In this study, a novel passive vibration control device, the three-element vibration absorber–inerter (TEVAI) is proposed. Inerter-based vibration absorbers, which utilize a mass that rotates due to relative translational motion, have recently been developed to take advantage of the potential high inertial mass (inertance) of a relatively small mass in rotation. In this work, a novel configuration of an inerter-based absorber is proposed, and its effectiveness at suppressing the vibration of a single-degree-of-freedom system is investigated. The proposed device is a development of two current passive devices: the tuned-mass-damper–inerter (TMDI), which is an inerter-base tuned mass damper (TMD), and the three-element dynamic vibration absorber (TEVA). Closed-form optimization solutions for this device connected to a single-degree-of-freedom primary structure and loaded with random base excitation are developed and presented. Furthermore, the effectiveness of this novel device, in comparison to the traditional TMD, TEVA, and TMDI, is also investigated. The results of this study demonstrate that the TEVAI possesses superior performance in the reduction of the maximum and root-mean-square (RMS) response of the underlying structure in comparison to the TMD, TEVA, and TMDI.

References

1.
Frahm
,
H.
,
1909
, “
Device for Damping Vibrations of Bodies
,” U.S. Patent No.
989958A
.https://patents.google.com/patent/US989958A/en
2.
Gutierrez Soto
,
M.
, and
Adeli
,
H.
,
2013
, “
Tuned Mass Dampers
,”
Arch. Comput. Methods Eng.
,
20
(
4
), pp.
419
431
.
3.
Den Hartog
,
J.
,
1956
,
Mechanical Vibrations
,
McGraw-Hill
,
New York
.
4.
Asami
,
T.
,
Nishihara
,
O.
, and
Baz
,
A. M.
,
2002
, “
Analytical Solutions to H∞ and H2 Optimization of Dynamic Vibration Absorbers Attached to Damped Linear Systems
,”
ASME J. Vib. Acoust.
,
124
(
2
), pp.
284
295
.
5.
Asami
,
T.
, and
Nishihara
,
O.
,
2003
, “
Closed-Form Exact Solution to H∞ Optimization of Dynamic Vibration Absorbers (Application to Different Transfer Functions and Damping Systems)
,”
ASME J. Vib. Acoust.
,
125
(
3
), pp.
398
405
.
6.
Warburton
,
G. B.
,
1981
, “
Optimum Absorber Parameters for Minimizing Vibration Response
,”
Earthquake Eng. Struct. Dyn.
,
9
(
3
), pp.
251
262
.
7.
Warburton
,
G. B.
,
1982
, “
Optimum Absorber Parameters for Various Combinations of Response and Excitation Parameters
,”
Earthquake Eng. Struct. Dyn.
,
10
(
3
), pp.
381
401
.
8.
Bakre
,
S. V.
, and
Jangid
,
R. S.
,
2007
, “
Optimum Parameters of Tuned Mass Damper for Damped Main System
,”
Struct. Control Health Monit.
,
14
(
3
), pp.
448
470
.
9.
Bekdaş
,
G.
, and
Nigdeli
,
S. M.
,
2011
, “
Estimating Optimum Parameters of Tuned Mass Dampers Using Harmony Search
,”
Eng. Struct.
,
33
(
9
), pp.
2716
2723
.
10.
Leung
,
A. Y. T.
,
Zhang
,
H.
,
Cheng
,
C. C.
, and
Lee
,
Y. Y.
,
2008
, “
Particle Swarm Optimization of TMD by Non‐Stationary Base Excitation During Earthquake
,”
Earthquake Eng. Struct. Dyn.
,
37
(
9
), pp.
1223
1246
.
11.
Spencer
,
B. F.
, Jr.
, and
Nagarajaiah
,
S.
,
2003
, “
State of the Art of Structural Control
,”
J. Struct. Eng.
,
129
(
7
), pp.
845
856
.
12.
Abe
,
M.
, and
Fujino
,
Y.
,
1994
, “
Dynamic Characterization of Multiple Tuned Mass Dampers and Some Design Formulas
,”
Earthquake Eng. Struct. Dyn.
,
23
(
8
), pp.
813
835
.
13.
Zuo
,
L.
,
2009
, “
Effective and Robust Vibration Control Using Series Multiple Tuned-Mass Dampers
,”
ASME J. Vib. Acoust.
,
131
(
3
), p.
031003
.
14.
Ren
,
M. Z.
,
2001
, “
A Variant Design of the Dynamic Vibration Absorber
,”
J. Sound Vib.
,
245
(
4
), pp.
