Abstract

In this research, we aim to combine origami units with vibration-filtering metastructures. By employing the bistable origami structure as resonant unit cells, we propose metastructures with low-frequency vibration isolation ability. The geometrical nonlinearity of the origami building block is harnessed for the adjustable stiffness of the metastructure’s resonant unit. The quantitative relationship between the overall stiffness and geometric parameter of the origami unit is revealed through the potential energy analysis. Both static and dynamic experiments are conducted on the bistable origami cell and the constructed beam-like metastructure to verify the adjustable stiffness and the tunable vibration isolation zone, respectively. Finally, a two-dimensional (2D) plate-like metastructure is designed and numerically studied for the control of different vibration modes. The proposed origami-based metastructures can be potentially useful in various engineering applications where structures with vibration isolation abilities are appreciated.

References

1.
Sihvola
,
A.
,
2007
, “
Metamaterials in Electromagnetics
,”
Metamaterials
,
1
(
1
), pp.
2
11
. 10.1016/j.metmat.2007.02.003
2.
Liu
,
Z.
,
Zhang
,
X.
,
Mao
,
Y.
,
Zhu
,
Y. Y.
,
Yang
,
Z.
,
Chan
,
C. T.
, and
Sheng
,
P.
,
2000
, “
Locally Resonant Sonic Materials
,”
Science
,
289
(
5485
), pp.
1734
1736
. 10.1126/science.289.5485.1734
3.
Yao
,
S.
,
Zhou
,
X.
, and
Hu
,
G.
,
2008
, “
Experimental Study on Negative Effective Mass in a 1D Mass–Spring System
,”
New J. Phys.
,
10
(
4
), p.
043020
. 10.1088/1367-2630/10/4/043020
4.
Liu
,
Z.
,
Chan
,
C. T.
, and
Sheng
,
P.
,
2005
, “
Analytic Model of Phononic Crystals With Local Resonances
,”
Phys. Rev. B
,
71
(
1
), p.
014103
. 10.1103/PhysRevB.71.014103
5.
Zhu
,
R.
,
Liu
,
X. N.
,
Hu
,
G. K.
,
Sun
,
C. T.
, and
Huang
,
G. L.
,
2014
, “
Negative Refraction of Elastic Waves at the Deep-Subwavelength Scale in a Single-Phase Metamaterial
,”
Nat. Commun.
,
5
(
1
), p.
5510
. 10.1038/ncomms6510
6.
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
. 10.1063/1.3597651
7.
Scheibner
,
C.
,
Souslov
,
A.
,
Banerjee
,
D.
,
Surowka
,
P.
,
Irvine
,
W. T.
, and
Vitelli
,
V.
,
2020
, “
Odd Elasticity
,”
Nat. Phys.
,
16
(
4
), pp.
475
480
. 10.1038/s41567-020-0795-y
8.
Frenzel
,
T.
,
Kadic
,
M.
, and
Wegener
,
M.
,
2017
, “
Three-Dimensional Mechanical Metamaterials With a Twist
,”
Science
,
358
(
6366
), pp.
1072
1074
. 10.1126/science.aao4640
9.
Coulais
,
C.
,
Sounas
,
D.
, and
Alù
,
A.
,
2017
, “
Static Non-Reciprocity in Mechanical Metamaterials
,”
Nature
,
542
(
7642
), pp.
461
464
. 10.1038/nature21044
10.
Zhu
,
R.
,
Liu
,
X. N.
,
Hu
,
G. K.
,
Sun
,
C. T.
, and
Huang
,
G. L.
,
2014
, “
A Chiral Elastic Metamaterial Beam for Broadband Vibration Suppression
,”
J. Sound Vib.
,
333
(
10
), pp.
2759
2773
. 10.1016/j.jsv.2014.01.009
11.
Chen
,
J. S.
,
Sharma
,
B.
, and
Sun
,
C. T.
,
2011
, “
Dynamic Behaviour of Sandwich Structure Containing Spring-Mass Resonators
,”
Compos. Struct.
,
93
(
8
), pp.
2120
2125
. 10.1016/j.compstruct.2011.02.007
12.
Yu
,
T.
