Graphical Abstract Figure
Graphical Abstract Figure
Close modal

Abstract

Underwater acoustic non-reciprocal transmission via dynamic-modulation structures with time-varying mass and stiffness is studied. The model system consists of spatiotemporally modulated discrete lattices immersed in the water background. Based on the transfer matrix method, an analytic model for the coupled continuum-discrete system is developed to calculate acoustic scattering responses in the frequency domain. Finite-difference time-domain computation is conducted for the coupled system to verify the theoretical model. Results show that acoustic non-reciprocal transmission in opposite directions appears at frequencies where there are asymmetric bandgaps in dispersion diagrams. Asymmetric transmission can be enhanced in magnitude by engineering the modulating amplitudes of time-varying parameters or increasing the number of lattice elements, while the frequency bandwidth can be broadened by cascading structural elements with different modulating frequencies due to the gap-combining effect. The model may find potential applications in underwater acoustic isolation and sonar communication.

References

1.
Lurie
,
K. A.
,
2007
,
An Introduction to the Mathematical Theory of Dynamic Materials
,
Springer
,
Cham, Switzerland
.
2.
Nassar
,
H.
,
Yousefzadeh
,
B.
,
Fleury
,
R.
,
Ruzzene
,
M.
,
Alù
,
A.
,
Daraio
,
C.
,
Norris
,
A. N.
,
Huang
,
G.
, and
Haberman
,
M. R.
,
2020
, “
Nonreciprocity in Acoustic and Elastic Materials
,”
Nature Rev. Mater.
,
5
(
9
), pp.
667
685
.
3.
Shui
,
L. Q.
,
Yue
,
Z. F.
,
Liu
,
Y. S.
,
Liu
,
Q. C.
,
Guo
,
J. J.
, and
He
,
X. D.
,
2015
, “
Novel Composites With Asymmetrical Elastic Wave Properties
,”
Compos. Sci. Technol.
,
113
(
Suppl. C
), pp.
19
30
.
4.
Trainiti
,
G.
, and
Ruzzene
,
M.
,
2016
, “
Non-Reciprocal Elastic Wave Propagation in Spatiotemporal Periodic Structures
,”
New J. Phys.
,
18
(
8
), p.
083047
.
5.
Milton
,
G. W.
, and
Mattei
,
O.
,
2017
, “
Field Patterns: A New Mathematical Object
,”
Proc. R. Soc. A: Math., Phys. Eng. Sci.
,
473
(
2198
), p.
20160819
.
6.
Nassar
,
H.
,
Chen
,
H.
,
Norris
,
A. N.
,
Haberman
,
M. R.
, and
Huang
,
G. L.
,
2017
, “
Non-Reciprocal Wave Propagation in Modulated Elastic Metamaterials
,”
Proc. R. Soc. A: Math., Phys. Eng. Sci.
,
473
(
2202
), p.
20170188
.
7.
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
.
8.
Vila
,
J.
,
Pal
,
R. K.
,
Ruzzene
,
M.
, and
Trainiti
,
G.
,
2017
, “
A Bloch-Based Procedure for Dispersion Analysis of Lattices With Periodic Time-Varying Properties
,”
J. Sound Vib.
,
406
(
Suppl. C
), pp.
363
377
.
9.
Attarzadeh
,
M. A.
,
Callanan
,
J.
, and
Nouh
,
M.
,
2020
, “
Experimental Observation of Nonreciprocal Waves in a Resonant Metamaterial Beam
,”
Phys. Rev. Appl.
,
13
(
2
), p.
021001
.
10.
Tessier Brothelande
,
S.
,
Croënne
,
C.
,
Allein
,
F.
,
Vasseur
,
J. O.
,
Amberg
,
M.
,
Giraud
,
F.
, and
Dubus
,
B.
,
2023
, “
Experimental Evidence of Nonreciprocal Propagation in Space-Time Modulated Piezoelectric Phononic Crystals
,”
Appl. Phys. Lett.
,
123
(
20
), p.
201701
.
11.
Wang
,
Y.
,
Yousefzadeh
,
B.
,
Chen
,
H.
,
Nassar
,
H.
,
Huang
,
G.
, and
Daraio
,
C.
,
2018
, “
Observation of Nonreciprocal Wave Propagation in a Dynamic Phononic Lattice
,”
Phys. Rev. Lett.
,
121
(
19
), p.
194301
.
12.
Yi
,
K.
,
Collet
,
M.
, and
Karkar
,
S.
,
2018
, “
Reflection and Transmission of Waves Incident on Time-Space Modulated Media
,”
Phys. Rev. B
,
98
(
5
), p.
054109
.
13.
Yi
,
K.
,
Karkar
,
S.
, and
Collet
,
M.
,
2018
, “
One-Way Energy Insulation Using Time-Space Modulated Structures
,”
J. Sound. Vib.
,
429
, pp.
162
175
.
14.
Karličić
,
D.
,
Cajić
,
M.
,
Paunović
,
S.
,
Obradović
,
A.
,
Adhikari
,
S.
, and
Christensen
,
J.
,
2023
, “
Non-Reciprocal Wave Propagation in Time-Modulated Elastic Lattices With Inerters
,”
Appl. Math. Modell.
,
117
(
May
), pp.
316
335
.
