,”
Appl. Phys. A
,
106
(
4
), pp.
807
811
.10.1007/s00339-011-6682-8
202.
Wang
,
T.-T.
,
Wang
,
Y.-F.
,
Wang
,
Y.-S.
, and
Laude
,
V.
,
2018
, “
Evanescent-Wave Tuning of a Locally Resonant Sonic Crystal
,”
Appl. Phys. Lett.
,
113
(
23
), p.
231901
.10.1063/1.5066058
203.
Jin
,
Y.
,
Pennec
,
Y.
,
Pan
,
Y.
, and
Djafari-Rouhani
,
B.
,
2016
, “
Phononic Crystal Plate With Hollow Pillars Actively Controlled by Fluid Filling
,”
Crystals
,
6
(
6
), p.
64
.10.3390/cryst6060064
204.
Wang
,
T.-T.
,
Wang
,
Y.-F.
,
Wang
,
Y.-S.
, and
Laude
,
V.
,
2017
, “
Tunable Fluid-Filled Phononic Metastrip
,”
Appl. Phys. Lett.
,
111
(
4
), p.
041906
.10.1063/1.4985167
205.
Zhang
,
Q.
,
Zhang
,
K.
, and
Hu
,
G. K.
,
2018
, “
Tunable Fluid-Solid Metamaterials for Manipulation of Elastic Wave Propagation in Broad Frequency Range
,”
Appl. Phys. Lett.
,
112
(
22
), p.
221906
.10.1063/1.5023307
206.
Wang
,
Y.-F.
,
Wang
,
T.-T.
,
Wang
,
Y.-S.
, and
Laude
,
V.
,
2017
, “
Reconfigurable Phononic-Crystal Circuits Formed by Coupled Acoustoelastic Resonators
,”
Phys. Rev. Appl.
,
8
(
1
), p.
014006
.10.1103/PhysRevApplied.8.014006
207.
Yuan
,
S.-M.
,
Ma
,
T.-X.
,
Chen
,
A.-L.
, and
Wang
,
Y.-S.
,
2018
, “
Liquid-Assisted Tunable Metasurface for Simultaneous Manipulation of Surface Elastic and Acoustic Waves
,”
AIP Adv.
,
8
(
3
), p.
035026
.10.1063/1.5011194
208.
Cheng
,
W.
,
Wang
,
J.
,
Jonas
,
U.
,
Fytas
,
G.
, and
Stefanou
,
N.
,
2006
, “
Observation and Tuning of Hypersonic Bandgaps in Colloidal Crystals
,”
Nat. Mater.
,
5
(
10
), pp.
830
–83
6
.10.1038/nmat1727
209.
Cebrecos
,
A.
,
Krattiger
,
D.
,
Maute
,
K.
,
Sánchez-Morcillo
,
V. J.
,
Park
,
K. C.
,
Oh
,
I. K.
, and
Hussein
,
M. I.
,
2015
, Fluidic Metamaterial: An Elastic Medium with a Time-Changing Band Structure, Proceeding of PHONONICS 2015, May 31–June 5, Paris, France.
210.
Casadei
,
F.
, and
Bertoldi
,
K.
,
2014
, “
Harnessing Fluid-Structure Interactions to Design Self-Regulating Acoustic Metamaterials
,”
J. Appl. Phys.
,
115
(
3
), p.
034907
.10.1063/1.4862643
211.
Zhang
,
Q.
,
Chen
,
Y.
,
Zhang
,
K.
, and
Hu
,
G.
,
2019
, “
Programmable Elastic Valley Hall Insulator With Tunable Interface Propagation Routes
,”
Extreme Mech. Lett.
,
28
, pp.
76
80
.10.1016/j.eml.2019.03.002
212.
Gei
,
M.
,
Movchan
,
A. B.
, and
Bigoni
,
D.
,
2009
, “
Band-Gap Shift and Defect-Induced Annihilation in Prestressed Elastic Structures
,”
J. Appl. Phys.
,
105
(
6
), p.
063507
.10.1063/1.3093694
213.
Gei
,
M.
,
2010
, “
Wave Propagation in Quasiperiodic Structures: Stop/Pass Band Distribution and Prestress Effects
,”
Int. J. Solids Struct.
,
47
(
22–23
), pp.
3067
3075
.10.1016/j.ijsolstr.2010.07.008
214.
Wang
,
Y. Z.
,
Li
,
F. M.
,
Kishimoto
,
K.
,
Wang
,
Y. S.
, and
Huang
,
W. H.
,
2008
, “
Wave Localization in Randomly Disordered Periodic Piezoelectric Rods With Initial Stress
,”
Acta Mech. Solida Sin.
,
21
(
6
), pp.
529
535
.10.1007/s10338-008-0863-9
215.
Wang
,
Y. Z.
,
Li
,
F. M.
,
Kishimoto
,
K.
,
Wang
,
Y. S.
, and
Huang
,
W. H.
,
2010
, “
Band Gaps of Elastic Waves in Three-Dimensional Piezoelectric Phononic Crystals With Initial Stress
,”
Eur. J. Mech. A-Solids
,
29
(
2
), pp.
182
189
.10.1016/j.euromechsol.2009.09.005
216.
Li
,
Z. N.
,
Wang
,
Y. Z.
, and
Wang
,
Y. S.
,
2020
, “
Tunable Nonreciprocal Transmission in Nonlinear Elastic Wave Metamaterial by Initial Stresses
,”
Int. J. Solids Struct.
,
182–183
, pp.
218
235
.10.1016/j.ijsolstr.2019.08.020
217.
Feng
,
R.
, and
Liu
,
K.
,
2012
, “
Tuning the Band-Gap of Phononic Crystals With an Initial Stress
,”
Phys. B: Condens. Matter
,
407
(
12
), pp.
2032
2036
.10.1016/j.physb.2012.01.135
218.
Feng
,
R.-X.
, and
Liu
,
K.-X.
,
2012
, “
Tuning of Band-Gap of Phononic Crystals With Initial Confining Pressure
,”
Chin. Phys. B
,
21
(
12
), p.
126301
.10.1088/1674-1056/21/12/126301
219.
Zhou
,
X.
, and
Chen
,
C.
,
2013
, “
Tuning the Locally Resonant Phononic Band Structures of Two-Dimensional Periodic Electroactive Composites
,”
Phys. B: Condens. Matter
,
431
, pp.
23
31
.10.1016/j.physb.2013.08.042
220.
Li
,
S.
, and
Sun
,
B.
,
2012
,
Advances in Soft Matter Mechanics
,
Springer
,
Berlin
.
221.
Li
,
B.
,
Cao
,
Y.-P.
,
Feng
,
X.-Q.
, and
Gao
,
H.
,
2012
, “
Mechanics of Morphological Instabilities and Surface Wrinkling in Soft Materials: A Review
,”
Soft Matter
,
8
(
21
), p.
5728
.10.1039/c2sm00011c
222.
Bertoldi
,
K.
, and
Boyce
,
M. C.
,
2008
, “
Mechanically Triggered Transformations of Phononic Band Gaps in Periodic Elastomeric Structures
,”
Phys. Rev. B
,
77
(
5
), p.
052105
.10.1103/PhysRevB.77.052105
223.
Bertoldi
,
K.
, and
Boyce
,
M. C.
,
2008
, “
Wave Propagation and Instabilities in Monolithic and Periodically Structured Elastomeric Materials Undergoing Large Deformations
,”
Phys. Rev. B
,
78
(
18
), p.
184107
.10.1103/PhysRevB.78.184107
224.
Geymonat
,
G.
,
Müller
,
S.
, and
Triantafyllidis
,
N.
,
1993
, “
Homogenization of Nonlinearly Elastic Materials, Microscopic Bifurcation and Macroscopic Loss of Rank-One Convexity
,”
Arch. Rat. Mech. Anal.