, and
Lesieutre
,
G. A.
,
2017
, “
Damping of Sandwich Panels via Three-Dimensional Manufactured Multimode Metamaterial Core
,”
AIAA J.
,
55
(
4
), pp.
1440
1449
. 10.2514/1.J055039
13.
Cai
,
C.
,
Zhou
,
J.
,
Wu
,
L.
,
Wang
,
K.
,
Xu
,
D.
, and
Ouyang
,
H.
,
2020
, “
Design and Numerical Validation of Quasi-Zero-Stiffness Metamaterials for Very Low-Frequency Band Gaps
,”
Compos. Struct.
,
236
, p.
111862
. 10.1016/j.compstruct.2020.111862
14.
Huang
,
H. H.
,
Sun
,
C. T.
, and
Huang
,
G. L.
,
2009
, “
On the Negative Effective Mass Density in Acoustic Metamaterials
,”
Int. J. Eng. Sci.
,
47
(
4
), pp.
610
617
. 10.1016/j.ijengsci.2008.12.007
15.
Yu
,
D.
,
Liu
,
Y.
,
Wang
,
G.
,
Zhao
,
H.
, and
Qiu
,
J.
,
2006
, “
Flexural Vibration Band Gaps in Timoshenko Beams With Locally Resonant Structures
,”
J. Appl. Phys.
,
100
(
12
), p.
124901
. 10.1063/1.2400803
16.
Zhu
,
R.
,
Huang
,
G. L.
,
Huang
,
H. H.
, and
Sun
,
C. T.
,
2011
, “
Experimental and Numerical Study of Guided Wave Propagation in a Thin Metamaterial Plate
,”
Phys. Lett. A
,
375
(
30–31
), pp.
2863
2867
. 10.1016/j.physleta.2011.06.006
17.
Miranda
,
E. J. P.
, Jr.
,
Nobrega
,
E. D.
,
Ferreira
,
A. H. R.
, and
Dos Santos
,
J. M. C.
,
2019
, “
Flexural Wave Band Gaps in a Multi-Resonator Elastic Metamaterial Plate Using Kirchhoff-Love Theory
,”
Mech. Syst. Sig. Process.
,
116
, pp.
480
504
. 10.1016/j.ymssp.2018.06.059
18.
Pai
,
P. F.
,
2010
, “
Metamaterial-Based Broadband Elastic Wave Absorber
,”
J. Intell. Mater. Syst. Struct.
,
21
(
5
), pp.
517
528
. 10.1177/1045389X09359436
19.
Chen
,
H.
,
Li
,
X. P.
,
Chen
,
Y. Y.
, and
Huang
,
G. L.
,
2017
, “
Wave Propagation and Absorption of Sandwich Beams Containing Interior Dissipative Multi-Resonators
,”
Ultrasonics
,
76
, pp.
99
108
. 10.1016/j.ultras.2016.12.014
20.
Bergamini
,
A.
,
Delpero
,
T.
,
Simoni
,
L. D.
,
Lillo
,
L. D.
,
Ruzzene
,
M.
, and
Ermanni
,
P.
,
2014
, “
Phononic Crystal With Adaptive Connectivity
,”
Adv. Mater.
,
26
(
9
), pp.
1343
1347
. 10.1002/adma.201305280
21.
Chen
,
Y. Y.
,
Huang
,
G. L.
, and
Sun
,
C. T.
,
2014
, “
Band Gap Control in an Active Elastic Metamaterial With Negative Capacitance Piezoelectric Shunting
,”
ASME J. Vib. Acoust.
,
136
(
6
), p.
061008
. 10.1115/1.4028378
22.
Zhu
,
R.
,
Chen
,
Y. Y.
,
Barnhart
,
M. V.
,
Hu
,
G. K.
,
Sun
,
C. T.
, and
Huang
,
G. L.
,
2016
, “
Experimental Study of an Adaptive Elastic Metamaterial Controlled by Electric Circuits
,”
Appl. Phys. Lett.
,
108
(
1
), p.
011905
. 10.1063/1.4939546
23.
Li
,
X.
,
Chen
,
Y.
,
Hu
,
G.
