A class of active nonreciprocal metamaterial (ANMM) is presented which consists of an acoustic duct with periodically placed active diaphragms that are controlled by a spatiotemporal modulation strategy. The acoustic nonreciprocities can be realized by modulating a system's properties spatiotemporally. Such an approach has been extensively employed by many investigators to break the reciprocity in acoustic and elastic metamaterials. However, our proposed ANMM distinguishes itself from the above-mentioned methods by introducing actively tunable space-time modulated feedback gain of the controllers. The controller is implemented in an analog manner to enable fast response at high modulation frequencies. By discretizing a 1D acoustic duct into multiple acoustic unit cavities, we introduced a time-varying gain with a phase difference between adjacent acoustic cavities. Directional band gaps of the modulated system are numerically analyzed as the asymmetric acoustic wave propagation can be realized by converting the acoustical energy from the fundamental mode to higher order modes. In addition, nonreciprocal behavior of the proposed ANMM was experimentally demonstrated using a waveguide with periodically placed condenser microphones (sensors) and speakers (actuators).
References
1.
C.
Liu
, Z. L.
Du
, Z.
Sun
, H. J.
Gao
, and X.
Guo
, “Frequency-preserved acoustic diode model with high forward power-transmission rate
,” Phys. Rev. Appl.
3
, 064014
(2015
).2.
B.
Liang
, B.
Yuan
, and J. C.
Cheng
, “Acoustic diode: Rectification of acoustic energy flux in one-dimensional systems
,” Phys. Rev. Lett.
103
, 104301
(2009
).3.
B.-I.
Popa
and S. A.
Cummer
, “Nonreciprocal and highly nonlinear active acoustic metamaterials
,” Nat. Commun.
5
, 3398
(2014
).4.
Z.-M.
Gu
, J.
Hu
, B.
Liang
, X.-Y.
Zou
, and J.-C.
Cheng
, “Broadband nonreciprocal transmission of sound with invariant frequency
,” Sci. Rep.
6
, 19824
(2016
).5.
A.
Merkel
, M.
Willatzen
, and J.
Christensen
, “Dynamic nonreciprocity in loss-compensated piezophononic media
,” Phys. Rev. Appl.
9
, 034033
(2018
).6.
K.
Petrover
and A.
Baz
, “Finite element modeling of one-dimensional nonreciprocal acoustic metamaterial with anti-parallel diodes
,” J. Acoust. Soc. Am.
148
(1
), 334
–346
(2020
).7.
S.
Raval
, K.
Petrover
, and A.
Baz
, “Experimental characterization of a one-dimensional nonreciprocal acoustic metamaterial with anti-parallel diodes
,” J. Appl. Phys.
129
, 074502
(2021
).8.
R.
Fleury
, D. L.
Sounas
, C. F.
Sieck
, M. R.
Haberman
, and A.
Alù
, “Sound isolation and giant linear nonreciprocity in a compact acoustic circulator
,” Science
343
, 516
–519
(2014
).9.
X.
Liu
, X.
Cai
, Q.
Guo
, and J.
Yang
, “Robust nonreciprocal acoustic propagation in a compact acoustic circulator empowered by natural convection
,” New J. Phys.
21
, 053001
(2019
).10.
M. A.
Attarzadeh
, S.
Maleki
, J. L.
Crassidis
, and M.
Nouh
, “Nonreciprocal wave phenomena in energy self-reliant gyric metamaterials
,” J. Acoust. Soc. Am.
146
, 789
–801
(2019
).11.
A.
Baz
, “Active synthesis of a gyroscopic-nonreciprocal acoustic metamaterial
,” J. Acoust. Soc. Am.
148
(3
), 1271
–1288
(2020
).12.
S.
Raval
, H.
Zhou
, and A.
Baz
, “Experimental implementation of an active synthesis of a gyroscopic-nonreciprocal acoustic metamaterial
,” J. Appl. Phys.
129
, 074501
(2021
).13.
Z.
Chen
, Y.
Peng
, H.
Li
, J.
Liu
, Y.
Ding
, B.
Liang
, X.-F.
