In this Letter, we provide an experimental demonstration of amplitude-dependent dispersion tuning of surface acoustic waves interacting with nonlinear resonators. Leveraging the similarity between the dispersion properties of plate edge waves and surface waves propagating in a semi-infinite medium, we use a setup consisting of a plate with a periodic arrangement of bead-magnet resonators along one of its edges. Nonlinear contact between the ferromagnetic beads and magnets is exploited to realize nonlinear local resonance effects. First, we experimentally demonstrate the nonlinear softening nature and amplitude-dependent dynamics of a single bead-magnet resonator on both rigid and compliant substrates. Next, the dispersion properties of the system in the linear regime are investigated. Finally, we demonstrate how the interplay of nonlinear local resonances with plate edge waves gives rise to amplitude-dependent dispersion properties. The findings will inform the design of more versatile surface acoustic wave devices that can passively adapt to loading conditions.
REFERENCES
1.
S.
Benchabane
and
A.
Reinhardt
, “
Elastic metamaterials for radiofrequency applications
,” in Fundamentals and Applications of Acoustic Metamaterials
(
Wiley
, 2019
), pp. 207
–262
.2.
K.
Länge
,
B. E.
Rapp
, and
M.
Rapp
, “
Surface acoustic wave biosensors: A review
,” Anal. Bioanal. Chem.
391
, 1509
–1519
(2008
).3.
S.
Brûlé
,
E. H.
Javelaud
,
S.
Enoch
, and
S.
Guenneau
, “
Experiments on seismic metamaterials: Molding surface waves
,” Phys. Rev. Lett.
112
, 133901
(2014
).4.
Muhammad
,
C. W.
Lim
, and
J. N.
Reddy
, “
Built-up structural steel sections as seismic metamaterials for surface wave attenuation with low frequency wide bandgap in layered soil medium
,” Eng. Struct.
188
, 440
–451
(2019
).5.
T. T.
Wu
,
J. C.
Hsu
,
J. H.
Sun
, and
S.
Benchabane
, “
Surface acoustic waves in phononic crystals
,” in Phononic Crystals: Fundamentals and Applications
(
Springer
,
New York
, 2015
), pp. 145
–189
.6.
A.
Khelif
,
Y.
Achaoui
,
S.
Benchabane
,
V.
Laude
, and
B.
Aoubiza
, “
Locally resonant surface acoustic wave band gaps in a two-dimensional phononic crystal of pillars on a surface
,” Phys. Rev. B
81
, 214303
(2010
).7.
M.
Addouche
,
M. A.
Al-Lethawe
,
A.
Choujaa
, and
A.
Khelif
, “
Superlensing effect for surface acoustic waves in a pillar-based phononic crystal with negative refractive index
,” Appl. Phys. Lett.
105
, 023501
(2014
).8.
R.
Fuentes-Domínguez
,
M.
Yao
,
A.
Colombi
,
P.
Dryburgh
,
D.
Pieris
,
A.
Jackson-Crisp
,
D.
Colquitt
,
A.
Clare
,
R. J.
Smith
, and
M.
Clark
, “
Design of a resonant Luneburg lens for surface acoustic waves
,” Ultrasonics
111
, 106306
(2021
).9.
N.
Cselyuszka
,
M.
Sečujski
,
N.
Engheta
, and
V.
Crnojević-Bengin
, “
Temperature-controlled acoustic surface waves
,” New J. Phys.
18
, 103006
(2016
).10.
A.
Palermo
,
Y.
Wang
,
P.
Celli
, and
C.
Daraio
, “
Tuning of surface-acoustic-wave dispersion via magnetically modulated contact resonances
,” Phys. Rev. Appl.
11
, 044057
(2019
).11.
A.
Palermo
,
P.
Celli
,
B.
Yousefzadeh
,
C.
Daraio
, and
A.
Marzani
, “
Surface wave non-reciprocity via time-modulated metamaterials
,” J. Mech. Phys. Solids
145
, 104181
(2020
).12.
Q.
Wu
,
H.
Chen
,
H.
Nassar
, and
G.
Huang
, “
Non-reciprocal Rayleigh wave propagation in space–time modulated surface
,” J. Mech. Phys. Solids
146
, 104196
(2021
).13.
R. K.
Narisetti
,
M. J.
Leamy
, and
M.
Ruzzene
, “
A perturbation approach for predicting wave propagation in one-dimensional nonlinear periodic structures
,” J. Vib. Acoust.
132
, 031001
(2010
).14.
W.
Jiao
and
S.
Gonella
, “
Doubly nonlinear waveguides with self-switching functionality selection capabilities
,” Phys. Rev. E
99
, 042206
(2019
).15.
A.
Mojahed
,
J.
Bunyan
,
S.
Tawfick
, and
A. F.
Vakakis
, “
Tunable acoustic nonreciprocity in strongly nonlinear waveguides with asymmetry
,” Phys. Rev. Appl.
12
, 034033
(2019
).16.
K. J.
Moore
,
J.
Bunyan
,
S.