,
122
(
3
), pp.
231
290
.10.1007/BF00380256
225.
Slesarenko
,
V.
, and
Rudykh
,
S.
,
2017
, “
Microscopic and Macroscopic Instabilities in Hyperelastic Fiber Composites
,”
J. Mech. Phys. Solids
,
99
, pp.
471
482
.10.1016/j.jmps.2016.11.002
226.
Mullin
,
T.
,
Deschanel
,
S.
,
Bertoldi
,
K.
, and
Boyce
,
M. C.
,
2007
, “
Pattern Transformation Triggered by Deformation
,”
Phys. Rev. Lett.
,
99
(
8
), p.
084301
.10.1103/PhysRevLett.99.084301
227.
Gao
,
N.
,
Li
,
J.
,
Bao
,
R. H.
, and
Chen
,
W. Q.
,
2019
, “
Harnessing Uniaxial Tension to Tune Poisson's Ratio and Wave Propagation in Soft Porous Phononic Crystals: An Experimental Study
,”
Soft Matter
,
15
(
14
), pp.
2921
2927
.10.1039/C8SM02468E
228.
Göncü
,
F.
,
Luding
,
S.
, and
Bertoldi
,
K.
,
2012
, “
Exploiting Pattern Transformation to Tune Phononic Band Gaps in a Two-Dimensional Granular Crystal
,”
J. Acoust. Soc. Am.
,
131
(
6
), pp.
EL475
EL480
.10.1121/1.4718384
229.
Jang
,
J.-H.
,
Koh
,
C. Y.
,
Bertoldi
,
K.
,
Boyce
,
M. C.
, and
Thomas
,
E. L.
,
2009
, “
Combining Pattern Instability and Shape-Memory Hysteresis for Phononic Switching
,”
Nano Lett.
,
9
(
5
), pp.
2113
2119
.10.1021/nl9006112
230.
Javid
,
F.
,
Liu
,
J.
,
Shim
,
J.
,
Weaver
,
J. C.
,
Shanian
,
A.
, and
Bertoldi
,
K.
,
2016
, “
Mechanics of Instability-Induced Pattern Transformations in Elastomeric Porous Cylinders
,”
J. Mech. Phys. Solids
,
96
, pp.
1
17
.10.1016/j.jmps.2016.06.015
231.
Kang
,
S. H.
,
Shan
,
S.
,
Noorduin
,
W. L.
,
Khan
,
M.
,
Aizenberg
,
J.
, and
Bertoldi
,
K.
,
2013
, “
Buckling-Induced Reversible Symmetry Breaking and Amplification of Chirality Using Supported Cellular Structures
,”
Adv. Mater.
,
25
(
24
), pp.
3380
3385
.10.1002/adma.201300617
232.
Overvelde
,
J. T. B.
, and
Bertoldi
,
K.
,
2014
, “
Relating Pore Shape to the Non-Linear Response of Periodic Elastomeric Structures
,”
J. Mech. Phys. Solids
,
64
, pp.
351
–3
66
.10.1016/j.jmps.2013.11.014
233.
Shan
,
S.
,
Kang
,
S. H.
,
Wang
,
P.
,
Qu
,
C.
,
Shian
,
S.
,
Chen
,
E. R.
, and
Bertoldi
,
K.
,
2014
, “
Harnessing Multiple Folding Mechanisms in Soft Periodic Structures for Tunable Control of Elastic Waves
,”
Adv. Funct. Mater.
,
24
(
31
), pp.
4935
4942
.10.1002/adfm.201400665
234.
Shim
,
J.
,
Wang
,
P.
, and
Bertoldi
,
K.
,
2015
, “
Harnessing Instability-Induced Pattern Transformation to Design Tunable Phononic Crystals
,”
Int. J. Solids Struct.
,
58
, pp.
52
61
.10.1016/j.ijsolstr.2014.12.018
235.
Wang
,
L.
, and
Bertoldi
,
K.
,
2012
, “
Mechanically Tunable Phononic Band Gaps in Three-Dimensional Periodic Elastomeric Structures
,”
Int. J. Solids Struct.
,
49
(
19–20
), pp.
2881
2885
.10.1016/j.ijsolstr.2012.05.008
236.
Wang
,
P.
,
Shim
,
J.
, and
Bertoldi
,
K.
,
2013
, “
Effects of Geometric and Material Nonlinearities on Tunable Band Gaps and Low-Frequency Directionality of Phononic Crystals
,”
Phys. Rev. B
,
88
(
1
), p.
014304
.10.1103/PhysRevB.88.014304
237.
Huang
,
Y. L.
,
Gao
,
N.
,
Chen
,
W. Q.
, and
Bao
,
R. H.
,
2018
, “
Extension/Compression-Controlled Complete Band Gaps in 2d Chiral Square-Lattice-Like Structures
,”
Acta Mech. Solida Sin.
,
31
(
1
), pp.
51
65
.10.1007/s10338-018-0004-z
238.
Gao
,
N.
,
Huang
,
Y. L.
,
Bao
,
R. H.
, and
Chen
,
W. Q.
,
2018
, “
Robustly Tuning Bandgaps in Two-Dimensional Soft Phononic Crystals With Criss-Crossed Elliptical Holes
,”
Acta Mech. Solida Sin.
,
31
(
5
), pp.
573
588
.10.1007/s10338-018-0044-4
239.
Babaee
,
S.
,
Viard
,
N.
,
Wang
,
P.
,
Fang
,
N. X.
, and
Bertoldi
,
K.
,
2016
, “
Harnessing Deformation to Switch On and Off the Propagation of Sound
,”
Adv. Mater.
,
28
(
8
), pp.
1631
1635
.10.1002/adma.201504469
240.
Li
,
S.
,
Zhao
,
D.
,
Niu
,
H.
,
Zhu
,
X. F.
, and
Zang
,
J. F.
,
2018
, “
Observation of Elastic Topological States in Soft Materials
,”
Nat. Commun.
,
9
(
1
), p.
1370
.10.1038/s41467-018-03830-8
241.
Rudykh
,
S.
, and
Boyce
,
M. C.
,
2014
, “
Transforming Wave Propagation in Layered Media Via Instability-Induced Interfacial Wrinkling
,”
Phys. Rev. Lett.
,
112
(
3
), p.
034301
.10.1103/PhysRevLett.112.034301
242.
Li
,
G. Y.
,
Xu
,
G.
,
Zheng
,
Y.
, and
Cao
,
Y.
,
2018
, “
Non-Leaky Modes and Bandgaps of Surface Acoustic Waves in Wrinkled Stiff-Film/Compliant-Substrate Bilayers
,”
J. Mech. Phys. Solids
,
112
, pp.
239
252
.10.1016/j.jmps.2017.11.024
243.
Bayat
,
A.
, and
Gordaninejad
,
F.
,
2015
, “
Switching Band-Gaps of a Phononic Crystal Slab by Surface Instability
,”
Smart Mater. Struct.
,
24
(
7
), p.
075009
.10.1088/0964-1726/24/7/075009
244.
Wang
,
P.
,
Casadei
,
F.
,
Shan
,
S.
,
Weaver
,
J. C.
, and
Bertoldi
,
K.
,
2014
, “
Harnessing Buckling to Design Tunable Locally Resonant Acoustic Metamaterials
,”
Phys. Rev. Lett.
,
113
(
1
), p.
014301
.10.1103/PhysRevLett.113.014301
245.
Zhou
,
W. J.
,
Wu
,
B.
,
Muhammad
,
Du
,
Q.
,
Huang
,
G. L.
,
,
C. F.
, and
Chen
,
W. Q.
,
2018
, “
Actively Tunable Transverse Waves in Soft Membrane-Type Acoustic Metamaterials
,”
J. Appl. Phys.
,
123
(
16
), p.
