Abstract
In this work, a new inertia modulated meta-structure is proposed to enable time-dependent inertia parameters, and thereby realize non-reciprocal wave propagation via spatiotemporal modulation. The designed cell structure is composed of an oscillatory disk and a mass that slides in a guide embedded in the disk frictionlessly with prescribed motion. Effective moment of inertia and damping coefficients of the rocking motion of the cell structure are rendered time-dependent due to the inertia and Coriolis forces of the periodically sliding mass, which allows us to implement the expected spatiotemporal modulation upon a super-cell. Non-reciprocal propagation behavior of the proposed meta-structure is verified via the theoretical solution of the dispersion relation as well as the dynamic response of a finite array. Effects of modulation parameters, including the frequency, amplitude, and phase, on the unidirectional propagation characteristic are thoroughly investigated.
References
1.
Padilla
, W. J.
, Basov
, D. N.
, and Smith
, D. R.
, 2006
, “Negative Refractive Index Metamaterials
,” Mater. Today
, 9
(7–8
), pp. 28
–35
. 2.
Burgos
, S. P.
, De Waele
, R.
, Polman
, A.
, and Atwater
, H. A.
, 2010
, “A Single-Layer Wide-Angle Negative-Index Metamaterial at Visible Frequencies
,” Nat. Mater.
, 9
(5
), pp. 407
–412
. 3.
Ding
, Y.
, Liu
, Z.
, Qiu
, C.
, and Shi
, J.
, 2007
, “Metamaterial With Simultaneously Negative Bulk Modulus and Mass Density
,” Phys. Rev. Lett.
, 99
(9
), p. 093904
. 4.
Liu
, X.-N.
, Hu
, G.-K.
, Huang
, G.-L.
, and Sun
, C.-T.
, 2011
, “An Elastic Metamaterial With Simultaneously Negative Mass Density and Bulk Modulus
,” Appl. Phys. Lett.
, 98
(25
), p. 251907
. 5.
Yu
, K.
, Fang
, N. X.
, Huang
, G.
, and Wang
, Q.
, 2018
, “Magnetoactive Acoustic Metamaterials
,” Adv. Mater.
, 30
(21
), p. 1706348
. 6.
Kodera
, T.
, Sounas
, D. L.
, and Caloz
, C.
, 2013
, “Magnetless Nonreciprocal Metamaterial (MNM) Technology: Application to Microwave Components
,” IEEE Trans. Microwave Theory Tech.
, 61
(3
), pp. 1030
–1042
. 7.
Brandenbourger
, M.
, Locsin
, X.
, Lerner
, E.
, and Coulais
, C.
, 2019
, “Nonreciprocal Robotic Metamaterials
,” Nat. Commun.
, 10
(1
), p. 4608
. 8.
Kadic
, M.
, Milton
, G. W.
, van Hecke
, M.
, and Wegener
, M.
, 2019
, “3D Metamaterials
,” Nat. Rev. Phys.
, 1
(3
), pp. 198
–210
. 9.
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
,” Nat. Rev. Mater.
, 5
(9
), pp. 667
–685
. 10.
Zheng
, Y.
, Zhang
, J.
, Qu
, Y.
, and Meng
, G.
, 2021
, “Adaptive Nonreciprocal Wave Attenuation in Linear Piezoelectric Metastructures Shunted With One-Way Electrical Transmission Lines
,” J. Sound Vib.
, 503
, p. 116113
. 11.
Tian
, T.
, Zhang
, Y.
, Zhang
, L.
, Wu
, L.
, Lin
, S.
, Zhou
, J.
, Duan
, C.-K.
, Jiang
, J.-H.
, and Du
, J.
, 2022
, “Experimental Realization of Nonreciprocal Adiabatic Transfer of Phonons in a Dynamically Modulated Nanomechanical Topological Insulator
,” Phys. Rev. Lett.
, 129
(21
), p. 215901
. 12.
Nagulu
, A.
, Reiskarimian
, N.
, and Krishnaswamy
, H.
, 2020
, “Non-Reciprocal Electronics Based on Temporal Modulation
,” Nat. Electron.
, 3
(5
), pp. 241
–250
. 13.
