Predeformation simultaneously changes the effective material stiffness as well as the geometric configuration and therefore may be utilized to tune wave propagation in soft phononic crystals (PCs). Moreover, the band gaps of soft PCs, as compared with those of the hard ones, are more sensitive to the external mechanical stimuli. A one-dimensional tunable soft acoustic diode based on soft functionally graded (FG) PCs is proposed. The two-way asymmetric propagation behavior is studied at the resonant frequency within the band gap. Numerical results show that the operating frequency (i.e., the resonant peak) of the soft graded acoustic diode can be altered by adjusting the mechanical biasing fields (including the longitudinal prestress and the lateral equibiaxial tension). The adjustment becomes significant when the strain-stiffening effect of the Gent hyperelastic material is properly harnessed. Furthermore, the prestress or equibiaxial tension can affect the two-way filtering of the soft FG PC in a separate and different manner. In addition, it is much easier to realize the tunable acoustic diode by exploiting soft FG materials with stronger compressibility. It is shown that the introduction of acoustic impedance is beneficial for predicting the tunable effects. The simulations and conclusions should provide a solid guidance for the design of tunable two-way unidirectional acoustic diodes made from soft hyperelastic materials.
Issue Section:
Research Papers
References
1.
Kushwaha
, M. S.
, Halevi
, P.
, Dobrzynski
, L.
, and Djafarirouhani
, B.
, 1993
, “Acoustic Band Structure of Periodic Elastic Composites
,” Phys. Rev. Lett.
, 71
(13
), pp. 2022
–2025
.2.
Liu
, Z.
, Zhang
, X. X.
, Mao
, Y. W.
, Zhu
, Z. Z.
, Yang
, Z. Y.
, Chan
, C. T.
, and Sheng
, P.
, 2000
, “Locally Resonant Sonic Materials
,” Science
, 289
(5485
), pp. 1734
–1736
.3.
Liang
, B.
, Yuan
, B.
, and Cheng
, J. C.
, 2009
, “Acoustic Diode: Rectification of Acoustic Energy Flux in One-Dimensional Systems
,” Phys. Rev. Lett.
, 103
(10
), p. 104301
.4.
Wang
, X. P.
, Wan
, L. L.
, Chen
, T. N.
, Liang
, Q. X.
, and Song
, A. L.
, 2016
, “Broadband Acoustic Diode by Using Two Structured Impedance-Matched Acoustic Metasurfaces
,” Appl. Phys. Lett.
, 109
(4
), p. 044102
.5.
Zheng
, L. Y.
, Wu
, Y.
, Ni
, X.
, Chen
, Z. G.
, Lu
, M. H.
, and Chen
, Y. F.
, 2014
, “Acoustic Cloaking by a Near-Zero-Index Phononic Crystal
,” Appl. Phys. Lett.
, 104
(16
), p. 161904
.6.
Zhao
, S. D.
, Wang
, Y. S.
, and Zhang
, C.
, 2017
, “High-Transmission Acoustic Self-Focusing and Directional Cloaking in a Graded Perforated Metal Slab
,” Sci. Rep.
, 7
(1
), p. 4368
.7.
Cummer
, S. A.
, Popa
, B. I.
, Schurig
, D.
, Smith
, D. R.
, Pendry
, J.
, Rahm
, M.
, and Starr
, A.
, 2008
, “Scattering Theory Derivation of a 3D Acoustic Cloaking Shell
,” Phys. Rev. Lett.
, 100
(2
), p. 024301
.8.
Morvan
, B.
, Tinel
, A.
, Vasseur
, J. O.
, Sainidou
, R.
, Rembert
, P.
, Hladky-Hennion
, A.-C.
, Swinteck
, N.
, and Deymier
, N.
, 2014
, “Ultra-Directional Source of Longitudinal Acoustic Waves Based on a Two-Dimensional Solid/Solid Phononic Crystal
,” J. Appl. Phys.
, 116
(21
), p. 214901
.9.
Chen
, Y. F.
, Meng
, F.
, Sun
, G. Y.
, Li
, G. Y.
, and Huang
, X. D.
, 2017
, “Topological Design of Phononic Crystals for Unidirectional Acoustic Transmission
,” J. Sound Vib.
, 410
, pp. 103
–123
.10.
Miyamoto
, Y.
, Kaysser
, W. A.
, Rabin
, B. H.
, Kawasaki
, A.
, and Ford
, R. G.