165304
.10.1063/1.5015979
246.
Huang
,
Y. L.
,
Li
,
J.
,
Chen
,
W. Q.
, and
Bao
,
R. H.
,
2019
, “
Tunable Bandgaps in Soft Phononic Plates With Spring-Mass-Like Resonators
,”
Int. J. Mech. Sci.
,
151
, pp.
300
313
.10.1016/j.ijmecsci.2018.11.029
247.
Galich
,
P. I.
,
Fang
,
N. X.
,
Boyce
,
M. C.
, and
Rudykh
,
S.
,
2017
, “
Elastic Wave Propagation in Finitely Deformed Layered Materials
,”
J. Mech. Phys. Solids
,
98
, pp.
390
410
.10.1016/j.jmps.2016.10.002
248.
Parnell
,
W. J.
,
2007
, “
Effective Wave Propagation in a Prestressed Nonlinear Elastic Composite Bar
,”
IMA J. Appl. Math.
,
72
(
2
), pp.
223
244
.10.1093/imamat/hxl033
249.
Huang
,
Y.
,
Shen
,
X. D.
,
Zhang
,
C. L.
, and
Chen
,
W. Q.
,
2014
, “
Mechanically Tunable Band Gaps in Compressible Soft Phononic Laminated Composites With Finite Deformation
,”
Phys. Lett. A
,
378
(
30–31
), pp.
2285
2289
.10.1016/j.physleta.2014.05.032
250.
Huang
,
Y.
,
Chen
,
W. Q.
,
Wang
,
Y. S.
, and
Yang
,
W.
,
2015
, “
Multiple Refraction Switches Realized by Stretching Elastomeric Scatterers in Sonic Crystals
,”
AIP Adv.
,
5
(
2
), p.
027138
.10.1063/1.4914018
251.
Shmuel
,
G.
, and
Band
,
R.
,
2016
, “
Universality of the Frequency Spectrum of Laminates
,”
J. Mech. Phys. Solids
,
92
, pp.
127
136
.10.1016/j.jmps.2016.04.001
252.
Barnwell
,
E. G.
,
Parnell
,
W. J.
, and
David Abrahams
,
I.
,
2016
, “
Antiplane Elastic Wave Propagation in Pre-Stressed Periodic Structures; Tuning, Band Gap Switching and Invariance
,”
Wave Motion
,
63
, pp.
98
110
.10.1016/j.wavemoti.2016.02.001
253.
Zhang
,
P.
, and
Parnell
,
W. J.
,
2017
, “
Soft Phononic Crystals With Deformation-Independent Band Gaps
,”
Proc. R. Soc. A
,
473
(
2200
), p.
20160865
.10.1098/rspa.2016.0865
254.
Hedayatrasa
,
S.
,
Abhary
,
K.
,
Uddin
,
M. S.
, and
Guest
,
J. K.
,
2016
, “
Optimal Design of Tunable Phononic Bandgap Plates Under Equibiaxial Stretch
,”
Smart Mater. Struct.
,
25
(
5
), p.
055025
.10.1088/0964-1726/25/5/055025
255.
Xin
,
F.
, and
Lu
,
T.
,
2016
, “
Tensional Acoustomechanical Soft Metamaterials
,”
Sci. Rep.
,
6
(
1
), p.
27432
.10.1038/srep27432
256.
Chen
,
Y. J.
,
Wu
,
B.
,
Su
,
Y. P.
, and
Chen
,
W. Q.
,
2019
, “
Tunable Two-Way Unidirectional Acoustic Diodes: Design and Simulation
,”
ASME J. Appl. Mech.
,
86
(
3
), p.
031010
.10.1115/1.4042321
257.
Raney
,
J. R.
,
Nadkarni
,
N.
,
Daraio
,
C.
,
Kochmann
,
D. M.
,
Lewis
,
J. A.
, and
Bertoldi
,
K.
,
2016
, “
Stable Propagation of Mechanical Signals in Soft Media Using Stored Elastic Energy
,”
Proc. Natl. Acad. Sci.
,
113
(
35
), pp.
9722
9727
.10.1073/pnas.1604838113
258.
Bertoldi
,
K.
,
Vitelli
,
V.
,
Christensen
,
J.
, and
van Hecke
,
M.
,
2017
, “
Flexible Mechanical Metamaterials
,”
Nat. Rev. Mater.
,
2
(
11
), p.
17066
.10.1038/natrevmats.2017.66
259.
Nesterenko
,
V. F.
,
2001
,
Dynamics of Heterogeneous Materials
,
Springer
,
New York
.
260.
Sen
,
S.
,
Hong
,
J. B.
,
Bang
,
J. H.
,
Avalos
,
E.
, and
Doney
,
R.
,
2008
, “
Solitary Waves in the Granular Chain
,”
Phys. Rep.
,
462
(
2
), pp.
21
66
.10.1016/j.physrep.2007.10.007
261.
Theocharis
,
G.
,
Boechler
,
N.
, and
Daraio
,
C.
,
2013
, “
Nonlinear Phononic Periodic Structures and Granular Crystals
,”
Acoustic Metamaterials and Phononic Crystals
,
Springer
,
Berlin, Germany
, pp.
217
251
.
262.
Porter
,
M. A.
,
Kevrekidis
,
P. G.
, and
Daraio
,
C.
,
2015
, “
Granular Crystals: Nonlinear Dynamics Meets Materials Engineering
,”
Phys. Today
,
68
(
11
), pp.
44
50
.10.1063/PT.3.2981
263.
Chong
,
C.
,
Porter
,
M. A.
,
Kevrekidis
,
P. G.
, and
Daraio
,
C.
,
2017
, “
Nonlinear Coherent Structures in Granular Crystals
,”
J. Phys.: Condens. Matter
,
29
(
41
), p.
413003
.10.1088/1361-648X/aa7672
264.
Nesterenko
,
V. F.
,
2018
, “
Waves in Strongly Nonlinear Discrete Systems
,”
Philos. Trans. R. Soc. A
,
376
(
2127
), p.
20170130
.10.1098/rsta.2017.0130
265.
Kim
,
E. H.
, and
Yang
,
J. K.
,
2019
, “
Wave Propagation in Granular Metamaterials
,”
Funct. Compos. Struct.
,
1
(
1
), p.
012002
.10.1088/2631-6331/ab0c7e
266.
Coste
,
C.
, and
Gilles
,
B.
,
1999
, “
On the Validity of Hertz Contact Law for Granular Material Acoustics
,”
Eur. Phys. J. B-Condens. Matter Complex Syst.
,
7
(
1
), pp.
155
168
.10.1007/s100510050598
267.
De Billy
,
M.
,
2000
, “
Experimental Study of Sound Propagation in a Chain of Spherical Beads
,”
J. Acoust. Soc. Am.
,
108
(
4
), pp.
1486
1495
.10.1121/1.1289365
268.
Herbold
,
E. B.
,
Kim
,
J.
,
Nesterenko
,
V. F.
,
Wang
,
S.
, and
Daraio
,
C.
,
2009
, “
Pulse Propagation in a Linear and Nonlinear Diatomic Periodic Chain: Effects of Acoustic Frequency Band-Gap
,”
Acta Mech.
,
205
(
1–4
), pp.
85
103
.10.1007/s00707-009-0163-6
269.
Boechler
,
N
,
Yang
,
J
,
Theocharis
,
G
,
Kevrekidis
,
P. G.
, and
Daraio
,
C.
,
2011
, “
Tunable Vibrational Band Gaps in One-Dimensional Diatomic Granular Crystals With Three-Particle Unit Cells
,”
J. Appl. Phys.
,
109
(
7
), p.
074906
.10.1063/1.3556455
270.
Li
,
F.
,
Ngo
,
D.
,
Yang
,
J.