, and
Huang
,
G.
,
2018
, “
A Self-Adaptive Metamaterial Beam With Digitally Controlled Resonators for Subwavelength Broadband Flexural Wave Attenuation
,”
Smart Mater. Struct.
,
27
(
4
), p.
045015
. 10.1088/1361-665X/aab167
24.
Overvelde
,
J. T. B.
,
De Jong
,
T. A.
,
Shevchenko
,
Y.
,
Becerra
,
S. A.
,
Whitesides
,
G. M.
,
Weaver
,
J. C.
,
Hoberman
,
C.
, and
Bertoldi
,
K.
,
2016
, “
A Three-Dimensional Actuated Origami-Inspired Transformable Metamaterial With Multiple Degrees of Freedom
,”
Nat. Commun.
,
7
(
1
), p.
10929
. 10.1038/ncomms10929
25.
Overvelde
,
J. T.
,
Weaver
,
J. C.
,
Hoberman
,
C.
, and
Bertoldi
,
K.
,
2017
, “
Rational Design of Reconfigurable Prismatic Architected Materials
,”
Nature
,
541
(
7637
), pp.
347
352
. 10.1038/nature20824
26.
Chen
,
Y.
,
Peng
,
R.
, and
You
,
Z.
,
2015
, “
Origami of Thick Panels
,”
Science
,
349
(
6246
), pp.
396
400
. 10.1126/science.aab2870
27.
Novelino
,
L. S.
,
Ze
,
Q.
,
Wu
,
S.
,
Paulino
,
G. H.
, and
Zhao
,
R.
,
2020
, “
Untethered Control of Functional Origami Microrobots With Distributed Actuation
,”
Proc. Natl. Acad. Sci. U. S. A.
,
117
(
39
), pp.
24096
24101
. 10.1073/pnas.2013292117
28.
Zhai
,
Z.
,
Wang
,
Y.
, and
Jiang
,
H.
,
2018
, “
Origami-Inspired, On-Demand Deployable and Collapsible Mechanical Metamaterials With Tunable Stiffness
,”
Proc. Natl. Acad. Sci. U. S. A.
,
115
(
9
), pp.
2032
2037
. 10.1073/pnas.1720171115
29.
Fang
,
H.
,
Zhang
,
Y.
, and
Wang
,
K. W.
,
2017
, “
Origami-Based Earthworm-Like Locomotion Robots
,”
Bioinspir. Biomim.
,
12
(
6
), p.
065003
. 10.1088/1748-3190/aa8448
30.
Yasuda
,
H.
,
Tachi
,
T.
,
Lee
,
M.
, and
Yang
,
J.
,
2017
, “
Origami-Based Tunable Truss Structures for Non-Volatile Mechanical Memory Operation
,”
Nat. Commun.
,
8
(
1
), pp.
862
. 10.1038/s41467-017-00670-w
31.
Babaee
,
S.
,
Pajovic
,
S.
,
Rafsanjani
,
A.
,
Shi
,
Y.
,
Bertoldi
,
K.
, and
Traverso
,
G.
,
2020
, “
Bioinspired Kirigami Metasurfaces as Assistive Shoe Grips
,”
Nat. Biomed. Eng.
,
4
(
8
), pp.
778
786
. 10.1038/s41551-020-0564-3
32.
Yasuda
,
H.
, and
Yang
,
J.
,
2015
, “
Reentrant Origami-Based Metamaterials With Negative Poisson’s Ratio and Bistability
,”
Phys. Rev. Lett.
,
114
(
18
), p.
185502
. 10.1103/PhysRevLett.114.185502
33.
Yang
,
N.
,
Zhang
,
M.
, and
Zhu
,
R.
,
2020
, “
3D Kirigami Metamaterials With Coded Thermal Expansion Properties
,”
Extreme Mech. Lett.
,
40
, p.
100912
. 10.1016/j.eml.2020.100912
34.
Manimala
,
J. M.
, and
Sun
,
C. T.
,
2014
, “
Microstructural Design Studies for Locally Dissipative Acoustic Metamaterials
,”
J. Appl. Phys.
,
115
(
2
), p.
023518
. 10.1063/1.4861632
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