, 1999
, Functionally Graded Materials: Design, Processing and Applications
, Kluwer
, Dordrecht, The Netherlands
.11.
Pompe
, W.
, Worch
, H.
, Epple
, M.
, Friess
, W.
, Gelinsky
, M.
, Greil
, P.
, Hempel
, U.
, Scharnweber
, D.
, and Schulte
, K.
, 2003
, “Functionally Graded Materials for Biomedical Applications
,” Mater. Sci. Eng. A
, 362
(1–2
), pp. 40
–60
.12.
Loy
, C. T.
, Lam
, K. Y.
, and Reddy
, J. N.
, 1999
, “Vibration of Functionally Graded Cylindrical Shells
,” Int. J. Mech. Sci.
, 41
(3
), pp. 309
–324
.13.
Chen
, W. Q.
, Wang
, H. M.
, and Bao
, R. H.
, 2007
, “On Calculating Dispersion Curves of Waves in Functionally Graded Elastic Plate
,” Compos. Struct.
, 81
(2
), pp. 233
–242
.14.
Cao
, X. S.
, Shi
, J. P.
, and Jin
, F.
, 2012
, “Lamb Wave Propagation in the Functionally Graded Piezoelectric–Piezomagnetic Material Plate
,” Acta Mech.
, 223
(5
), pp. 1081
–1091
.15.
Fomenko
, S. I.
, Golub
, M. V.
, Zhang
, C.
, Bui
, T. Q.
, and Wang
, Y. S.
, 2014
, “In-Plane Elastic Wave Propagation and Band-Gaps in Layered Functionally Graded Phononic Crystals
,” Int. J. Solids Struct.
, 51
(13
), pp. 2491
–2503
.16.
Guo
, X.
, Wei
, P. J.
, Lan
, M.
, and Li
, L.
, 2016
, “Dispersion Relations of Elastic Waves in One-Dimensional Piezoelectric/Piezomagnetic Phononic Crystal With Functionally Graded Interlayers
,” Ultrasonics
, 70
, pp. 158
–171
.17.
Torrent
, D.
, Pennec
, Y.
, and Djafari-Rouhani
, B.
, 2014
, “Omnidirectional Refractive Devices for Flexural Waves Based on Graded Phononic Crystals
,” J. Appl. Phys.
, 116
(22
), p. 224902
.18.
Liang
, Y. J.
, Chen
, L. W.
, Wang
, C. C.
, and Chang
, I. L.
, 2014
, “An Acoustic Absorber Implemented by Graded Index Phononic Crystals
,” J. Appl. Phys.
, 115
(24
), p. 244513
.19.
Liang
, B.
, Zou
, X. Y.
, Yuan
, B.
, and Cheng
, J. C.
, 2010
, “Frequency-Dependence of the Acoustic Rectifying Efficiency of an Acoustic Diode Model
,” Appl. Phys. Lett.
, 96
(23
), p. 233511
.20.
Li
, X. F.
, Ni
, X.
, Feng
, L.
, Lu
, M. H.
, He
, C.
, and Chen
, Y. F.
, 2011
, “Tunable Unidirectional Sound Propagation Through a Sonic-Crystal-Based Acoustic Diode
,” Phys. Rev. Lett.
, 106
(8
), p. 084301
.21.
Li
, Z. N.
, Wang
, Y. Z.
, and Wang
, Y. S.
, 2018
, “Nonreciprocal Phenomenon in Nonlinear Elastic Wave Metamaterials With Continuous Properties
,” Int. J. Solids Struct.
, 150
, pp. 125
–134
.22.
Chen
, Y. J.
, Huang
, Y.
, Lü
, C. F.
, and Chen
, W. Q.
, 2017
, “A Two-Way Unidirectional Narrow-Band Acoustic Filter Realized by a Graded Phononic Crystal
,” ASME J. Appl. Mech.
, 84
(9
), p. 091003
.23.
Goffaux
, C.
, and Vigneron
, J. P.
, 2001
, “Theoretical Study of a Tunable Phononic Band Gap System
,” Phys. Rev. B
, 64
(7
), p. 075118
.24.
Wang
, Y. Z.
, Li
, F. M.
, Huang
, W. H.
, Jiang
, X. A.
, Wang
, Y. S.
, and Kishimoto
, K.
, 2008
, “Wave Band Gaps in Two-Dimensional Piezoelectric/Piezomagnetic Phononic Crystals
,” Int. J. Solids Struct.
, 45
(14–15
), pp. 4203
–4210
.25.
