Abstract

When optimized, tuned mass dampers (TMDs) can effectively mitigate the vibration of the primary structure, because additional resonance and damping are introduced by the auxiliary mass-spring-damper system. Similar effect can be realized without auxiliary mass when an electromagnetic transducer shunt with the R-L-C resonant circuit is placed between the primary structure and the base. This paper is to analytically optimize the parameters of the R-L-C circuits for vibration mitigation. Both H2 and H optimization criteria are investigated, which are to minimize the root-mean-square (RMS) vibration under random excitation and the peak magnitude in the frequency domain, respectively. The concise closed-form solutions of the optimal parameters are then summarized together with the ones obtained the using fixed-point method, for practical implementation convenience. The H2 and H optimizations of energy harvesting are also discussed in this paper. Furthermore, we also investigate the sensitivity of system performances to the tuning parameter changes of the electromagnetic shunt circuit.

References

1.
Den Hartog
,
J. P.
,
1947
,
Mechanical Vibration
,
McGraw-Hill
,
New York
.
2.
Xu
,
K.
, and
Igusa
,
T.
,
1992
, “
Dynamic Characteristics of Multiple Substructures With Closely Spaced Frequencies
,”
Earthquake Eng. Struct. Dyn.
,
21
(
12
), pp.
1059
1070
.
3.
Yamaguchi
,
H.
, and
Hampornchai
,
N.
,
1993
, “
Fundamental Characteristics of Multiple Tuned Mass Dampers for Suppressing Harmonically Forced Oscillations
,”
Earthquake Eng. Struct. Dyn.
,
22
(
1
), pp.
51
62
.
4.
Zuo
,
L.
, and
Nayfeh
,
S.
,
2002
, “
Design of Multi-Degree-of-Freedom Tuned-Mass Dampers: A Minimax Approach
,”
AIAA
Paper No. 2002-1283.
5.
Snowdon
,
J.
,
1974
, “
Dynamic Vibration Absorbers That Have Increased Effectiveness
,”
ASME J. Eng. Ind.
,
96
(
3
), pp.
940
945
.
6.
Zuo
,
L.
,
2009
, “
Effective and Robust Vibration Control Using Series Multiple Tuned-Mass Dampers
,”
ASME J. Vib. Acoust.
,
131
(
3
), p.
031003
.
7.
Warburton
,
G.
,
1982
, “
Optimum Absorber Parameters for Various Combinations of Response and Excitation Parameters
,”
Earthquake Eng. Struct. Dyn.
,
10
(
3
), pp.
381
401
.
8.
Asami
,
T.
,
Nishihara
,
O.
, and
Baz
,
A. M.
,
2002
, “
Analytical Solutions to H∞ and H2 Optimization of Dynamic Vibration Absorber Attached to Damped Linear Systems
,”
ASME J. Vib. Acoust.
,
124
(2), pp.
67
78
.
9.
Forward
,
R. L.
,
1979
, “
Electronic Damping of Vibrations in Optical Structures
,”
Appl. Opt.
,
18
(
5
), pp.
690
697
.
10.
Hagood
,
N. W.
, and
von Flotow
,
A.
,
1991
, “
Damping of Structural Vibrations With Piezoelectric Materials and Passive Electrical Networks
,”
J. Sound Vib.
,
146
(
2
), pp.
243
268
.
11.
Moheimani
,
S. O. R.
,
2003
, “
A Survey of Recent Innovations in Vibration Damping and Control Using Shunted Piezoelectric Transducers
,”
IEEE Trans. Control Syst. Technol.
,
11
(
4
), pp.
482
494
.
12.
Lesieutre
,
G. A.
,
1998
, “
Vibration Damping and Control Using Shunted Piezoelectric Materials
,”
Shock Vib. Dig.
,
30
(
3
), pp.
187
195
.
13.
Behrens
,
S.
,
Fleming
,
A. J.
, and
Moheimani
,
S.
,
2003
, “
Electromagnetic Shunt Damping
,”
IEEE/ASME International Conference on Advanced Intelligent Mechatronics
(
AIM 2003
), Kobe, Japan, July 20–24, pp.
1145
1150
.
14.
Behrens
,
S.
,
Fleming
,
A. J.
, and
Moheimani
,
S.
,
2003
, “
Passive Vibration Control Via Electromagnetic Shunt Damping
,”
IEEE/ASME Trans. Mechatron.
,
10
(
1
), pp.
118
122
.
15.
Inoue
,
T.
,
Ishida
,
Y.
, and
Sumi
,
M.
,
2008
, “
Vibration Suppression Using Electromagnetic Resonant Shunt Damper
,”
ASME J. Vib. Acoust.
,
130
(
4
), p.
041003
.
16.
Zuo
,
L.
, and
Cui
,
W.
,
2013
, “
Dual-Functional Energy-Harvesting and Vibration Control: Electromagnetic Resonant Shunt Series Tuned Mass Dampers
,”
ASME J. Vib. Acoust.
,
135
(
5
), pp.
510181
510189
.
17.
Lefeuvre
,
E.
,
Audigier
,
D.
,
Richard
,
C.
, and
Guyomar
,
D.
,
2007
, “
Buck-Boost Converter for Sensorless Power Optimization of Piezoelectric Energy Harvester
,”
IEEE Trans. Power Electron.
,
22
(
5
), pp.
2018
2025
.
18.
Zhou
,
K.
,
Doyle
,
J. C.
, and
Glover
,
K.
,
1995
,
Robust and Optimal Control
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
19.
Gradshtenyn
,
I. S.
, and
Ryzhik
,
I. M.
,
1994
,
Table of Integrals Series, and Products
,
Academic Press
, Boston.
20.
Tang
,
X.
, and
Zuo
,
L.
,
2012
, “
Vibration Energy Harvesting From Random Force and Motion Excitations
,”
Smart Mater. Struct.
,
21
(
7
), p.
075025
.
21.
Nishihara
,
O.
, and
Asami
,
T.
,
2002
, “
Closed-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers
,”
ASME J. Vib. Acoust.
,
124
(
4
), pp.
576
582
.
22.
Tang
,
X.
, and
Zuo
,
L.
,
2011
, “
Enhanced Vibration Energy Harvesting Using Dual-Mass Systems
,”
J. Sound Vib.
,
330
(
21
), pp.
5199
5209
.
23.
Stephen
,
N. G.
,
2006
, “
On Energy Harvesting From Ambient Vibration
,”
J. Sound Vib.
,
293
(1–2), pp.
409
425
.
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