We report the design and characterization of a self-assembled, locally resonant acoustic metamaterial for Lamb waves, composed of a monolayer of 1.02 μm polystyrene microspheres adhered to a 1.27 μm thick free-standing silicon membrane. A laser-induced transient grating technique is used to generate Lamb waves in the metamaterial and to measure its acoustic response. The measurements reveal a microsphere contact resonance and the lowest frequency spheroidal microsphere resonance. The measured dispersion curves show hybridization of flexural Lamb waves with the microsphere contact resonance. We compare the measured dispersion with an analytical model using the contact resonance frequency as a single fitting parameter, and find that it well describes the observed hybridization. This study may lead to an improved understanding of microscale contact mechanics and to the design of new types of acoustic metamaterials.

1.
M. I.
Hussein
,
M. J.
Leamy
, and
M.
Ruzzene
,
Appl. Mech. Rev.
66
,
40802
(
2014
).
2.
F.
Lemoult
,
N.
Kaina
,
M.
Fink
, and
G.
Lerosey
,
Nat. Phys.
9
,
55
(
2012
).
3.
Y.
Lai
,
Y.
Wu
,
P.
Sheng
, and
Z. Q.
Zhang
,
Nat. Mater.
10
,
620
(
2011
).
4.
Z. Y.
Liu
,
X. X.
Zhang
,
Y. W.
Mao
,
Y. Y.
Zhu
,
Z. Y.
Yang
,
C. T.
Chan
, and
P.
Sheng
,
Science
289
,
1734
(
2000
);
[PubMed]
N.
Fang
,
D. J.
Xi
,
J. Y.
Xu
,
M.
Ambati
,
W.
Srituravanich
,
C.
Sun
, and
X.
Zhang
,
Nat. Mater.
5
,
452
(
2006
);
[PubMed]
S.
Zhang
,
L. L.
Yin
, and
N.
Fang
,
Phys. Rev. Lett.
102
,
194301
(
2009
).
[PubMed]
5.
J.
Mei
,
G.
Ma
,
M.
Yang
,
Z.
Yang
,
W.
Wen
, and
P.
Sheng
,
Nat. Commun.
3
,
756
(
2012
).
6.
S.
Zhang
,
C. G.
Xia
, and
N.
Fang
,
Phys. Rev. Lett.
106
,
024301
(
2011
).
7.
Related phenomena are also observed when the metamaterial unit cell is of suprawavelength dimension.8 
8.
M.
Rupin
,
F.
Lemoult
,
G.
Lerosey
, and
P.
Roux
,
Phys. Rev. Lett.
112
,
234301
(
2014
).
9.
T.
Kraus
,
D.
Brodoceanu
,
N.
Pazos-Perez
, and
A.
Fery
,
Adv. Funct. Mater.
23
,
4529
(
2013
);
O. D.
Velev
and
S.
Gupta
,
Adv. Mater.
21
,
1897
(
2009
);
F.
Li
,
D. P.
Josephson
, and
A.
Stein
,
Angew. Chem. Int. Ed.
50
,
360
(
2011
);
N.
Vogel
,
M.
Retsch
,
C. A.
Fustin
,
A.
del Campo
, and
U.
Jonas
,
Chem. Rev.
115
,
6265
(
2015
).
[PubMed]
10.
W.
Cheng
,
J. J.
Wang
,
U.
Jonas
,
G.
Fytas
, and
N.
Stefanou
,
Nat. Mater.
5
,
830
(
2006
).
11.
J. H.
Lee
,
C. Y.
Koh
,
J. P.
Singer
,
S. J.
Jeon
,
M.
Maldovan
,
O.
Stein
, and
E. L.
Thomas
,
Adv. Mater.
26
,
532
(
2014
).
12.
J. F.
Galisteo-López
,
M.
Ibisate
,
R.
Sapienza
,
L. S.
Froufe-Pérez
,
Á.
Blanco
, and
C.
López
,
Adv. Mater.
23
,
30
(
2011
);
[PubMed]
G.
von Freymann
,
V.
Kitaev
,
B. V.
Lotsch
, and
G. A.
Ozin
,
Chem. Soc. Rev.
42
,
2528
(
2013
).
[PubMed]
13.
B.