Tawfick
,
O. V.
Gendelman
,
S.
Li
,
M.
Leamy
, and
A. F.
Vakakis
, “
Nonreciprocity in the dynamics of coupled oscillators with nonlinearity, asymmetry, and scale hierarchy
,” Phys. Rev. E
97
, 012219
(2018
).17.
M. D.
Fronk
,
S.
Tawfick
,
C.
Daraio
,
S.
Li
,
A.
Vakakis
, and
M. J.
Leamy
, “
Acoustic non-reciprocity in lattices with nonlinearity, internal hierarchy, and asymmetry: Computational study
,” J. Vib. Acoust.
141
, 051011
(2019
).18.
W.
Jiao
and
S.
Gonella
, “
Intermodal and subwavelength energy trapping in nonlinear metamaterial waveguides
,” Phys. Rev. Appl.
10
, 024006
(2018
).19.
V.
Zega
,
P. B.
Silva
,
M. G.
Geers
, and
V. G.
Kouznetsova
, “
Experimental proof of emergent subharmonic attenuation zones in a nonlinear locally resonant metamaterial
,” Sci. Rep.
10
, 12041
(2020
).20.
R. K.
Narisetti
,
M.
Ruzzene
, and
M. J.
Leamy
, “
Study of wave propagation in strongly nonlinear periodic lattices using a harmonic balance approach
,” Wave Motion
49
, 394
–410
(2012
).21.
K.
Manktelow
,
R. K.
Narisetti
,
M. J.
Leamy
, and
M.
Ruzzene
, “
Finite-element based perturbation analysis of wave propagation in nonlinear periodic structures
,” Mech. Syst. Signal Process.
39
, 32
–46
(2013
).22.
R.
Khajehtourian
and
M. I.
Hussein
, “
Dispersion characteristics of a nonlinear elastic metamaterial
,” AIP Adv.
4
, 124308
(2014
).23.
B. S.
Lazarov
and
J. S.
Jensen
, “
Low-frequency band gaps in chains with attached non-linear oscillators
,” Int. J. Non-Linear Mech.
42
, 1186
–1193
(2007
).24.
K. L.
Manktelow
,
M.
Ruzzene
, and
M. J.
Leamy
, “
Wave propagation in nonlinear lattice materials
,” in Dynamics of Lattice Materials
(
John Wiley & Sons, Ltd
,
Chichester, UK
, 2017
), pp. 107
–137
.25.
X.
Fang
,
J.
Wen
,
D.
Yu
,
G.
Huang
, and
J.
Yin
, “
Wave propagation in a nonlinear acoustic metamaterial beam considering third harmonic generation
,” New J. Phys.
20
, 123028
(2018
).26.
N.
Boechler
,
J. K.
Eliason
,
A.
Kumar
,
A. A.
Maznev
,
K. A.
Nelson
, and
N.
Fang
, “
Interaction of a contact resonance of microspheres with surface acoustic waves
,” Phys. Rev. Lett.
111
, 036103
(2013
).27.
S. P.
Wallen
,
J.
Lee
,
D.
Mei
,
C.
Chong
,
P. G.
Kevrekidis
, and
N.
Boechler
, “
Discrete breathers in a mass-in-mass chain with Hertzian local resonators
,” Phys. Rev. E
95
, 022904
(2017
).28.
A. H.
Nayfeh
and
D. T.
Mook
, Nonlinear Oscillations
(
Wiley
, 1995
).29.
E.
Rigaud
and
J.
Perret-Liaudet
, “
Experiments and numerical results on non-linear vibrations of an impacting Hertzian contact. Part 1: Harmonic excitation
,” J. Sound Vib.
265
, 289
–307
(2003
).30.
J.
Perret-Liaudet
and
E.
Rigaud
, “
Experiments and numerical results on non-linear vibrations of an impacting Hertzian contact. Part 2: Random excitation
,” J. Sound Vib.
265
, 309
–327
(2003
).31.
A.
Merkel
,
G.
Theocharis
,
F.
Allein
,
J. P.
Groby
,
V.
Gusev
, and
V.
Tournat
, “
Testing a bead-rod contact with a nonlinear resonance method
,” J. Sound Vib.
441
, 84
–95
(2019
).32.
K. L.
Manktelow
,
M. J.
Leamy
, and
M.
Ruzzene
, “
Analysis and experimental estimation of nonlinear dispersion in a periodic string
,” J. Vib. Acoust.
136
, 031016
(2014
).33.
A.
Palermo
,
B.
Yousefzadeh
,
C.
Daraio
, and
A.
Marzani
, “
Rayleigh wave propagation in nonlinear metasurfaces
,” J. Sound Vib.
520
, 116599
(2022
).34.
35.
M. V.
Wilde
,
M. V.
Golub
, and
A. A.
Eremin
, “
Experimental and theoretical investigation of transient edge waves excited by a piezoelectric transducer bonded to the edge of a thick elastic plate
,” J. Sound Vib.
441
, 26
–49
(2019
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.