, and
Daraio
,
C.
,
2012
, “
Tunable Phononic Crystals Based on Cylindrical Hertzian Contact
,”
Appl. Phys. Lett.
,
101
(
17
), p.
171903
.10.1063/1.4762832
271.
Yang
,
J
, and
Daraio
,
C.
,
2013
, “
Frequency- and Amplitude-Dependent Transmission of Stress Waves in Curved One-Dimensional Granular Crystals Composed of Diatomic Particles
,”
Exp. Mech.
,
53
(
3
), pp.
469
483
.10.1007/s11340-012-9652-y
272.
Meidani
,
M.
,
Kim
,
E.
,
Li
,
F.
,
Yang
,
J.
, and
Ngo
,
D.
,
2015
, “
Tunable Evolutions of Wave Modes and Bandgaps in Quasi-1D Cylindrical Phononic Crystals
,”
J. Sound Vib.
,
334
, pp.
270
281
.10.1016/j.jsv.2014.09.010
273.
Theocharis
,
G.
,
Kavousanakis
,
M.
,
Kevrekidis
,
P. G.
,
Daraio
,
C.
,
Porter
,
M. A.
, and
Kevrekidis
,
I. G.
,
2009
, “
Localized Breathing Modes in Granular Crystals With Defects
,”
Phys. Rev. E.
,
80
(
6
), p.
066601
.10.1103/PhysRevE.80.066601
274.
Man
,
Y.
,
Boechler
,
N.
,
Theocharis
,
G.
,
Kevrekidis
,
P. G.
, and
Daraio
,
C.
,
2012
, “
Defect Modes in One-Dimensional Granular Crystals
,”
Phys. Rev. E.
,
85
(
3
), p.
037601
.10.1103/PhysRevE.85.037601
275.
Lydon
,
J.
,
Serra-Garcia
,
M.
, and
Daraio
,
C.
,
2014
, “
Local to Extended Transitions of Resonant Defect Modes
,”
Phys. Rev. Lett.
,
113
(
18
), p.
185503
.10.1103/PhysRevLett.113.185503
276.
Fermi
,
E.
,
Pasta
,
J. R.
, and
Ulam
,
S.
,
1955
, Studies of Nonlinear Problems, Los Alamos Scientific Laboratory, Los Alamos.
277.
Kim
,
E.
,
Martinez
,
A. J.
,
Phenisee
,
S. E.
,
Kevrekidis
,
P. G.
,
Porter
,
M. A.
, and
Yang
,
J. Y.
,
2018
, “
Direct Measurement of Superdiffusive Energy Transport in Disordered Granular Chains
,”
Nat. Commun.
,
9
(
1
), p.
640
.10.1038/s41467-018-03015-3
278.
Nesterenko
,
V. F.
,
1983
, “
Propagation of Nonlinear Compression Pulses in Granular Media
,”
J. Appl. Mech. Tech. Phys.
,
24
(
5
), 733–743.10.1007/BF00905892
279.
Lazaridi
,
A. N.
, and
Nesterenko
,
V. F.
,
1985
, “
Observation of a New Type of Solitary Waves in a One-Dimensional Granular Medium
,”
J. Appl. Mech. Tech. Phys.
,
26
(
3
), 405–408.10.1007/BF00910379
280.
Nesterenko
,
V. F.
,
1992
, “
Nonlinear Waves in “Sonic Vacuum”,
” Fiz. Goreniya Vzryva,
28
(
2
), 121–122. https://www.researchgate.net/publication/279706471_Nonlinear_waves_in_a_'sound_vacuum'
281.
Theocharis
,
G.
,
Boechler
,
N.
,
Kevrekidis
,
P. G.
,
Job
,
S.
,
Porter
,
M. A.
, and
Daraio
,
C.
,
2010
, “
Intrinsic Energy Localization Through Discrete Gap Breathers in One-Dimensional Diatomic Granular Crystals
,”
Phys. Rev. E.
,
82
(
5
), p.
056604
.10.1103/PhysRevE.82.056604
282.
Boechler
,
N.
,
Theocharis
,
G.
,
Job
,
S.
,
Kevrekidis
,
P. G.
,
Porter
,
M. A.
, and
Daraio
,
C.
,
2010
, “
Discrete Breathers in One-Dimensional Diatomic Granular Crystals
,”
Phys. Rev. Lett.
,
104
(
24
), p.
244302
.10.1103/PhysRevLett.104.244302
283.
Chong
,
C.
,
Kevrekidis
,
P. G.
,
Theocharis
,
G.
, and
Daraio
,
C.
,
2013
, “
Dark Breathers in Granular Crystals
,”
Phys. Rev. E.
,
87
(
4
), p.
042202
.10.1103/PhysRevE.87.042202
284.
Chong
,
C.
,
Li
,
F.
,
Yang
,
J.
,
Williams
,
M. O.
, and
Kevrekidis
,
I. G.
,
Kevrekidis
,
P. G.
, and
Daraio
,
C.
,
2014
, “
Damped-Driven Granular Chains: An Ideal Playground for Dark Breathers and Multibreathers
,”
Phys. Rev. E.
,
89
(
3
), p.
032924
.10.1103/PhysRevE.89.032924
285.
Porter
,
M. A.
,
Daraio
,
C.
,
Herbold
,
E. B.
,
Szelengowicz
,
I.
, and
Kevrekidis
,
P. G.
,
2008
, “
Highly Nonlinear Solitary Waves in Periodic Dimer Granular Chains
,”
Phys. Rev. E.
,
77
(
1
), p.
015601
.10.1103/PhysRevE.77.015601
286.
Jayaprakash
,
K. R.
,
Starosvetsky
,
Y.
, and
Vakakis
,
A. F.
,
2011
, “
New Family of Solitary Waves in Granular Dimer Chains With No Precompression
,”
Phys. Rev. E.
,
83
(
3
), p.
036606
.10.1103/PhysRevE.83.036606
287.
Jayaprakash
,
K. R.
,
Vakakis
,
A. F.
, and
Starosvetsky
,
Y.
,
2012
, “
Solitary Waves in a General Class of Granular Dimer Chains
,”
J. Appl. Phys.
,
112
(
3
), p.
034908
.10.1063/1.4740060
288.
Molinari
,
A.
, and
Daraio
,
C.
,
2009
, “
Stationary Shocks in Periodic Highly Nonlinear Granular Chains
,”
Phys. Rev. E.
,
80
(
5
), p.
056602
.10.1103/PhysRevE.80.056602
289.
Daraio
,
C.
,
Nesterenko
,
V. F.
,
Herbold
,
E. B.
, and
Jin
,
S.
,
2006
, “
Energy Trapping and Shock Disintegration in a Composite Granular Medium
,”
Phys. Rev. Lett.
,
96
(
5
), p.
058002
.10.1103/PhysRevLett.96.058002
290.
Boechler
,
N.
,
Theocharis
,
G.
, and
Daraio
,
C.
,
2011
, “
Bifurcation-Based Acoustic Switching and Rectification
,”
Nat. Mater.
,
10
(
9
), pp.
665
668
.10.1038/nmat3072
291.
Sen
,
S.
,
Manciu
,
M.
, and
Wright
,
J. D.
,
1998
, “
Solitonlike Pulses in Perturbed and Driven Hertzian Chains and Their Possible Applications in Detecting Buried Impurities
,”
Phys. Rev. E.
,
57
(
2
), pp.
2386
2397
.10.1103/PhysRevE.57.2386
292.
Hascoët
,
E.
, and
Herrmann
,
H. J.
,
2000
, “
Shocks in Non-Loaded Bead Chains With Impurities
,”
Eur. Phys. J. B-Condens. Matter Complex Syst.
,
14
(
1
), pp.
183
190
.10.1007/s100510050119
293.
Job
,
S.
,
Santibanez
,
F.