Sepúlveda
,
P. C.
Angelome
,
L. M.
Lechuga
, and
L. M.
Liz-Marzán
,
Nano Today
4
,
244
(
2009
);
M.
Grzelczak
,
J.
Vermant
,
E. M.
Furst
, and
L. M.
Liz-Marzan
,
ACS Nano
4
,
3591
(
2010
);
[PubMed]
A.
Klinkova
,
R. M.
Choueiri
, and
E.
Kumacheva
,
Chem. Soc. Rev.
43
,
3976
(
2014
).
[PubMed]
14.
W. L.
Min
,
B.
Jiang
, and
P.
Jiang
,
Adv. Mater.
20
,
3914
(
2008
).
15.
T.
Still
,
W.
Cheng
,
M.
Retsch
,
R.
Sainidou
,
J.
Wang
,
U.
Jonas
,
N.
Stefanou
, and
G.
Fytas
,
Phys. Rev. Lett.
100
,
194301
(
2008
);
[PubMed]
M.
Caleap
and
B.
Drinkwater
,
Proc. Natl. Acad. Sci. U. S. A.
111
,
6226
(
2014
);
[PubMed]
T.
Brunet
,
A.
Merlin
,
B.
Mascaro
,
K.
Zimny
,
J.
Leng
,
O.
Poncelet
,
C.
Aristégui
, and
O.
Mondain-Monval
,
Nat. Mater.
14
,
384
(
2014
);
[PubMed]
P. J.
Beltramo
,
D.
Schneider
,
G.
Fytas
, and
E. M.
Furst
,
Phys. Rev. Lett.
113
,
205503
(
2014
).
[PubMed]
16.
N.
Boechler
,
J.
Eliason
,
A.
Kumar
,
A. A.
Maznev
,
K. A.
Nelson
, and
N.
Fang
,
Phys. Rev. Lett.
111
,
036103
(
2013
).
17.
H.
Lamb
,
Proc. R. Soc. London, Ser. A
93
,
114
(
1917
).
18.
T. T.
Wu
,
J. C.
Hsu
, and
J. H.
Sun
,
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
58
,
2146
(
2011
).
19.
V.
Yantchev
and
I.
Katardjiev
,
J. Micromech. Microeng.
23
,
043001
(
2013
).
20.
J.
Cuffe
,
O.
Ristow
,
E.
Chávez
,
A.
Shchepetov
,
P. O.
Chapuis
,
F.
Alzina
,
M.
Hettich
,
M.
Prunilla
,
J.
Ahopelto
,
T.
Dekorsy
, and
C. M.
Sotomayor Torres
,
Phys. Rev. Lett.
110
,
095503
(
2013
).
21.
Y.
Pennec
,
B.
Djafari-Rouhani
,
H.
Larabi
,
J. O.
Vasseur
, and
A. C.
Hladky-Hennion
,
Phys. Rev. B
78
,
104105
(
2008
);
B. L.
Davis
and
M. I.
Hussein
,
Phys. Rev. Lett.
112
,
055505
(
2014
);
[PubMed]
V. E.
Gusev
and
O. B.
Wright
,
New J. Phys.
16
,
123053
(
2014
).
22.
T. C.
Wu
,
T. T.
Wu
, and
J. C.
Hsu
,
Phys. Rev. B
79
,
104306
(
2009
);
M.
Oudich
,
M.
Senesi
,
M.
Badreddine Assouar
,
M.
Ruzenne
,
J. H.
Sun
,
B.
Vincent
,
Z.
Hou
, and
T. T.
Wu
,
Phys. Rev. B
84
,
165136
(
2011
);
R.
Zhu
,
X. N.
Liu
,
G. K.
Hu
,
C. T.
Sun
, and
G. L.
Huang
,
Nat. Commun.
5
,
5510
(
2014
);
[PubMed]
B.
Bonello
,
R.
Marchal
,
R.
Moiseyenko
,
Y.
Pennec
,
B.
Djafari-Rouhani
,
J.
Zhao
, and
O.
Boyko
, in
Proceedings of ASME 2014 International Mechanical Engineering Congress and Exposition, Montreal, Quebec, Canada
(
2014
), p.
V013T16A019
.
23.
H.
Hertz
,
J. Reine Angew. Math.
92
,
156
(
1882
).
