In this paper, inerter-based dynamic vibration absorbers (IDVAs) are applied in elastic metamaterials to broaden low-frequency band gaps. A discrete mass-spring lattice system and a distributed metamaterial beam carrying a periodic array of IDVAs are, respectively, considered. The IDVA consists of a spring and an inerter connected to a traditional mass-spring resonator. Compared to the traditional resonators, the special designed IDVAs generate two local-resonance (LR) band gaps for the discrete lattice system, a narrow low-frequency band gap and a wider high-frequency one. For the distributed IDVA-based metamaterial beam, in addition to the generated two separated LR band gaps, the Bragg band gap can also be significantly broadened and the three band gaps are very close to each other. Being able to amplify inertia, the IDVAs can be relatively light even operated for opening up low-frequency band gaps. When further introducing a dissipative damping mechanism into the IDVA-based metamaterials, the two close-split LR band gaps in the lattice system are merged into one wide band gap. As for the metamaterial beam with the dissipative IDVAs, an even wider band gap can be acquired due to the overlap of the adjacent LR and Bragg-scattering band gaps.

References

References
1.
Kushwaha
,
M. S.
,
Halevi
,
P.
,
Dobrzynski
,
L.
, and
Djafari-Rouhani
,
B.
,
1993
, “
Acoustic Band Structure of Periodic Elastic Composites
,”
Phys. Rev. Lett.
,
71
(
13
), p.
2022
.
2.
Hussein
,
M. I.
,
Hulbert
,
G. M.
, and
Scott
,
R. A.
,
2006
, “
Dispersive Elastodynamics of 1D Banded Materials and Structures: Design
,”
J. Sound Vib.
,
289
(
4–5
), pp.
779
806
.
3.
Vasseur
,
J. O.
,
Deymier
,
P. A.
,
Chenni
,
B.
,
Djafari-Rouhani
,
B.
,
Dobrzynski
,
L.
, and
Prevost
,
D.
,
2001
, “
Experimental and Theoretical Evidence for the Existence of Absolute Acoustic Band Gaps in Two-Dimensional Solid Phononic Crystals
,”
Phys. Rev. Lett.
,
86
(
14
), p.
3012
.
4.
Tanaka
,
Y.
,
Tomoyasu
,
Y.
, and
Tamura
,
S. I.
,
2000
, “
Band Structure of Acoustic Waves in Phononic Lattices: Two-Dimensional Composites With Large Acoustic Mismatch
,”
Phys. Rev. B
,
62
(
11
), pp.
7387
7392
.
5.
Mohammadi
,
S.
,
Eftekhar
,
A. A.
,
Khelif
,
A.
, and
Moubchir
,
H.
,
2007
, “
Complete Phononic Bandgaps and Bandgap Maps in Two-Dimensional Silicon Phononic Crystal Plates
,”
Electron. Lett.
,
43
(
16
), pp.
898
899
.
6.
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
.
7.
Mead
,
D. J.
,
1996
, “
Wave Propagation in Continuous Periodic Structures: Research Contributions From Southampton, 1964–1995
,”
J. Sound Vib.
,
190
(
3
), pp.
495
524
.
8.
Zhang
,
P.
, and
To
,
A. C.
,
2013
, “
Broadband Wave Filtering of Bioinspired Hierarchical Phononic Crystal
,”
Appl. Phys. Lett.
,
102
(
12
), p.
121910
.
9.
Vasseur
,
J. O.
,
Hladky-Hennion
,
A. C.
,
Djafari-Rouhani
,
B.
,
Duval
,
F.
,
Dubus
,
B.
, and
Pennec
,
Y.
,
2007
, “
Waveguiding in Two-Dimensional Piezoelectric Phononic Crystal Plates
,”
J. Appl. Phys.
,
101
(
11
), p.
114904
.
10.
Khelif
,
A.
,
Choujaa
,
A.
,
Benchabane
,
S.
,
Djafari-Rouhani
,
B.
, and
Laude
,
V.
,
2004
, “
Guiding and Bending of Acoustic Waves in Highly Confined Phononic Crystal Waveguides
,”
Appl. Phys. Lett.
,
84
(
22
), pp.
4400
4402
.
11.
Liu
,
Z.
,
Zhang
,
X. X.
,
Mao
,
Y. W.
,
Zhu
,
Y. Y.
,
Yang
,
Z. Y.
,
Chan
,
C. T.
, and
Sheng
,
P.
,
2000
, “
Locally Resonant Sonic Materials
,”
Science
,
289
(
5485
), pp.
1734
1736
.
12.
Fang
,
N.
,
Xi
,
D.
,
Xu
,
J.
,
Ambati
,
M.
,
Srituravanich
,
W.
,
Sun
,
C.
, and
Zhang
,
X.
,
2006
, “
Ultrasonic Metamaterials With Negative Modulus
,”
Nat. Mater.
,
5
(
6
), p.
452
.
13.
Liu
,
Z.
,
Chan
,
C. T.
, and
Sheng
,
P.