,
Tapia
,
F.
, and
Melo
,
F.
,
2009
, “
Wave Localization in Strongly Nonlinear Hertzian Chains With Mass Defect
,”
Phys. Rev. E.
,
80
(
2
), p.
025602
.10.1103/PhysRevE.80.025602
294.
Starosvetsky
,
Y.
,
Jayaprakash
,
K. R.
, and
Vakakis
,
A. F.
,
2012
, “
Scattering of Solitary Waves and Excitation of Transient Breathers in Granular Media by Light Intruders and No Precompression
,”
ASME J. Appl. Mech.
,
79
(
1
), p.
011001
.10.1115/1.4003360
295.
Kevrekidis
,
P. G.
,
Vainchtein
,
A.
,
Garcia
,
M. S.
, and
Daraio
,
C.
,
2013
, “
Interaction of Traveling Waves With Mass-With-Mass Defects Within a Hertzian Chain
,”
Phys. Rev. E.
,
87
(
4
), p.
042911
.10.1103/PhysRevE.87.042911
296.
Doney
,
R. L.
, and
Sen
,
S.
,
2005
, “
Impulse Absorption by Tapered Horizontal Alignments of Elastic Spheres
,”
Phys. Rev. E.
,
72
(
4
), p.
041304
.10.1103/PhysRevE.72.041304
297.
Doney
,
R. L.
,
Agul
,
J. H.
, and
Sen
,
S.
,
2009
, “Energy Partitioning and Impulse Dispersion in the Decorated, Tapered, Strongly Nonlinear Granular Alignment: A System With Many Potential Applications,”
J. Appl. Phys.
,
106
(
6
), p.
064905
.10.1063/1.3190485
298.
Chaunsali
,
R.
,
Kim
,
E.
, and
Yang
,
J.
,
2018
, “
Demonstration of Accelerating and Decelerating Nonlinear Impulse Waves in Functionally Graded Granular Chains
,”
Philos. Trans. R. Soc. A.
,
376
(
2127
), p.
20170136
.10.1098/rsta.2017.0136
299.
Yang
,
J.
,
Dunatunga
,
S.
, and
Daraio
,
C.
,
2012
, “
Amplitude-Dependent Attenuation of Compressive Waves in Curved Granular Crystals Constrained by Elastic Guides
,”
Acta. Mech.
,
223
(
3
), 549–562.10.1007/s00707-011-0568-x
300.
Cai
,
L.
,
Yang
,
J.
,
Rizzo
,
P.
,
Ni
,
X.
, and
Daraio
,
C.
,
2013
, “
Propagation of Highly Nonlinear Solitary Waves in a Curved Granular Chain
,”
Granul. Matter
,
15
, pp.
357
366
.10.1007/s10035-013-0414-z
301.
Ngo
,
D.
,
Fraternali
,
F.
, and
Daraio
,
C.
,
2012
, “
Highly Nonlinear Solitary Wave Propagation in Y-Shaped Granular Crystals With Variable Branch Angles
,”
Phys. Rev. E.
,
85
(
3
), p.
036602
.10.1103/PhysRevE.85.036602
302.
Leonard
,
A.
,
Ponson
,
L.
, and
Daraio
,
C.
,
2014
, “
Wave Mitigation in Ordered Networks of Granular Chains
,”
J. Mech. Phys. Solids
,
73
, pp.
103
117
.10.1016/j.jmps.2014.08.004
303.
Ngo
,
D.
,
Khatri
,
D.
, and
Daraio
,
C.
,
2011
, “
Highly Nonlinear Solitary Waves in Chains of Ellipsoidal Particles
,”
Phys. Rev. E.
,
84
(
2
), p.
026610
.10.1103/PhysRevE.84.026610
304.
Khatri
,
D.
,
Ngo
,
D.
, and
Daraio
,
C.
,
2012
, “
Highly Nonlinear Solitary Waves in Chains of Cylindrical Particles
,”
Granular Matter
,
14
(
1
), pp.
63
69
.10.1007/s10035-011-0297-9
305.
Chaunsali
,
R.
,
Kim
,
E.
,
Thakkar
,
A.
,
Kevrekidis
,
P. G.
, and
Yang
,
J.
,
2017
, “
Demonstrating an In Situ Topological Band Transition in Cylindrical Granular Chains
,”
Phys. Rev. Lett.
,
119
(
2
), p.
024301
.10.1103/PhysRevLett.119.024301
306.
Ngo
,
D.
,
Griffiths
,
S.
,
Khatri
,
D.
, and
Daraio
,
C.
,
2013
, “
Highly Nonlinear Solitary Waves in Chains of Hollow Spherical Particles
,”
Granular Matter
,
15
(
2
), pp.
149
155
.10.1007/s10035-012-0377-5
307.
Kim
,
H.
,
Kim
,
E.
,
Chong
,
C.
,
Kevrekidis
,
P. G.
, and
Yang
,
J.
,
2018
, “
Demonstration of Dispersive Rarefaction Shocks in Hollow Elliptical Cylinder Chains
,”
Phys. Rev. Lett.
,
120
(
19
), p.
194101
.10.1103/PhysRevLett.120.194101
308.
Daraio
,
C.
, and
Nesterenko
,
V. F.
,
2006
, “Strongly Nonlinear Wave Dynamics in Chain of Polymer Coated Beads,”
Phys. Rev. E.
,
73
(
2
), p.
026612
.10.1103/PhysRevE.73.026612
309.
Rosas
,
A.
, and
Lindenberg
,
K.
,
2003
, “
Pulse Dynamics in a Chain of Granules With Friction
,”
Phys. Rev. E
,
68
(
4
), p.
041304
.10.1103/PhysRevE.68.041304
310.
Rosas
,
A.
,
Romero
,
A. H.
,
Nesterenko
,
V. F.
, and
Lindenberg
,
K.
,
2007
, “
Observation of Two-Wave Structure in Strongly Nonlinear Dissipative Granular Chains
,”
Phys. Rev. Lett.
,
98
(
16
), p.
164301
.10.1103/PhysRevLett.98.164301
311.
Herbold
,
E. B.
, and
Nesterenko
,
V. F.
,
2007
, “
Shock Wave Structure in a Strongly Nonlinear Lattice With Viscous Dissipation
,”
Phys. Rev. E
,
75
(
2
), p.
021304
.10.1103/PhysRevE.75.021304
312.
Carretero-González
,
R.
,
Khatri
,
D.
,
Porter
,
M. A.
,
Kevrekidis
,
P. G.
, and
Daraio
,
C.
,
2009
, “
Dissipative Solitary Waves in Granular Crystals
,”
Phys. Rev. Lett.
,
102
(
2
), p.
024102
.10.1103/PhysRevLett.102.024102
313.
Jayaprakash
,
K. R.
,
Starosvetsky
,
Y.
,
Vakakis
,
A. F.
,
Peeters
,
M.
, and
Kerschen
,
G.
,
2011
, “
Nonlinear Normal Modes and Band Zones in Granular Chains With No Pre-Compression
,”
Nonlinear Dyn.
,
63
(
3
), pp.
359
385
.10.1007/s11071-010-9809-0
314.
Lydon
,
J.
,
Jayaprakash
,
K. R.
,
Ngo
,
D.
,
Starosvetsky
,
Y.
,
Vakakis
,
A. F.
, and
Daraio
,
C.
,
2013
, “
Frequency Bands of Strongly Nonlinear Homogeneous Granular Systems
,”
Phys. Rev. E
,
88
(
1
), p.
012206
.10.1103/PhysRevE.88.012206
315.
Herbold
,
E. B.
, and
Nesterenko
,
V. F.
,
2013
, “Propagation of Rarefaction Pulse in Discrete Materials With Strain-Softening Behavior,”
Phys. Rev. Lett.
,
110
(
14
), p.