Wang
, L. F.
, and Bertoldi
, K.
, 2012
, “Mechanically Tunable Phononic Band Gaps in Three-Dimensional Periodic Elastomeric Structures
,” Int. J. Solids Struct.
, 49
(19–20
), pp. 2881
–2885
.26.
Huang
, Y.
, Chen
, W. Q.
, Wang
, Y. S.
, and Yang
, W.
, 2015
, “Multiple Refraction Switches Realized by Stretching Elastomeric Scatterers in Sonic Crystals
,” AIP Adv.
, 5
(2
), p. 027138
.27.
Zhang
, P.
, and Parnell
, W. J.
, 2017
, “Soft Phononic Crystals With Deformation-Independent Band Gaps
,” Proc. R. Soc. A
, 473
(2200
), p. 0865.https://royalsocietypublishing.org/doi/full/10.1098/rspa.2016.086528.
Ogden
, R. W.
, 2009
, “Incremental Elastic Motions Superimposed on a Finite Deformation in the Presence of an Electromagnetic Field
,” Int. J. Non-Linear Mech.
, 44
(5
), pp. 570
–580
.29.
Huang
, Y.
, Shen
, X. D.
, Zhang
, C. L.
, and Chen
, W. Q.
, 2014
, “Mechanically Tunable Band Gaps in Compressible Soft Phononic Laminated Composites With Finite Deformation
,” Phys. Lett. A
, 378
(30–31
), pp. 2285
–2289
.30.
Galich
, P. I.
, Fang
, N. X.
, Boyce
, M. C.
, and Rudykh
, S.
, 2017
, “Elastic Wave Propagation in Finitely Deformed Layered Materials
,” J. Mech. Phys. Solids
, 98
, pp. 390
–410
.31.
Wu
, B.
, Zhou
, W. J.
, Bao
, R. H.
, and Chen
, W. Q.
, 2018
, “Tuning Elastic Waves in Soft Phononic Crystal Cylinders Via Large Deformation and Electromechanical Coupling
,” ASME J. Appl. Mech.
, 85
(3
), p. 031004
.32.
Wu
, B.
, Su
, Y. P.
, Chen
, W. Q.
, and Zhang
, C. Z.
, 2016
, “On Guided Circumferential Waves in Soft Electroactive Tubes Under Radially Inhomogeneous Biasing Fields
,” J. Mech. Phys. Solids
, 99
, pp. 116
–145
.33.
Dorfmann
, A.
, and Ogden
, R. W.
, 2010
, “Electroelastic Waves in a Finitely Deformed Electroactive Material
,” IMA J. Appl. Math.
, 75
(4
), pp. 603
–636
.34.
Zhu
, J.
, Chen
, H. Y.
, Wu
, B.
, Chen
, W. Q.
, and Balogun
, O.
, 2018
, “Tunable Band Gaps and Transmission Behavior of SH Waves With Oblique Incident Angle in Periodic Dielectric Elastomer Laminates
,” Int. J. Mech. Sci.
, 146–147
, pp. 81
–90
.35.
Bian
, Z. G.
, Peng
, W.
, and Song
, J. Z.
, 2014
, “Thermal Tuning of Band Structures in a One-Dimensional Phononic Crystal
,” ASME J. Appl. Mech.
, 81
(4
), p. 041008
.36.
Wu
, B.
, Su
, Y. P.
, Liu
, D. Y.
, Chen
, W. Q.
, and Zhang
, C. Z.
, 2018
, “On Propagation of Axisymmetric Waves in Pressurized Functionally Graded Elastomeric Hollow Cylinders
,” J. Sound Vib.
, 421
, pp. 17
–47
.37.
Wang
, P.
, Shim
, J. M.
, and Bertoldi
, K.
, 2013
, “Effects of Geometric and Material Nonlinearities on Tunable Band Gaps and Low-Frequency Directionality of Phononic Crystals
,” Phys. Rev. B
, 88
(1
), p. 014304
.38.
Chen
, W. Q.
, and Ding
, H. J.
, 2002
, “On Free Vibration of a Functionally Graded Piezoelectric Rectangular Plate
,” Acta Mech.
, 153
(3–4
), pp. 207
–216
.39.
Mizuno
, S.
, 2001
, “Theoretical Study on Resonant Transmission of Acoustic Phonons Propagating Through a Superlattice-Liquid Interface
,” Phys. Rev. B
, 63
(3
), p. 035301
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