,
2005
, “
Analytic Model of Phononic Crystals With Local Resonances
,”
Phys. Rev. B
,
71
(
1
), p.
014103
.
14.
Chen
,
H.
,
Zeng
,
H.
,
Ding
,
C.
, and
Luo
,
C.
,
2012
, “
Double-Negative Acoustic Metamaterial Based on Hollow Steel Tube Meta-Atom
,”
J. Appl. Phys.
,
113
(
10
), p.
104902
.
15.
Lai
,
Y.
,
Wu
,
Y.
,
Sheng
,
P.
, and
Zhang
,
Z. Q.
,
2011
, “
Hybrid Elastic Solids
,”
Nat. Mater.
,
10
(
8
), p.
620
.
16.
Wang
,
G.
,
Wen
,
X.
,
Wen
,
J.
, and
Liu
,
Y. Z.
,
2006
, “
Quasi-One-Dimensional Periodic Structure With Locally Resonant Band Gap
,”
ASME J. Appl. Mech.
,
73
(
1
), pp.
167
170
.
17.
Liu
,
Y.
,
Yu
,
D.
,
Li
,
L.
,
Zhao
,
H.
,
Wen
,
J.
, and
Wen
,
X.
,
2007
, “
Design Guidelines for Flexural Wave Attenuation of Slender Beams With Local Resonators
,”
Phys. Lett. A
,
362
(
5–6
), pp.
344
347
.
18.
Yu
,
D.
,
Liu
,
Y.
,
Wang
,
G.
,
Cai
,
L.
, and
Qiu
,
J.
,
2006
, “
Low Frequency Torsional Vibration Gaps in the Shaft With Locally Resonant Structures
,”
Phys. Lett. A
,
348
(
3–6
), pp.
410
415
.
19.
Song
,
A.
,
Wang
,
X.
,
Chen
,
T.
,
Jiang
,
P.
, and
Bao
,
K.
,
2016
, “
Low-Frequency Bandgaps of Two-Dimensional Phononic Crystal Plate Composed of Asymmetric Double-Sided Cylinder Stubs
,”
Int. J. Mod. Phys. B
,
30
(
7
), pp.
2022
2158
.
20.
Lazarov
,
B. S.
, and
Jensen
,
J. S.
,
2007
, “
Low-Frequency Band Gaps in Chains With Attached Non-Linear Oscillators
,”
Int. J. Non-Linear Mech.
,
42
(
10
), pp.
1186
1193
.
21.
Jensen
,
J. S.
,
2003
, “
Phononic Band Gaps and Vibrations in One- and Two-Dimensional Mass–Spring Structures
,”
J. Sound Vib.
,
266
(
5
), pp.
1053
1078
.
22.
Xiao
,
Y.
,
Wen
,
J.
, and
Wen
,
X.
,
2012
, “
Broadband Locally Resonant Beams Containing Multiple Periodic Arrays of Attached Resonators
,”
Phys. Lett. A
,
376
(
16
), pp.
1384
1390
.
23.
Wang
,
T.
,
Sheng
,
M. P.
, and
Qin
,
Q. H.
,
2016
, “
Multi-Flexural Band Gaps in an Euler–Bernoulli Beam With Lateral Local Resonators
,”
Phys. Lett. A
,
380
(
4
), pp.
525
529
.
24.
Baravelli
,
E.
, and
Ruzzene
,
M.
,
2013
, “
Internally Resonating Lattices for Bandgap Generation and Low-Frequency Vibration Control
,”
J. Sound Vib.
,
332
(
25
), pp.
6562
6579
.
25.
Chen
,
Y. Y.
,
Barnhart
,
M. V.
,
Chen
,
J. K.
,
Hu
,
G. K.
,
Sun
,
C. T.
, and
Huang
,
G. L.
,
2016
, “
Dissipative Elastic Metamaterials for Broadband Wave Mitigation at Subwavelength Scale
,”
Compos. Struct.
,
136
, pp.
358
371
.
26.
Tan
,
K. T.
,
Huang
,
H. H.
, and
Sun
,
C. T.
,
2012
, “
Optimizing the Band Gap of Effective Mass Negativity in Acoustic Metamaterials
,”
Appl. Phys. Lett.
,
101
(
24
), p.
241902
.
27.
Khajehtourian
,
R.
, and
Hussein
,
M. I.
,
2014
, “
Dispersion Characteristics of a Nonlinear Elastic Metamaterial
,”
AIP Adv.
,
4
(
12
), pp.
377
382
.
28.
Nadkarni
,
N.
,
Daraio
,
C.
, and
Kochmann
,
D. M.
,
2014
, “
Dynamics of Periodic Mechanical Structures Containing Bistable Elastic Elements: From Elastic to Solitary Wave Propagation
,”
Phys. Rev. E
,
90
(
2
), p.
023204
.
29.
Wang
,
P.
,
Casadei
,
F.
,
Shan
,
S.
,
Weaver
,
J. C.
, and
Bertoldi
,
K.
,
2014
, “
Harnessing Buckling to Design Tunable Locally Resonant Acoustic Metamaterials
,”
Phys. Rev. Lett.