144101
.10.1103/PhysRevLett.110.144101
316.
Xu
,
Y.
, and
Nesterenko
,
V. F.
,
2014
, “
Propagation of Short Stress Pulses in Discrete Strongly Nonlinear Tunable Metamaterials
,”
Philos. Trans. R. Soc. A
,
372
(
2023
), p.
20130186
.10.1098/rsta.2013.0186
317.
Bonanomi
,
L.
,
Theocharis
,
G.
, and
Daraio
,
C.
,
2015
, “
Wave Propagation in Granular Chains With Local Resonances
,”
Phys. Rev. E
,
91
(
3
), p.
033208
.10.1103/PhysRevE.91.033208
318.
Martínez
,
A. J.
,
Porter
,
M. A.
, and
Kevrekidis
,
P. G.
,
2018
, “Quasiperiodic Granular Chains and Hofstadter Butterflies,” Phil. Trans. R. Soc. A,
376
(
2127
), p.
20170139
.
319.
Gantzounis
,
G.
,
Serra-Garcia
,
M.
,
Homma
,
K.
,
Mendoza
,
J. M.
, and
Daraio
,
C.
,
2013
, “
Granular Metamaterials for Vibration Mitigation
,”
J. Appl. Phys.
,
114
(
9
), p.
093514
.10.1063/1.4820521
320.
Liu
,
L.
,
James
,
G.
,
Kevrekidis
,
P.
, and
Vainchtein
,
A.
,
2016
, “
Breathers in a Locally Resonant Granular Chain With Precompression
,”
Phys. D: Nonlinear Phenom.
,
331
, pp.
27
47
.10.1016/j.physd.2016.05.007
321.
Liu
,
L.
,
James
,
G.
,
Kevrekidis
,
P.
, and
Vainchtein
,
A.
,
2016
, “Strongly Nonlinear Waves in Locally Resonant Granular Chains,”
Nonlinearity
,
29
(
11
), p. 3496.10.1088/0951-7715/29/11/3496
322.
Wallen
,
S. P.
,
Lee
,
J.
,
Mei
,
D.
,
Chong
,
C.
,
Kevrekidis
,
P. G.
, and
Boechler
,
N.
,
2017
, “Discrete Breathers in a Mass-in-Mass Chain With Hertzian Local Resonators,”
Phys. Rev. E
,
95
(
2
), p. 022904.10.1103/PhysRevE.95.022904
323.
Kim
,
E.
, and
Yang
,
J.
,
2014
, “
Wave Propagation in Single Column Woodpile Phononic Crystals: Formation of Tunable Band Gaps
,”
J. Mech. Phys. Solids
,
71
, pp.
33
45
.10.1016/j.jmps.2014.06.012
324.
Kim
,
E.
,
Li
,
F.
,
Chong
,
C.
,
Theocharis
,
G.
,
Yang
,
J.
, and
Kevrekidis
,
P. G.
,
2015
, “
Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures
,”
Phys. Rev. Lett.
,
114
(
11
), p.
118002
.10.1103/PhysRevLett.114.118002
325.
Kim
,
E.
,
Kim
,
Y. H. N.
, and
Yang
,
J.
,
2015
, “
Nonlinear Stress Wave Propagation in 3D Woodpile Elastic Metamaterials
,”
Int. J. Solids Struct.
,
58
, pp.
128
135
.10.1016/j.ijsolstr.2014.12.024
326.
Kim
,
E.
,
Yang
,
J.
,
Hwang
,
H.
, and
Shul
,
C. W.
,
2017
, “Impact and Blast Mitigation Using Locally Resonant Woodpile Metamaterials,”
Int. J. Impact Eng.
,
101
, pp. 24–31.10.1016/j.ijimpeng.2016.09.006
327.
Kore
,
R.
,
Waychal
,
A.
,
Agarwal
,
S.
,
Yadav
,
P.
,
Uddin
,
A.
,
Sahoo
,
N.
, and
Shelke
,
A.
,
2016
, “
Impact Induced Solitary Wave Propagation Through a Woodpile Structure
,”
Smart Mater. Struct.
,
25
(
2
), p.
025027
.10.1088/0964-1726/25/2/025027
328.
Cabaret
,
J.
,
Tournat
,
V.
, and
Béquin
,
P.
,
2012
, “
Amplitude-Dependent Phononic Processes in a Diatomic Granular Chain in the Weakly Nonlinear Regime
,”
Phys. Rev. E
,
86
(
4
), p.
041305
.10.1103/PhysRevE.86.041305
329.
Yang
,
J.
,
Silvestro
,
C.
,
Sangiorgio
,
S. N.
,
Borkowski
,
S. L.
,
Ebramzadeh
,
E.
,
De Nardo
,
L.
, and
Daraio
,
C.
,
2011
, “Nondestructive Evaluation of Orthopaedic Implant Stability in THA Using Highly Nonlinear Solitary Waves,”
Smart Mater. Struct.
,
21
(
1
), p. 012002.10.1088/0964-1726/21/1/012002
330.
Ni
,
X.
,
Rizzo
,
P.
,
Yang
,
J.
,
Katri
,
D.
, and
Daraio
,
C.
,
2012
, “Monitoring the Hydration of Cement Using Highly Nonlinear Solitary Waves,”
NDT & E Int.
,
52
, pp. 76–85.10.1016/j.ndteint.2012.05.003
331.
Kim
,
E.
,
Restuccia
,
F.
,
Yang
,
J.
, and
Daraio
,
C.
,
2015
, “
Solitary Wave-Based Delamination Detection in Composite Plates Using a Combined Granular Crystal Sensor and Actuator
,”
Smart Mater. Struct.
,
24
(
12
), p.
125004
.10.1088/0964-1726/24/12/125004
332.
Singhal
,
T.
,
Kim
,
E.
,
Kim
,
T. Y.
, and
Yang
,
J.
,
2017
, “
Weak Bond Detection in Composites Using Highly Nonlinear Solitary Waves
,”
Smart Mater. Struct.
,
26
(
5
), p.
055011
.10.1088/1361-665X/aa6823
333.
Fraternali
,
F.
,
Porter
,
M. A.
, and
Daraio
,
C.
,
2009
, “
Optimal Design of Composite Granular Protectors
,”
Mech. Adv. Mater. Struct.
,
17
(
1
), pp.
1
19
.10.1080/15376490802710779
334.
Spadoni
,
A.
, and
Daraio
,
C.
,
2010
, “
Generation and Control of Sound Bullets With a Nonlinear Acoustic Lens
,”
Proc. Natl. Acad. Sci.
,
107
(
16
), pp.
7230
7234
.10.1073/pnas.1001514107
335.
Donahue
,
C. M.
,
Anzel
,
P. W.
,
Bonanomi
,
L.
,
Keller
,
T. A.
, and
Daraio
,
C.
,
2014
, “Experimental Realization of a Nonlinear Acoustic Lens With a Tunable Focus,”
Appl. Phys. Lett.
,
104
(
1
), p. 014103.10.1063/1.4857635
336.
Ni
,
X.
,
Rizzo
,
P.
, and
Daraio
,
C.
,
2011
, “Actuators for the Generation of Highly Nonlinear Solitary Waves,”
Rev. Sci. Instrum.
,
82
(
3
), p. 034902.10.1063/1.3556442
337.
Shelke
,
A.
,
Uddin
,
A.
, and
Yang
,
J.
,
2014
, “
Impact Identification in Sandwich Structures Using Solitary Wave-Supporting Granular Crystals Sensors
,”
AIAA J.
,
52
(
10
), pp.
2283
2290
.10.2514/1.J052868
338.
Li
,
F.
,
Chong
,
C.
,
Yang
,
J. K.
,
Kevrekidis
,
P. G.
, and
Daraio
,
C.