15.
Croënne
,
C.
,
Vasseur
,
J. O.
,
Bou Matar
,
O.
,
Ponge
,
M.-F.
,
Deymier
,
P. A.
,
Hladky-Hennion
,
A.-C.
, and
Dubus
,
B.
,
2017
, “
Brillouin Scattering-Like Effect and Non-Reciprocal Propagation of Elastic Waves Due to Spatio-Temporal Modulation of Electrical Boundary Conditions in Piezoelectric Media
,”
Appl. Phys. Lett.
,
110
(
6
), p.
061901
.
16.
Fleury
,
R.
,
Sounas
,
D. L.
,
Haberman
,
M. R.
, and
Alù
,
A.
,
2015
, “
Nonreciprocal Acoustics
,”
Acoust. Today
,
11
(
3
), pp.
14
21
.
17.
Xu
,
X.
,
Wu
,
Q.
,
Chen
,
H.
,
Nassar
,
H.
,
Chen
,
Y.
,
Norris
,
A.
,
Haberman
,
M.
, and
Huang
,
G.
,
2020
, “
Physical Observation of a Robust Acoustic Pumping in Waveguides With Dynamic Boundary
,”
Phys. Rev. Lett.
,
125
(
25
), p.
253901
.
18.
Zhu
,
X.
,
Li
,
J.
,
Shen
,
C.
,
Peng
,
X.
,
Song
,
A.
,
Li
,
L.
, and
Cummer
,
S. A.
,
2020
, “
Non-Reciprocal Acoustic Transmission Via Space-Time Modulated Membranes
,”
Appl. Phys. Lett.
,
116
(
3
), p.
034101
.
19.
Shen
,
C.
,
Zhu
,
X.
,
Li
,
J.
, and
Cummer
,
S. A.
,
2019
, “
Nonreciprocal Acoustic Transmission in Space-Time Modulated Coupled Resonators
,”
Phys. Rev. B
,
100
(
5
), p.
054302
.
20.
Huang
,
Y.
, and
Zhou
,
X.
,
2022
, “
Non-Reciprocal Sound Transmission in Electro-Acoustic Systems With Time-Modulated Circuits
,”
Acta Mech. Solida Sinica
,
35
(
6
), pp.
940
948
.
21.
Chen
,
Z.
,
Peng
,
Y.
,
Li
,
H.
,
Liu
,
J.
,
Ding
,
Y.
,
Liang
,
B.
,
Zhu
,
X.-F.
,
Lu
,
Y.
,
Cheng
,
J.
, and
Alù
,
A.
,
2021
, “
Efficient Nonreciprocal Mode Transitions in Spatiotemporally Modulated Acoustic Metamaterials
,”
Sci. Adv.
,
7
(
45
), p.
eabj1198
.
22.
Zhang
,
Y.
,
Wu
,
K.
,
Wang
,
C.
, and
Huang
,
L.
,
2021
, “
Towards Altering Sound Frequency at Will by a Linear Meta-Layer With Time-Varying and Quantized Properties
,”
Commun. Phys.
,
4
(
1
), p.
220
.
23.
Zhou
,
H.
, and
Baz
,
A.
,
2022
, “
Active Nonreciprocal Metamaterial Using a Spatiotemporal Modulation Control Strategy
,”
Appl. Phys. Lett.
,
121
(
6
), p.
061701
.
24.
Huang
,
J.
, and
Zhou
,
X.
,
2019
, “
A Time-Varying Mass Metamaterial for Non-Reciprocal Wave Propagation
,”
Int. J. Solids Struct.
,
164
, pp.
25
36
.
25.
Huang
,
J.
, and
Zhou
,
X.
,
2020
, “
Non-Reciprocal Metamaterials With Simultaneously Time-Varying Stiffness and Mass
,”
ASME J. Appl. Mech.
,
87
(
7
), p.
071003
.
26.
Liao
,
Y.
, and
Zhou
,
X.
,
2022
, “
Topological Pumping in Doubly Modulated Mechanical Systems
,”
Phys. Rev. Appl.
,
17
(
3
), p.
034076
.
27.
Yee
,
K.
,
1966
, “
Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media
,”
IEEE Trans. Anten. Propag.
,
14
(
3
), pp.
302
307
.
28.
Botteldooren
,
D.
,
1995
, “
Finite-Difference Time-Domain Simulation of Low-Frequency Room Acoustic Problems
,”
J. Acoust. Soc. Am.
,
98
(
6
), pp.
3302
3308
.
29.
Wang
,
Z.
, and
Zhou
,
X.
,
2016
, “
Time Domain Characteristics of Wave Motion in Dispersive and Anisotropic Continuum Acoustic Metamaterials
,”
J. Acoust. Soc. Am.
,
140
(
6
), pp.
4276
4287
.
30.
Toyoda
,
M.
, and
Eto
,
D.
,
2019
, “
Prediction of Microperforated Panel Absorbers Using the Finite-Difference Time-Domain Method
,”
Wave Motion
,
86
, pp.
110
124
.
31.
Geng
,
L.
,
Zhang
,
W.
,
Zhang
,
X.
, and
Zhou
,
X.
,
2021
, “
Topological Mode Switching in Modulated Structures With Dynamic Encircling of an Exceptional Point
,”
Proc. R. Soc. A: Math., Phys. Eng. Sci.
,
477
(
2245
), p.
20200766
.
32.
Geng
,
L.
,
Zhang
,
W.
,
Zhang
,
X.
, and
Zhou
,
X.
,
2021
, “
Chiral Mode Transfer of Symmetry-Broken States in Anti-Parity-Time-Symmetric Mechanical System
,”
Proc. R. Soc. A: Math., Phys. Eng. Sci.
,
477
(
2256
), p.
20210641
.
33.
Yuan
,
J.
,
Geng
,
L.
,
Huang
,
J.
,
Guo
,
Q.
,
Yang
,
J.
,
Hu
,
G.
, and
Zhou
,
X.
,
2022
, “
Exceptional Points Induced by Time-Varying Mass to Enhance the Sensitivity of Defect Detection
,”
Phys. Rev. Appl.
,
18
(
6
), p.
064055
.
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