,
113
(
1
), p.
014301
.
30.
Xiao
,
Y.
,
Wen
,
J.
,
Yu
,
D.
, and
Wen
,
X.
,
2013
, “
Flexural Wave Propagation in Beams With Periodically Attached Vibration Absorbers: Band-Gap Behavior and Band Formation Mechanisms
,”
J. Sound Vib.
,
332
(
4
), pp.
867
893
.
31.
Xiao
,
Y.
,
Mace
,
B. R.
,
Wen
,
J.
, and
Wen
,
X.
,
2011
, “
Formation and Coupling of Band Gaps in a Locally Resonant Elastic System Comprising a String With Attached Resonators
,”
Phys. Lett. A
,
375
(
12
), pp.
1485
1491
.
32.
Frandsen
,
N. M.
,
Bilal
,
O. R.
,
Jensen
,
J. S.
, and
Hussein
,
M. I.
,
2016
, “
Inertial Amplification of Continuous Structures: Large Band Gaps From Small Masses
,”
J. Appl. Phys.
,
119
(
12
), p.
124902
.
33.
Smith
,
M. C.
,
2002
, “
Synthesis of Mechanical Networks: The Inerter
,”
IEEE Trans. Autom. Control
,
47
(
10
), pp.
1648
1662
.
34.
Ge
,
Z.
, and
Wang
,
W.
,
2018
, “
Modeling, Testing, and Characteristic Analysis of a Planetary Flywheel Inerter
,”
Shock Vib.
,
2018
, p. 2631539.
35.
Shen
,
Y.
,
Chen
,
L.
,
Yang
,
X.
,
Shi
,
D.
, and
Yang
,
J.
,
2016
, “
Improved Design of Dynamic Vibration Absorber by Using the Inerter and Its Application in Vehicle Suspension
,”
J. Sound Vib.
,
361
, pp.
148
158
.
36.
Smith
,
M. C.
, and
Wang
,
F. C.
,
2004
, “
Performance Benefits in Passive Vehicle Suspensions Employing Inerters
,”
Veh. Syst. Dyn.
,
42
(
4
), pp.
235
257
.
37.
Lazar
,
I. F.
,
Neild
,
S. A.
, and
Wagg
,
D. J.
,
2014
, “
Using an Inerter-Based Device for Structural Vibration Suppression
,”
Earthquake Eng. Struct. Dyn.
,
43
(
8
), pp.
1129
1147
.
38.
Hu
,
Y.
,
Chen
,
M. Z. Q.
, and
Shu
,
Z.
,
2014
, “
Passive Vehicle Suspensions Employing Inerters With Multiple Performance Requirements
,”
J. Sound Vib.
,
333
(
8
), pp.
2212
2225
.
39.
Hu
,
Y.
, and
Chen
,
M. Z. Q.
,
2015
, “
Performance Evaluation for Inerter-Based Dynamic Vibration Absorbers
,”
Int. J. Mech. Sci.
,
99
, pp.
297
307
.
40.
Brzeski
,
P.
,
Pavlovskaia
,
E.
,
Kapitaniak
,
T.
, and
Perlikowski
,
P.
,
2015
, “
The Application of Inerter in Tuned Mass Absorber
,”
Int. J. Non-Linear Mech.
,
70
, pp.
20
29
.
41.
Kulkarni
,
P. P.
, and
Manimala
,
J. M.
,
2016
, “
Longitudinal Elastic Wave Propagation Characteristics of Inertant Acoustic Metamaterials
,”
J. Appl. Phys.
,
119
(
24
), p.
245101
.
42.
Kulkarni
,
P. P.
, and
Manimala
,
J. M.
,
2018
, “
Nonlinear and Inertant Acoustic Metamaterials and Their Device Implications
,”
Dynamic Behavior of Materials
, Vol.
1
,
Springer
,
Cham, Switzerland
, pp.
217
234
.
43.
Lee
,
U.
,
2009
,
Spectral Element Method in Structural Dynamics
,
Wiley
,
Singapore
.
44.
Xiao
,
Y.
,
Wen
,
J.
,
Wang
,
G.
, and
Wen
,
X.
,
2013
, “
Theoretical and Experimental Study of Locally Resonant and Bragg Band Gaps in Flexural Beams Carrying Periodic Arrays of Beam-Like Resonators
,”
J. Sound Vib.
,
135
(
4
), p.
041006
.
45.
Wang
,
F. C.
,
Hong
,
M. F.
, and
Lin
,
T. C.
,
2011
, “
Designing and Testing a Hydraulic Inerter
,”
Proc. Inst. Mech. Eng., Part C
,
225
(
1
), pp.
66
72
.
46.
Evangelou
,
S.
,
Sharp
,
R.
, and
Smith
,
M.
,
2006
, “
Control of Motorcycle Steering Instabilities-Passive Mechanical Compensators Incorporating Inerters
,”
IEEE Control Syst. Mag.
,
26
(
5
), pp.
78
88
.
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