Graphical Abstract Figure
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
. 