24.
V. F.
Nesterenko
,
Dynamics of Heterogeneous Materials
(
Springer-Verlag
,
New York
,
2001
).
25.
G.
Theocharis
,
N.
Boechler
, and
C.
Daraio
, “
Nonlinear periodic phononic structures and granular crystals
,” in
Acoustic Metamaterials and Phononic Crystals
(
Springer
,
Berlin, Heidelberg
,
2013
), pp.
217
251
.
26.
J. A.
Rogers
,
A. A.
Maznev
,
M.
Banet
, and
K. A.
Nelson
,
Annu. Rev. Mater. Sci.
30
,
117
(
2000
).
27.
J. A.
Johnson
,
A. A.
Maznev
,
M. T.
Bulsara
,
E. A.
Fitzgerald
,
T. C.
Harman
,
S.
Calawa
,
C. J.
Vineis
,
G.
Turner
, and
K. A.
Nelson
,
J. Appl. Phys.
111
,
023503
(
2012
).
28.
N.
Vogel
,
S.
Goerres
,
K.
Landfester
, and
C. K.
Weiss
,
Macro. Chem. Phys.
212
,
1719
(
2011
).
29.
J. A.
Rogers
and
K. A.
Nelson
,
J. Appl. Phys.
75
,
1534
(
1994
).
30.
See supplementary material at http://dx.doi.org/10.1063/1.4928564 for additional modeling details and experimental data.
31.
H. J.
McSkimin
and
P.
Andreatch
, Jr.
,
J. Appl. Phys.
35
,
2161
(
1964
).
32.
W. M.
Ewing
,
W. S.
Jardetzky
, and
F.
Press
,
Elastic Waves in Layered Media
(
McGraw-Hill Book Company, Inc.
,
New York
,
1957
).
33.
L. P.
Solie
and
B. A.
Auld
,
J. Acoust. Soc. Am.
54
,
50
(
1973
).
34.
J. P.
Jones
,
J. Appl. Mech.
31
,
213
(
1964
).
35.
J.
von Neumann
and
E.
Wigner
,
Phys. Z.
30
,
467
(
1929
).
36.
Y.
Sato
and
T.
Usami
,
Geophys. Mag.
31
,
15
(
1962
).
37.
Y.
Guillet
,
B.
Audoin
,
M.
Ferrie
, and
S.
Ravaine
,
Phys. Rev. B
86
,
035456
(
2012
).
38.
S.
Biggs
and
G.
Spinks
,
J. Adhes. Sci. Technol.
12
,
461
(
1998
).
39.
K. L.
Mittal
and
R.
Jaiswal
,
Particle Adhesion and Removal
(
Scrivener Publishing LLC
,
Beverly, MA
,
2015
).
40.
T.
Dehoux
,
T. A.
Kelf
,
M.
Tomoda
,
O.
Matsuda
,
O. B.
Wright
,
K.
Ueno
,
Y.
Nishijima
,
S.
Juodkazis
,
H.
Misawa
,
V.
Tournat
, and
V. E.
Gusev
,
Opt. Lett.
34
,
3740
(
2009
).
41.
V. M.
Muller
,
B. V.
Derjaguin
, and
Y. P.
Toporov
,
Colloids Surf.
7
,
251
(
1983
);
42.
J.
Israelachvili
,
Intermolecular and Surface Forces
(
Elsevier, Inc.
,
Burlington, MA
,
2011
).
43.
H.
Zhou
,
M.
Götzinger
, and
W.
Peukert
,
Powder Technol.
135
,
82
(
2003
);
M. D. M.
Peri
and
C.
Centinkaya
,
J. Colloid Interface Sci.
288
,
432
(
2005
);
[PubMed]
R.
Tykhoniuk
,
J.
Tomas
,
S.
Ludig
,
M.
Kappl
,
L.
Heim
, and
H. J.
Butt
,
Chem. Eng. Sci.
62
,
2843
(
2007
).
44.
J. N. D.
Amour
,
J. J. R.
Stalgren
,
K. K.
Kanazawa
,
C. W.
Frank
,
M.
Rodahl
, and
D.
Johannsmann
,
Phys. Rev. Lett.
96
,
058301
(
2006
).
45.

Supplementary Material

You do not currently have access to this content.