762
770
.
15.
Cheung
,
Y. L.
, and
Wong
,
W. O.
,
2011
, “
H2 Optimization of a Non-Traditional Dynamic Vibration Absorber for Vibration Control of Structures Under Random Force Excitation
,”
J. Sound Vib.
,
330
(
6
), pp.
1039
1044
.
16.
Cheung
,
Y. L.
, and
Wong
,
W. O.
,
2011
, “
H-Infinity Optimization of a Variant Design of the Dynamic Vibration Absorber—Revisited and New Results
,”
J. Sound Vib.
,
330
(
16
), pp.
3901
3912
.
17.
Asami
,
T.
, and
Nishihara
,
O.
,
2002
, “
H2 Optimization of the Three-Element Type Dynamic Vibration Absorbers
,”
ASME J. Vib. Acoust.
,
124
(
4
), pp.
583
592
.
18.
Asami
,
T.
, and
Nishihara
,
O.
,
1999
, “
Analytical and Experimental Evaluation of an Air Damped Dynamic Vibration Absorber: Design Optimizations of the Three-Element Type Model
,”
ASME J. Vib. Acoust.
,
121
(
3
), pp.
334
342
.
19.
Anh
,
N. D.
,
Nguyen
,
N. X.
, and
Hoa
,
L. T.
,
2013
, “
Design of Three-Element Dynamic Vibration Absorber for Damped Linear Structures
,”
J. Sound Vib.
,
332
(
19
), pp.
4482
4495
.
20.
Smith
,
M. C.
,
2002
, “
Synthesis of Mechanical Networks: The Inerter
,”
IEEE Trans. Autom. Control
,
47
(
10
), pp.
1648
1662
.
21.
Papageorgiou
,
C.
, and
Smith
,
M. C.
,
2005
, “
Laboratory Experimental Testing of Inerters
,”
44th IEEE Conference on Decision and Control and European Control Conference
(
CDC-ECC
), Seville, Spain, Dec. 15, pp.
3351
3356
.
22.
Garrido
,
H.
,
Curadelli
,
O.
, and
Ambrosini
,
D.
,
2013
, “
Improvement of Tuned Mass Damper by Using Rotational Inertia Through Tuned Viscous Mass Damper
,”
Eng. Struct.
,
56
, pp.
2149
2153
.
23.
Hwang
,
J.-S.
,
Kim
,
J.
, and
Kim
,
Y.-M.
,
2007
, “
Rotational Inertia Dampers With Toggle Bracing for Vibration Control of a Building Structure
,”
Eng. Struct.
,
29
(
6
), pp.
1201
1208
.
24.
Ikago
,
K.
,
Saito
,
K.
, and
Inoue
,
N.
,
2012
, “
Seismic Control of Single-Degree-of-Freedom Structure Using Tuned Viscous Mass Damper: The Tuned Viscous Mass Damper
,”
Earthquake Eng. Struct. Dyn.
,
41
(
3
), pp.
453
474
.
25.
Hu
,
Y.
, and
Chen
,
M. Z. Q.
,
2015
, “
Performance Evaluation for Inerter-Based Dynamic Vibration Absorbers
,”
Int. J. Mech. Sci.
,
99
, pp.
297
307
.
26.
Javidialesaadi
,
A.
, and
Wierschem
,
N. E.
,
2018
, “
Optimal Design of Rotational Inertial Double Tuned Mass Dampers Under Random Excitation
,”
Eng. Struct.
,
165
, pp.
412
421
.
27.
Lazar
,
I. F.
,
Neild
,
S. A.
, and
Wagg
,
D. J.
,
2016
, “
Vibration Suppression of Cables Using Tuned Inerter Dampers
,”
Eng. Struct.
,
122
, pp.
62
71
.
28.
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
.
29.
Chen
,
M. Z. Q.
,
Hu
,
Y.
,
Li
,
C.
, and
Chen
,
G.
,
2016
, “
Application of Semi-Active Inerter in Semi-Active Suspensions Via Force Tracking
,”
ASME J. Vib. Acoust.
,
138
(
4
), p.
041014
.
30.
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
.
31.
Marian
,
L.
, and
Giaralis
,
A.
,
2014
, “
Optimal Design of a Novel Tuned Mass-Damper–Inerter (TMDI) Passive Vibration Control Configuration for Stochastically Support-Excited Structural Systems
,”
Probab. Eng. Mech.
,
38
, pp.
156
164
.
32.
Giaralis
,
A.
, and
Petrini
,
F.
