Abstract

Controlling and manipulating elastic/acoustic waves via artificially structured metamaterials, phononic crystals, and metasurfaces have gained an increasing research interest in the last decades. Unlike others, a metasurface is a single layer in the host medium with an array of subwavelength-scaled patterns introducing an abrupt phase shift in the wave propagation path. In this study, an elastic metasurface composed of an array of slender beam resonators is proposed to control the elastic wavefront of low-frequency flexural waves. The phase gradient based on Snell’s law is achieved by tailoring the thickness of thin beam resonators connecting two elastic host media. Through analytical and numerical models, the phase-modulated metasurfaces are designed and verified to accomplish three dynamic wave functions, namely, deflection, non-paraxial propagation, and focusing. An oblique incident wave is also demonstrated to show the versatility of the proposed design for focusing of wave energy incident from multiple directions. Experimentally measured focusing metasurface has nearly three times wave amplification at the designed focal point which validates the design and theoretical models. Furthermore, the focusing metasurface is exploited for low-frequency energy harvesting and the piezoelectric harvester is improved by almost nine times in terms of the harvested power output as compared to the baseline harvester on the pure plate without metasurface.

References

References
1.
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
2.
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
3.
Ma
,
G.
, and
Sheng
,
P.
,
2016
, “
Acoustic Metamaterials: From Local Resonances to Broad Horizons
,”
Sci. Adv.
,
2
(
2
), p.
e1501595
. 10.1126/sciadv.1501595
4.
Jin
,
Y.
,
Djafari-Rouhani
,
B.
, and
Torrent
,
D.
,
2019
, “
Gradient Index Phononic Crystals and Metamaterials
,”
Nanophotonics
,
8
(
5
), pp.
685
701
. 10.1515/nanoph-2018-0227
5.
Deymier
,
P. A.
,
2013
,
Acoustic Metamaterials and Phononic Crystals
,
Springer-Verlag
,
Berlin
.
6.
Laude
,
V.
,
2015
,
Phononic Crystals: Artificial Crystals for Sonic, Acoustic, and Elastic Waves
,
Walter de Gruyter GmbH and Co KG.
,
Berlin
.
7.
Page
,
J. H.
,
Sheng
,
P.
,
Schriemer
,
H. P.
,
Jones
,
I.
,
Jing
,
X.
, and
Weitz
,
D. A.
,
1996
, “
Group Velocity in Strongly Scattering Media
,”
Science
,
271
(
5249
), pp.
634
637
. 10.1126/science.271.5249.634
8.
Matlack
,
K. H.
,
Bauhofer
,
A.
,
Krödel
,
S.
,
Palermo
,
A.
, and
Daraio
,
C.
,
2016
, “
Composite 3D-Printed Metastructures for Low-Frequency and Broadband Vibration Absorption
,”
Proc. Natl. Acad. Sci. U.S.A.
,
113
(
30
), pp.
8386
8390
. 10.1073/pnas.1600171113
9.
Li
,
Y.
,
Baker
,
E.
,
Reissman
,
T.
,
Sun
,
C.
, and
Liu
,
W. K.
,
2017
, “
Design of Mechanical Metamaterials for Simultaneous Vibration Isolation and Energy Harvesting
,”
Appl. Phys. Lett.
,
111
(
25
), p.
251903
. 10.1063/1.5008674
10.
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
11.
Craster
,
R. V.
, and
Guenneau
,
S.
,
2012
,
Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking
,
Springer
,
London
.
12.
Lee
,
M. K.
, and
Kim
,
Y. Y.
,
2016
, “
Add-On Unidirectional Elastic Metamaterial Plate Cloak
,”
Sci. Rep.
,
6
(
1
), pp.
1
10
.
13.
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
14.
Lee
,
H. J.
,
Lee
,
J. K.
, and
Kim
,
Y. Y.
,
2015
, “
Elastic Metamaterial-Based Impedance-Varying Phononic Bandgap Structures for Bandpass Filters
,”
J. Sound Vib.
,
353
, pp.
58
74
. 10.1016/j.jsv.2015.05.012
15.
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
16.
Climente
,
A.
,
Torrent
,
D.
, and
Sánchez-Dehesa
,
J.
,
2010
, “
Sound Focusing by Gradient Index Sonic Lenses
,”
Appl. Phys. Lett.
,
97
(
10
), p.
104103
. 10.1063/1.3488349
17.
Jin
,
Y.