,
2014
, “
Wave Transmission in Time- and Space-Variant Helicoidal Phononic Crystals
,”
Phys. Rev. E
,
90
(
5
), p.
052301
.10.1103/PhysRevE.90.053201
339.
Li
,
F.
,
Anzel
,
P.
,
Yang
,
J. K.
,
Kevrekidis
,
P. G.
, and
Daraio
,
C.
,
2014
, “
Granular Acoustic Switches and Logic Elements
,”
Nat. Commun.
,
5
(
1
), p.
5311
.10.1038/ncomms6311
340.
Velický
,
B.
, and
Caroli
,
C.
,
2002
, “
Pressure Dependence of the Sound Velocity in a Two-Dimensional Lattice of Hertz-Mindlin Balls: Mean-Field Description
,”
Phys. Rev. E
,
65
(
2
), p.
021307
.10.1103/PhysRevE.65.021307
341.
Pavlov
,
I. S.
,
Potapov
,
A. I.
, and
Maugin
,
G. A.
,
2006
, “
A 2D Granular Medium With Rotating Particles
,”
Int. J. Solids Struct.
,
43
(
20
), pp.
6194
6207
.10.1016/j.ijsolstr.2005.06.012
342.
Coste
,
C.
, and
Gilles
,
B.
,
2008
, “
Sound Propagation in a Constrained Lattice of Beads: High-Frequency Behavior and Dispersion Relation
,”
Phys. Rev. E
,
77
(
2
), p.
021302
.10.1103/PhysRevE.77.021302
343.
Merkel
,
A.
,
Tournat
,
V.
, and
Gusev
,
V.
,
2011
, “
Experimental Evidence of Rotational Elastic Waves in Granular Phononic Crystals
,”
Phys. Rev. Lett.
,
107
(
22
), p.
225502
.10.1103/PhysRevLett.107.225502
344.
Tournat
,
V.
,
Pèrez-Arjona
,
I.
,
Merkel
,
A.
,
Sanchez-Morcillo
,
V.
, and
Gusev
,
V.
,
2011
, “
Elastic Waves in Phononic Monolayer Granular Membranes
,”
New J. Phys.
,
13
(
7
), p.
073042
.10.1088/1367-2630/13/7/073042
345.
Leonard
,
A.
,
Fraternali
,
F.
, and
Daraio
,
C.
,
2013
, “Directional Wave Propagation in a Highly Nonlinear Square Packing of Spheres,”
Exp. Mech.
,
53
, pp. 327–337.10.1007/s11340-011-9544-6
346.
Leonard
,
A.
,
Chong
,
C.
,
Kevrekidis
,
P. G.
, and
Daraio
,
C.
,
2014
, “Traveling Waves in 2D Hexagonal Granular Crystal Lattices,”
Granul. Matter
,
16
, pp. 531–542.10.1007/s10035-014-0487-3
347.
Szelengowicz
,
I.
,
Hasan
,
M. A.
,
Starosvetsky
,
Y.
,
Vakakis
,
A.
, and
Daraio
,
C.
,
2013
, “
Energy Equipartition in Two-Dimensional Granular Systems With Spherical Intruders
,”
Phys. Rev. E
,
87
(
3
), p.
032204
.10.1103/PhysRevE.87.032204
348.
Manjunath
,
M.
,
Awasthi
,
A. P.
, and
Geubelle
,
P. H.
,
2014
, “
Family of Plane Solitary Waves in Dimer Granular Crystals
,”
Phys. Rev. E
,
90
(
3
), p.
032209
.10.1103/PhysRevE.90.032209
349.
Chong
,
C.
,
Kevrekidis
,
P. G.
,
Ablowitz
,
M. J.
, and
Ma
,
Y. P.
,
2016
, “
Conical Wave Propagation and Diffraction in Two-Dimensional Hexagonally Packed Granular Lattices
,”
Phys. Rev. E
,
93
(
1
), p.
012909
.10.1103/PhysRevE.93.012909
350.
Hiraiwa
,
M.
,
Wallen
,
S. P.
, and
Boechler
,
N.
,
2017
, “
Acoustic Wave Propagation in Disordered Microscale Granular Media Under Compression
,”
Granular Matter
,
19
(
3
), p.
62
.10.1007/s10035-017-0744-3
351.
Zheng
,
L. Y.
,
Theocharis
,
G.
,
Tournat
,
V.
, and
Gusev
,
V.
,
2018
, “
Quasitopological Rotational Waves in Mechanical Granular Graphene
,”
Phys. Rev. B
,
97
(
6
), p.
060101
.10.1103/PhysRevB.97.060101
352.
Merkel
,
A.
,
Tournat
,
V.
, and
Gusev
,
V.
,
2014
, “
Directional Asymmetry of the Nonlinear Wave Phenomena in a Three-Dimensional Granular Phononic Crystal Under Gravity
,”
Phys. Rev. E
,
90
(
2
), p.
023206
.10.1103/PhysRevE.90.023206
353.
Pichard
,
H.
,
Duclos
,
A.
,
Groby
,
J. P.
,
Tournat
,
V.
,
Zheng
,
L.
, and
Gusev
,
V. E.
,
2016
, “
Surface Waves in Granular Phononic Crystals
,”
Phys. Rev. E
,
93
(
2
), p.
023008
.10.1103/PhysRevE.93.023008
354.
Wallen
,
S. P.
, and
Boechler
,
N.
,
2017
, “
Shear to Longitudinal Mode Conversion Via Second Harmonic Generation in a Two-Dimensional Microscale Granular Crystal
,”
Wave Motion
,
68
, pp.
22
30
.10.1016/j.wavemoti.2016.08.009
355.
Hiraiwa
,
M.
,
Ghanem
,
M. A.
,
Wallen
,
S. P.
,
Khanolkar
,
A.
,
Maznev
,
A. A.
, and
Boechler
,
N.
,
2016
, “
Complex Contact-Based Dynamics of Microsphere Monolayers Revealed by Resonant Attenuation of Surface Acoustic Waves
,”
Phys. Rev. Lett.
,
116
(
19
), p.
198001
.10.1103/PhysRevLett.116.198001
356.
Lazarov
,
B. S.
, and
Jensen
,
J. S.
,
2007
, “
Low-Frequency Band Gaps in Chains With Attached Non-Linear Oscillators
,”
Int. J. Non-Linear Mech.
,
42
(
10
), pp.
1186
1193
.10.1016/j.ijnonlinmec.2007.09.007
357.
Nadkarni
,
N.
,
Daraio
,
C.
, and
Kochmann
,
D. M.
,
2014
, “
Dynamics of Periodic Mechanical Structures Containing Bistable Elastic Elements: From Elastic to Solitary Wave Propagation
,”
Phys. Rev. E
,
90
(
2
), p.
023204
.10.1103/PhysRevE.90.023204
358.
Moleron
,
M.
,
Leonard
,
A.
, and
Daraio
,
C.
,
2014
, “
Solitary Waves in a Chain of Repelling Magnets
,”
J. Appl. Phys.
,
115
, p.
194901
.10.1063/1.4872252
359.
Narisetti
,
R. K.
,
Leamy
,
M. J.
, and
Ruzzene
,
M.
,
2010
, “
A Perturbation Approach for Predicting Wave Propagation in One-Dimensional Nonlinear Periodic Structures
,”
ASME J. Vib. Acoust.
,
132
(
3
), p.
031001
.10.1115/1.4000775
360.
Fronk
,
M. D.
, and
Leamy
,
M. J.
,
2017
, “Higher-Order Dispersion, Stability, and Waveform Invariance in Nonlinear Monoatomic and Diatomic Systems,”
ASME J. Vib. Acoust.
,
139
(
5
), p. 051003.10.1115/1.4036501
361.
Zaera
,
R.
,
Vila
,
J.