,
2017
, “
Wind-Induced Vibration Mitigation in Tall Buildings Using the Tuned Mass-Damper-Inerter
,”
J. Struct. Eng.
,
143
(
9
), p.
04017127
.
33.
Masri
,
S. F.
, and
Caffrey
,
J. P.
,
2017
, “
Transient Response of a SDOF System With an Inerter to Nonstationary Stochastic Excitation
,”
ASME J. Appl. Mech.
,
84
(
4
), p.
041005
.
34.
Giaralis
,
A.
, and
Taflanidis
,
A. A.
,
2017
, “
Optimal Tuned Mass-Damper-Inerter (TMDI) Design for Seismically Excited MDOF Structures With Model Uncertainties Based on Reliability Criteria
,”
Struct. Control Health Monit.
,
25
(
2
), p.
e2082
.
35.
Pietrosanti
,
D.
,
De Angelis
,
M.
, and
Basili
,
M.
,
2017
, “
Optimal Design and Performance Evaluation of Systems With Tuned Mass Damper Inerter (TMDI)
,”
Earthquake Eng. Struct. Dyn.
,
46
(
8
), pp.
1367
1388
.
36.
Javidialesaadi
,
A.
, and
Wierschem
,
N.
,
2017
, “
Seismic Performance Evaluation of Inerter-Based Tuned Mass Dampers Dampers
,”
3RD Huixian International Forum on Earthquake Engineering for Young Researchers
,
University of Illinois
,
Urbana-Champaign, IL
.
37.
Asai
,
T.
,
Ikago
,
K.
, and
Araki
,
Y.
,
2015
, “
Outrigger Tuned Viscous Mass Damping System for High-Rise Buildings Subject to Earthquake Loadings
,”
Sixth International Conference on Advances in Experimental Structural Engineering
, Urbana-Champaign, IL, Aug. 1–2.http://sstl.cee.illinois.edu/papers/aeseancrisst15/214_Asai_Outrigger.pdf
38.
Zuo
,
L.
, and
Nayfeh
,
S. A.
,
2006
, “
The Two-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation
,”
ASME J. Vib. Acoust.
,
128
(
1
), pp.
56
65
.
39.
Gradshtein, I. S., Ryzhik, I. M., and Jeffrey, A.,
2007
,
Table of Integrals Series, and Products
,
Academic Press
, Amsterdam, The Netherlands.
40.
James
,
H. M.
, Nichols, N. B., and Phillips, R. S., eds.,
1947
,
Theory of Servomechanisms
,
McGraw-Hill
,
New York
.
41.
Chen
,
M. Z. Q.
,
Hu
,
Y.
,
Huang
,
L.
, and
Chen
,
G.
,
2014
, “
Influence of Inerter on Natural Frequencies of Vibration Systems
,”
J. Sound Vib.
,
333
(
7
), pp.
1874
1887
.
42.
Cheung
,
Y. L.
, and
Wong
,
W. O.
,
2009
, “
H∞ and H2 Optimizations of a Dynamic Vibration Absorber for Suppressing Vibrations in Plates
,”
J. Sound Vib.
,
320
(
1–2
), pp.
29
42
.
43.
MathWorks,
2016
,
MATLAB R2016b-Academic Use
,
The Mathworks Inc.
,
Natick, MA
.
44.
Gonzalez-Buelga
,
A.
,
Lazar
,
I. F.
,
Jiang
,
J. Z.
,
Neild
,
S. A.
, and
Inman
,
D. J.
,
2017
, “
Assessing the Effect of Nonlinearities on the Performance of a Tuned Inerter Damper: Effect of Nonlinearities on a Tuned Inerter Damper Performance
,”
Struct. Control Health Monit.
,
24
(
3
), p.
e1879
.
45.
Sugimura
,
Y.
,
Goto
,
W.
,
Tanizawa
,
H.
,
Saito
,
K.
, and
Nimomiya
,
T.
,
2012
, “
Response Control Effect of Steel Building Structure Using Tuned Viscous Mass Damper
,”
15th World Conference on Earthquake Engineering
(
WCEE
), Lisbon, Portugal, Sept. 24–28.http://www.iitk.ac.in/nicee/wcee/article/WCEE2012_0138.pdf
46.
Asai
,
T.
, and
Watanabe
,
Y.
,
2017
, “
Outrigger Tuned Inertial Mass Electromagnetic Transducers for High-Rise Buildings Subject to Long Period Earthquakes
,”
Eng. Struct.
,
153
, pp.
404
410
.
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