Zhu
, Y.
Lu
, J.
Cheng
, and A.
Alù
, “Efficient nonreciprocal mode transitions in spatiotemporally modulated acoustic metamaterials
,” Sci. Adv.
7
, eabj1198
(2021
).14.
E.
Riva
, D. E.
Quadrelli
, J.
Marconia
, G.
Cazzulani
, and F.
Braghin
, “Design and experimental analysis of nonreciprocal wave propagation in a space-time modulated beam
,” Proc. SPIE
11376
, 1137613
(2020
).15.
J.
Huang
and X.
Zhou
, “Nonreciprocal metamaterials with simultaneously time-varying stiffness and mass
,” J. Appl. Mech.
87
, 071003
(2020
).16.
B. M.
Goldsberry
, S. P.
Wallen
, and M. R.
Haberman
, “Nonreciprocal vibrations of finite elastic structures with spatiotemporally modulated material properties
,” Phys. Rev. B
102
(1
), 014312
(2020
).17.
B. M.
Goldsberry
, S. P.
Wallen
, and M. R.
Haberman
, “Nonreciprocal wave propagation in mechanically-modulated continuous elastic metamaterials
,” J. Acoust. Soc. Am.
146
(1
), 782
–788
(2019
).18.
C.
Shen
, J.
Li
, Z.
Jia
, Y.
Xie
, and S. A.
Cummer
, “Nonreciprocal acoustic transmission in cascaded resonators via spatiotemporal modulation
,” Phys. Rev. B
99
(13
), 134306
(2019
).19.
C.
Shen
, X.
Zhu
, J.
Li
, and S. A.
Cummer
, “Nonreciprocal acoustic transmission in space-time modulated coupled resonators
,” Phys. Rev. B
100
(5
), 054302
(2019
).20.
M. A.
Hasan
, L.
Calderin
, P.
Lucas
, K.
Runge
, and P. A.
Deymier
, “Geometric phase invariance in spatiotemporal modulated elastic system
,” J. Sound Vib.
459
, 114843
(2019
).21.
Q.
Chen
, “Tunable mechanical bandgaps in elastic metamaterials: Patterning, straining, and spatiotemporal modulation
,” Ph.D. dissertation (University of Illinois at Urbana-Champaign
, Urbana, Illinois
, 2019
).22.
M. A.
Attarzadeh
, H.
Al Ba'ba'a
, and M.
Nouh
, “On the wave dispersion and nonreciprocal power flow in space-time traveling acoustic metamaterials
,” Appl. Acoust.
133
, 210
–214
(2018
).23.
D.
Torrent
, W. J.
Parnell
, and A. N.
Norris
, “Loss compensation in time-dependent elastic metamaterials
,” Phys. Rev. B
97
(1
), 014105
(2018
).24.
J.
Marconi
, G.
Cazzulani
, M.
Ruzzene
, and F.
Braghin
, “A physical interpretation for broken reciprocity in spatiotemporal modulated periodic rods
,” ASME Paper No. SMASIS2017-3877, 2017
.25.
J.
Vila
, R. K.
Pal
, M.
Ruzzene
, and G. A.
Trainiti
, “A bloch-based procedure for dispersion analysis of lattices with periodic time-varying properties
,” J. Sound Vib.
406
, 363
–377
(2017
).26.
M.
Ruzzene
and G.
Trainiti
, “On time-dependence of mechanical metamaterials properties
,” J. Acoust. Soc. Am.
142
(4
), 2548
(2017
).27.
M. H.
Ansari
, M. A.
Attarzadeh
, M.
Nouh
, and M. A.
Karami
, “Application of magnetoelastic materials in spatiotemporally modulated phononic crystals for nonreciprocal wave propagation
,” Smart Mater. Struct.
27
(1
), 015030
(2017
).28.
G.
Trainiti
and M.
Ruzzene
, “Nonreciprocal elastic wave propagation in spatiotemporal periodic structures
,” New J. Phys.
18
, 083047
(2016
).29.
Q.
Wang
, Y.
Yang
, X.
Ni
, Y.