Shao
, L.
, Mao
, W.
, Maity
, S.
, Sinclair
, N.
, Hu
, Y.
, Yang
, L.
, and Lončar
, M.
, 2020
, “Non-Reciprocal Transmission of Microwave Acoustic Waves in Nonlinear Parity–Time Symmetric Resonators
,” Nat. Electron.
, 3
(5
), pp. 267
–272
. 14.
Shalaby
, M.
, Peccianti
, M.
, Ozturk
, Y.
, and Morandotti
, R.
, 2013
, “A Magnetic Non-Reciprocal Isolator for Broadband Terahertz Operation
,” Nat. Commun.
, 4
(1
), p. 1558
. 15.
Xu
, M.
, Yamamoto
, K.
, Puebla
, J.
, Baumgaertl
, K.
, Rana
, B.
, Miura
, K.
, Takahashi
, H.
, Grundler
, D.
, Maekawa
, S.
, and Otani
, Y.
, 2020
, “Nonreciprocal Surface Acoustic Wave Propagation Via Magneto-Rotation Coupling
,” Sci. Adv.
, 6
(32
), p. eabb1724
. 16.
Mahmoud
, A. M.
, Davoyan
, A. R.
, and Engheta
, N.
, 2015
, “All-Passive Nonreciprocal Metastructure
,” Nat. Commun.
, 6
(1
), p. 8359
. 17.
Dobrykh
, D.
, Yulin
, A.
, Slobozhanyuk
, A.
, Poddubny
, A.
, and Kivshar
, Y. S.
, 2018
, “Nonlinear Control of Electromagnetic Topological Edge States
,” Phys. Rev. Lett.
, 121
(16
), p. 163901
. 18.
Sounas
, D. L.
, and Alù
, A.
, 2017
, “Non-Reciprocal Photonics Based on Time Modulation
,” Nat. Photonics
, 11
(12
), pp. 774
–783
. 19.
Correas-Serrano
, D.
, Alù
, A.
, and Gomez-Diaz
, J. S.
, 2018
, “Magnetic-Free Nonreciprocal Photonic Platform Based on Time-Modulated Graphene Capacitors
,” Phys. Rev. B
, 98
(16
), p. 165428
. 20.
Raney
, J. R.
, Nadkarni
, N.
, Daraio
, C.
, Kochmann
, D. M.
, Lewis
, J. A.
, and Bertoldi
, K.
, 2016
, “Stable Propagation of Mechanical Signals in Soft Media Using Stored Elastic Energy
,” Proc. Natl. Acad. Sci.
, 113
(35
), pp. 9722
–9727
. 21.
Librandi
, G.
, Tubaldi
, E.
, and Bertoldi
, K.
, 2021
, “Programming Nonreciprocity and Reversibility in Multistable Mechanical Metamaterials
,” Nat. Commun.
, 12
(1
), p. 3454
. 22.
Pal
, A.
, and Sitti
, M.
, 2023
, “Programmable Mechanical Devices Through Magnetically Tunable Bistable Elements
,” Proc. Natl. Acad. Sci.
, 120
(15
), p. e2212489120
. 23.
Yin
, J.
, Huang
, J.
, Zhang
, S.
, Zhang
, H.
, and Chen
, B.
, 2014
, “Ultrawide Low Frequency Band Gap of Phononic Crystal in Nacreous Composite Material
,” Phys. Lett. A
, 378
(32–33
), pp. 2436
–2442
. 24.
Lucklum
, F.
, and Vellekoop
, M. J.
, 2018
, “Bandgap Engineering of Threedimensional Phononic Crystals in a Simple Cubic Lattice
,” Appl. Phys. Lett.
, 113
(20
), p. 201902
. 25.
Wang
, Q.
, Li
, J.
, Zhang
, Y.
, Xue
, Y.
, and Li
, F.
, 2021
, “Bandgap Properties in Metamaterial Sandwich Plate With Periodically Embedded Plate-Type Resonators
,” Mech. Syst. Signal Process
, 151
, p. 107375
. 26.
Yu
, Z.
, and Fan
, S.