,
Fernandez-Saez
,
J.
, and
Ruzzene
,
M.
,
2018
, “Propagation of Solitons in a Two-Dimensional Nonlinear Square Lattice,”
Int. J. Non-Linear Mech.
,
106
, pp. 188–204.10.1016/j.ijnonlinmec.2018.08.002
362.
Silverberg
,
J. L.
,
Na
,
J. H.
,
Evans
,
A. A.
,
Liu
,
B.
,
Hull
,
T. C.
,
Santangelo
,
C. D.
,
Lang
,
R. J.
,
Hayward
,
R. C.
, and
Cohen
,
I.
,
2015
, “
Origami Structures With a Critical Transition to Bistability Arising From Hidden Degrees of Freedom
,”
Nat. Mater.
,
14
(
5
), p.
540
.10.1038/nmat4275
363.
Pratapa
,
P. P.
,
Liu
,
K.
, and
Paulino
,
G. H.
,
2019
, “
Geometric Mechanics of Origami Patterns Exhibiting Poisson's Ratio Switch by Breaking Mountain and Valley Assignment
,”
Phys. Rev. Lett.
,
122
(
15
), p.
155501
.10.1103/PhysRevLett.122.155501
364.
Fang
,
H. B.
,
Li
,
S. Y.
,
Ji
,
H. M.
, and
Wang
,
K. W.
,
2016
, “
Uncovering the Deformation Mechanisms of Origami Metamaterials by Introducing Generic Degree-Four Vertices
,”
Phys. Rev. E
,
94
(
4
), p.
043002
.10.1103/PhysRevE.94.043002
365.
Fang
,
H. B.
,
Li
,
S. Y.
, and
Wang
,
K. W.
,
2016
, “
Self-Locking Degree-4 Vertex Origami Structures
,”
Proc. R. Soc. A
,
472
(
2195
), p. 20160682.10.1098/rspa.2016.0682
366.
Fang
,
H. B.
,
Chu
,
S. C. A.
,
Xia
,
Y. T.
, and
Wang
,
K. W.
,
2018
, “
Programmable Self-Locking Origami Mechanical Metamaterials
,”
Adv. Mater.
,
30
(
15
), p.
1706311
.10.1002/adma.201706311
367.
Harne
,
R. L.
, and
Lynd
,
D. T.
,
2016
, “
Origami Acoustics: Using Principles of Folding Structural Acoustics for Simple and Large Focusing of Sound Energy
,”
Smart Mater. Struct.
,
25
(
8
), p.
085031
.10.1088/0964-1726/25/8/085031
368.
Lynd
,
D. T.
, and
Harne
,
R. L.
,
2017
, “
Strategies to Predict Radiated Sound Fields From Foldable, Miura-Ori-Based Transducers for Acoustic Beamfolding
,”
J. Acoust. Soc. Am.
,
141
(
1
), pp.
480
489
.10.1121/1.4974204
369.
Babaee
,
S.
,
Overvelde
,
J. T.
,
Chen
,
E. R.
,
Tournat
,
V.
, and
Bertoldi
,
K.
,
2016
, “
Reconfigurable Origami-Inspired Acoustic Waveguides
,”
Sci. Adv.
,
2
(
11
), p.
e1601019
.10.1126/sciadv.1601019
370.
Thota
,
M.
,
Li
,
S. Y.
, and
Wang
,
K. W.
,
2017
, “
Lattice Reconfiguration and Phononic Band-Gap Adaptation Via Origami Folding
,”
Phys. Rev. B
,
95
(
6
), p.
064307
.10.1103/PhysRevB.95.064307
371.
Thota
,
M.
, and
Wang
,
K. W.
,
2017
, “
Reconfigurable Origami Sonic Barriers With Tunable Bandgaps for Traffic Noise Mitigation
,”
J. Appl. Phys.
,
122
(
15
), p.
154901
.10.1063/1.4991026
372.
Yasuda
,
H.
, and
Yang
,
J.
,
2015
, “
Reentrant Origami-Based Metamaterials With Negative Poisson's Ratio and Bistability
,”
Phys. Rev. Lett.
,
114
(
18
), p.
185502
.10.1103/PhysRevLett.114.185502
373.
Yasuda
,
H.
,
Tachi
,
T.
,
Lee
,
M.
, and
Yang
,
J. K.
,
2017
, “
Origami-Based Tunable Truss Structures for Nonvolatile Mechanical Memory Operation
,”
Nat. Commun.
,
8
(
1
), p.
962
.10.1038/s41467-017-00670-w
374.
Yasuda
,
H.
,
Chen
,
Z. S.
, and
Yang
,
J. K.
,
2016
, “
Multitransformable Leaf-Out Origami With Bistable Behavior
,”
ASME J. Mech. Rob.
,
8
(
3
), p.
031013
.10.1115/1.4031809
375.
Yasuda
,
H.
,
Chong
,
C.
,
Charalampidis
,
E. G.
,
Kevrekidis
,
P. G.
, and
Yang
,
J.
,
2016
, “
Formation of Rarefaction Waves in Origami-Based Metamaterials
,”
Phys. Rev. E
,
93
(
4
), p.
043004
.10.1103/PhysRevE.93.043004
376.
Boatti
,
E.
,
Vasios
,
N.
, and
Bertoldi
,
K.
,
2017
, “
Origami Metamaterials for Tunable Thermal Expansion
,”
Adv. Mater.
,
29
(
26
), p.
1700360
.10.1002/adma.201700360
377.
Fang
,
H. B.
,
Wang
,
K. W.
, and
Li
,
S. Y.
,
2017
, “
Asymmetric Energy Barrier and Mechanical Diode Effect From Folding Multi-Stable Stacked-Origami
,”
Extreme Mech. Lett.
,
17
, pp.
7
15
.10.1016/j.eml.2017.09.008
378.
Li
,
S. Y.
, and
Wang
,
K. W.
,
2017
, “
Plant-Inspired Adaptive Structures and Materials for Morphing and Actuation: A Review
,”
Bioinspiration Biomimetics
,
12
(
1
), p.
011001
.10.1088/1748-3190/12/1/011001
379.
Faber
,
J. A.
,
Arrieta
,
A. F.
, and
Studart
,
A. R.
,
2018
, “
Bioinspired Spring Origami
,”
Science
,
359
(
6382
), pp.
1386
1391
.10.1126/science.aap7753
380.
Liu
,
B.
,
Silverberg
,
J. L.
,
Evans
,
A. A.
,
Santangelo
,
C. D.
,
Lang
,
R. J.
,
Hull
,
T. C.
, and
Cohen
,
T.
,
2018
, “
Topological Kinematics of Origami Metamaterials
,”
Nat. Phys.
,
14
(
8
), pp.
811
815
.10.1038/s41567-018-0150-8
381.
Haghpanah
,
B.
,
Ebrahimi
,
H.
,
Mousanezhad
,
D.
,
Hopkins
,
J.
, and
Vaziri
,
A.
,
2016
, “
Programmable Elastic Metamaterials
,”
Adv. Eng. Mater.
,
16
, p.
643
.10.1002/adem.201500295
382.
Wang
,
Z.
,
Zhang
,
Q.
,
Zhang
,
K.
, and
Hu
,
G.
,
2016
, “
Tunable Digital Metamaterial for Broadband Vibration Isolation at Low Frequency
,”
Adv. Mater.
,
28
(
44
), pp.
9857
9861
.10.1002/adma.201604009
383.
Liu
,
H.
,
Zhang
,
Q.
,
Zhang
,
K.
,
Hu
,
G.
, and
Duan
,
H.
,
2019
, “
Designing 3d Digital Metamaterial for Elastic Waves: From Elastic Wave Polarizer to Vibration Control
,”
Adv. Sci.
,
6
(
16
), p.
1900401
.10.1002/advs.201900401