Xu
, X.
Sun
, Z.
Chen
, L.
Feng
, X.
Liu
, M.
Lu
, and Y.
Chen
, “Acoustic asymmetric transmission based on time-dependent dynamical scattering
,” Sci. Rep.
5
, 10880
(2015
).30.
C. P.
Wiederhold
, D. L.
Sounas
, and A.
Alù
, “Nonreciprocal acoustic propagation and leaky-wave radiation in a waveguide with flow
,” J. Acoust. Soc. Am.
146
, 802
(2019
).31.
J.
Palacios
, L.
Calderin
, A.
Chon
, I.
Frankel
, J.
Alqasimi
, F.
Allein
, R.
Gorelik
, T.
Lata
, R.
Curradi
, G.
Lambert-Milak
, A.
Oke
, N.
Smith
, M.
Abi Ghanem
, P.
Lucas
, N.
Boechler
, and P.
Deymier
, “Temperature-controlled spatiotemporally modulated phononic crystal for achieving nonreciprocal acoustic wave propagation
,” J. Acoust. Soc. Am.
151
(6
), 3669
–3675
(2022
).32.
M. A.
Attarzadeh
, J.
Callanan
, and M.
Nouh
, “Experimental observation of nonreciprocal waves in a resonant metamaterial beam
,” Phys. Rev. Appl.
13
(2
), 021001
(2020
).33.
J.
Marconi
, E.
Riva
, M.
Di Ronco
, G.
Cazzulani
, F.
Braghin
, and M.
Ruzzene
, “Experimental observation of nonreciprocal band gaps in a space-time modulated beam using a shunted piezoelectric array
,” Phys. Rev. Appl.
13
(3
), 031001
(2020
).34.
M.
Moghaddaszadeh
, R.
Adlakha
, M. A.
Attarzadeh
, A.
Aref
, and M.
Nouh
, “Nonreciprocal elastic wave beaming in dynamic phased arrays
,” Phys. Rev. Appl.
16
(3
), 034033
(2021
).35.
S.
Wan
, L.
Cao
, Y.
Zeng
, T.
Guo
, M.
Oudich
, and B.
Assouar
, “Low-frequency nonreciprocal flexural wave propagation via compact cascaded time-modulated resonators
,” Appl. Phys. Lett.
120
(23
), 231701
(2022
).36.
A.
Baz
, “Active nonreciprocal acoustic metamaterials using a switching controller
,” J. Acoust. Soc. Am.
143
(3
), 1376
(2018
).37.
A.
Baz
, “Nonreciprocal acoustic metamaterials with programmable virtual resistors
,” J. Acoust. Soc. Am.
145
(3
), 1686
(2019
).38.
A.
Baz
, “Active nonreciprocal metamaterial using an eigen-structure assignment control strategy
,” J. Acoust. Soc. Am.
147
(4
), 2656
(2020
).39.
R.
Fleury
, D.
Sounas
, M. R.
Haberman
, and A.
Alù
, “Nonreciprocal acoustics
,” Acoust. Today
11
(3
), 14
–21
(2015
).40.
H.
Nassar
, M.
Hussein
, B.
Yousefzadeh
, R.
Fleury
, M.
Ruzzene
, A.
Alù
, C.
Daraio
, A. N.
Norris
, G.
Huang
, and M. R.
Haberman
, “Nonreciprocity in acoustic and elastic materials
,” Nat. Rev. Mater.
5
(9
), 667
–685
(2020
).41.
I.
Kovacic
, R.
Rand
, and S.
Sah
, “Mathieu's equation and its generalizations: Overview of stability charts and their features
,” ASME Appl. Mech. Rev.
70
(2
), 020802
(2018
).42.
43.
E. S.
Cassedy
and A. A.
Oliner
, “Dispersion relations in time-space periodic media: Part I—Stable interactions
,” Proc. IEEE
51
(10
), 1342
–1359
(1963
).44.
E. S.
Cassedy
, “Dispersion relations in time-space periodic media part II—Unstable interactions
,” Proc. IEEE
55
(7
), 1154
–1168
(1967
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