, 2009
, “Complete Optical Isolation Created by Indirect Interband Photonic Transitions
,” Nat. Photonics
, 3
(2
), pp. 91
–94
. 27.
Sounas
, D. L.
, Caloz
, C.
, and Alu
, A.
, 2013
, “Giant Non-Reciprocity at the Subwavelength Scale Using Angular Momentum-Biased Metamaterials
,” Nat. Commun.
, 4
(1
), p. 2407
. 28.
Cassedy
, E. S.
, 1967
, “Dispersion Relations in Time-Space Periodic Media Part II—Unstable Interactions
,” Proc. IEEE
, 55
(7
), pp. 1154
–1168
. 29.
Trainiti
, G.
, and Ruzzene
, M.
, 2016
, “Non-Reciprocal Elastic Wave Propagation in Spatiotemporal Periodic Structures
,” New J. Phys.
, 18
(8
), p. 083047
. 30.
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
, pp. 363
–377
. 31.
Swinteck
, N.
, Matsuo
, S.
, Runge
, K.
, Vasseur
, J. O.
, Lucas
, P.
, and Deymier
, P. A.
, 2015
, “Bulk Elastic Waves With Unidirectional Backscattering-Immune Topological States in a Time-Dependent Superlattice
,” J. Appl. Phys.
, 118
(6
), p. 063103
. 32.
Nassar
, H.
, Chen
, H.
, Norris
, A.
, Haberman
, M.
, and Huang
, G.
, 2017
, “Nonreciprocal Wave Propagation in Modulated Elastic Metamaterials
,” Proc. R. Soc. A
, 473
(2202
), p. 20170188
.33.
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
. 34.
Hu
, X.
, Hang
, Z.
, Li
, J.
, Zi
, J.
, and Chan
, C. T.
, 2006
, “Anomalous Doppler Effects in Phononic Band Gaps
,” Phys. Rev. E
, 73
(1
), p. 015602
. 35.
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
. 36.
Chen
, Y.
, Li
, X.
, Nassar
, H.
, Norris
, A. N.
, Daraio
, C.
, and Huang
, G.
, 2019
, “Nonreciprocal Wave Propagation in a Continuum-Based Metamaterial With Space-Time Modulated Resonators
,” Phys. Rev. Appl.
, 11
(6
), p. 064052
. 37.
Wan
, S.
, Cao
, L.
, Zeng
, Y.
, Guo
, T.
, Oudich
, M.
, and Assouar
, B.
, 2022
, “Low-Frequency Nonreciprocal Flexural Wave Propagation Via Compact Cascaded Time-Modulated Resonators
,” Appl. Phys. Lett.
, 120
(23
), p. 231701
. 38.
Marconi
, J.
, Riva
, E.
, Di Ronco
, M.
, Cazzulani
, G.
, Braghin
, F.
, and Ruzzene
, M.
, 2020
, “Experimental Observation of Nonreciprocal Band Gaps in a Spacetime-Modulated Beam Using a Shunted Piezoelectric Array
,” Phys. Rev. Appl.
, 13
(3
), p. 031001
. 39.
Sugino
, C.
, Ruzzene
, M.
, and Erturk
, A.
, 2020
, “Nonreciprocal Piezoelectric Metamaterial Framework and Circuit Strategies
,” Phys. Rev. B
, 102
(1
), p. 014304
. 40.
Nash
, L. M.
, Kleckner
, D.
, Read
, A.
, Vitelli
, V.
, Turner
, A. M.
, and Irvine
, W. T.
, 2015
, “Topological Mechanics of Gyroscopic Metamaterials
,” Proc. Natl. Acad. Sci.
, 112
(47
), pp. 14495
–14500
. 41.
Huang
, J.
, and Zhou
, X.
, 2019
, “A Time-Varying Mass Metamaterial for Nonreciprocal Wave Propagation
,” Int. J. Solids Struct.
, 164
, pp. 25
–36
. 42.
Huang
, J.
, and Zhou
, X.
, 2020
, “Non-Reciprocal Metamaterials With Simultaneously Time-Varying Stiffness and Mass
,” ASME J. Appl. Mech.
, 87
(7
), p. 071003
. Copyright © 2023 by ASME
You do not currently have access to this content.