,
Torrent
,
D.
,
Pennec
,
Y.
,
Pan
,
Y.
, and
Djafari-Rouhani
,
B.
,
2016
, “
Gradient Index Devices for the Full Control of Elastic Waves in Plates
,”
Sci. Rep.
,
6
(
1
), p.
24437
. 10.1038/srep24437
18.
Tol
,
S.
,
Degertekin
,
F. L.
, and
Erturk
,
A.
,
2017
, “
Phononic Crystal Luneburg Lens for Omnidirectional Elastic Wave Focusing and Energy Harvesting
,”
Appl. Phys. Lett.
,
111
(
1
), p.
013503
. 10.1063/1.4991684
19.
Tol
,
S.
,
Degertekin
,
F. L.
, and
Erturk
,
A.
,
2019
, “
3D-Printed Phononic Crystal Lens for Elastic Wave Focusing and Energy Harvesting
,”
Addit. Manuf.
,
29
, p.
100780
.
20.
Zhu
,
Y.
,
Cao
,
L.
,
Merkel
,
A.
,
Fan
,
S. W.
, and
Assouar
,
B.
,
2020
, “
Bifunctional Superlens for Simultaneous Flexural and Acoustic Wave Superfocusing
,”
Appl. Phys. Lett.
,
116
(
25
), p.
253502
. 10.1063/5.0004428
21.
Chen
,
Z.
,
Guo
,
B.
,
Yang
,
Y.
, and
Cheng
,
C.
,
2014
, “
Metamaterials-Based Enhanced Energy Harvesting: A Review
,”
Phys. B
,
438
, pp.
1
8
. 10.1016/j.physb.2013.12.040
22.
Danawe
,
H.
,
Okudan
,
G.
,
Ozevin
,
D.
, and
Tol
,
S.
,
2020
, “
Conformal Gradient-Index Phononic Crystal Lens for Ultrasonic Wave Focusing in Pipe-Like Structures
,”
Appl. Phys. Lett.
,
117
(
2
), p.
021906
. 10.1063/5.0012316
23.
Sukhovich
,
A.
,
Merheb
,
B.
,
Muralidharan
,
K.
,
Vasseur
,
J. O.
,
Pennec
,
Y.
,
Deymier
,
P. A.
, and
Page
,
J. H.
,
2009
, “
Experimental and Theoretical Evidence for Subwavelength Imaging in Phononic Crystals
,”
Phys. Rev. Lett.
,
102
(
15
), p.
154301
. 10.1103/PhysRevLett.102.154301
24.
Zhu
,
J.
,
Christensen
,
J.
,
Jung
,
J.
,
Martin-Moreno
,
L.
,
Yin
,
X.
,
Fok
,
L.
,
Zhang
,
X.
, and
Garcia-Vidal
,
F. J.
,
2010
, “
A Holey-Structured Metamaterial for Acoustic Deep-Subwavelength Imaging
,”
Nat. Phys.
,
7
(
1
), pp.
52
55
. 10.1038/nphys1804
25.
Gonella
,
S.
,
To
,
A. C.
, and
Liu
,
W. K.
,
2009
, “
Interplay Between Phononic Bandgaps and Piezoelectric Microstructures for Energy Harvesting
,”
J. Mech. Phys. Solids
,
57
(
3
), pp.
621
633
. 10.1016/j.jmps.2008.11.002
26.
Chen
,
T.
,
Li
,
S.
, and
Sun
,
H.
,
2012
, “
Metamaterials Application in Sensing
,”
Sensors
,
12
(
3
), pp.
2742
2765
. 10.3390/s120302742
27.
Tol
,
S.
,
Degertekin
,
F. L.
, and
Erturk
,
A.
,
2016
, “
Gradient-Index Phononic Crystal Lens-Based Enhancement of Elastic Wave Energy Harvesting
,”
Appl. Phys. Lett.
,
109
(
6
), p.
063902
. 10.1063/1.4960792
28.
Chen
,
Z.
,
Yang
,
Y.
,
Lu
,
Z.
, and
Luo
,
Y.
,
2013
, “
Broadband Characteristics of Vibration Energy Harvesting Using One-Dimensional Phononic Piezoelectric Cantilever Beams
,”
Phys. B
,
410
, pp.
5
12
. 10.1016/j.physb.2012.10.029
29.
Sugino
,
C.
, and
Erturk
,
A.
,
2018
, “
Analysis of Multifunctional Piezoelectric Metastructures for Low-Frequency Bandgap Formation and Energy Harvesting
,”
J. Phys. D: Appl. Phys.
,
51
(
21
), p.
215103
. 10.1088/1361-6463/aab97e
30.
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
31.
Assouar
,
B.
,
Liang
,
B.
,
Wu
,
Y.
,
Li
,
Y.
,
Cheng
,
J. C.
, and
Jing
,
Y.
,
2018
, “
Acoustic Metasurfaces
,”
Nat. Rev. Mater.
,
3
(
12
), pp.
460
472
. 10.1038/s41578-018-0061-4
32.
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
), pp.
1
5
.
33.
Li
,
Y.
,
Jiang
,
X.
,
Liang
,
B.
,
Cheng
,
J.-C.
, and
Zhang
,
L.
,
2015
, “
Metascreen-Based Acoustic Passive Phased Array
,”
Phys. Rev. Appl.
,
4
(
2
), p.
024003
. 10.1103/PhysRevApplied.4.024003
34.
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
35.
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
36.
Su
,
X.
, and
Norris
,
A. N.
,
2016
, “
Focusing, Refraction, and Asymmetric Transmission of Elastic Waves in Solid Metamaterials With Aligned Parallel Gaps
,”
J. Acoust. Soc. Am.
,
139
(
6
), pp.
3386
3394
. 10.1121/1.4950770
37.
Shen
,
X.
,
Sun
,
C. T.
,
Barnhart
,
M. V.
, and
Huang
,
G.
,
2018
, “
Elastic Wave Manipulation by Using a Phase-Controlling Meta-Layer
,”
J. Appl. Phys.
,
123
(
9
), p.
091708
. 10.1063/1.4996018
38.
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
39.
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
40.
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
41.
Cao
,
L.
,
Yang
,
Z.
,
Xu
,
Y.
, and
Assouar
,
B.
,
2018
, “
Deflecting Flexural Wave With High Transmission by Using Pillared Elastic Metasurface
,”
Smart Mater. Struct.
,
27
(
7
), p.
075051
. 10.1088/1361-665X/aaca51
42.
Cao
,
L.
,
Yang
,
Z.
,
Xu
,
Y.
,
Fan
,
S. W.
,
Zhu
,
Y.
,
Chen
,
Z.
,
Vincent
,
B.
, and
Assouar
,
B.
,
2020
, “
Disordered Elastic Metasurfaces
,”
Phys. Rev. Appl.
,
13
(
1
), p.
014054
. 10.1103/PhysRevApplied.13.014054
43.
Cao
,
L.
,
Yang
,
Z.
,
Xu
,
Y.
,
Chen
,
Z.
,
Zhu
,
Y.
,
Fan
,
S. W.
,
Donda
,
K.
,
Vincent
,
B.
, and
Assouar
,
B.
,
2021
, “
Pillared Elastic Metasurface With Constructive Interference for Flexural Wave Manipulation
,”
Mech. Syst. Sig. Process.
,
146
, p.
107035
. 10.1016/j.ymssp.2020.107035
44.
Lin
,
Z.
, and
Tol
,
S.
,
2020
, “
Elastic Metasurfaces for Low-Frequency Flexural Wavefront Control
,”
International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Virtual
,
Aug. 17–19
.
45.
Froehly
,
L.
,
Courvoisier
,
F.
,
Mathis
,
A.
,
Jacquot
,
M.
,
Furfaro
,
L.
,
Giust
,
R.
,
Lacourt
,
P. A.
, and
Dudley
,
J. M.
,
2011
, “
Arbitrary Accelerating Micron-Scale Caustic Beams in Two and Three Dimensions
,”
Opt. Exp.
,
19
(
17
), pp.
16455
16465
. 10.1364/OE.19.016455
46.
Zhang
,
P.
,
Li
,
T.
,
Zhu
,
J.
,
Zhu
,
X.
,
Yang
,
S.
,
Wang
,
Y.
,
Yin
,
X.
, and
Zhang
,
X.
,
2014
, “
Generation of Acoustic Self-Bending and Bottle Beams by Phase Engineering
,”
Nat. Commun.
,
5
(
1
), pp.
1
9
.
47.
Graff
,
K. F.
,
1991
, “Waves in Membranes, Thin Plates, and Shells,”
Wave Motion in Elastic Solids
,
Dover Publications, Inc.
,
New York
, pp.
213
272
.
You do not currently have access to this content.