Optimal vibration absorbers are designed using the definition of H-infinity norm and numerical optimization. The cases of both constant amplitude excitation and rotating unbalance excitation are considered. The design procedure is quite general, and can easily handle multiple modes of vibration. A general procedure to construct a root loci plot is also developed. Using a cantilever beam, numerical results are presented.

References

1.
Den Hartog
,
J. P.
,
1985
,
Mechanical Vibrations
,
Dover Publications
, Mineola, NY.
2.
Sinha
,
A.
,
2010
,
Vibration of Mechanical Systems
,
Cambridge University Press
, Cambridge, UK.
3.
Sun
,
J. Q.
,
Jolly
,
M. R.
, and
Norris
,
M. A.
,
1995
, “
Passive, Adaptive and Active Tuned Vibration Absorbers—A Survey
,”
ASME J. Vib. Acoust.
,
117
(
B
), pp.
234
242
.10.1115/1.2838668
4.
Sinha
,
A.
,
2009
, “
Optimal Damped Vibration Absorber for Narrow Band Random Excitations: A Mixed H2/HOptimization
,”
Probab. Eng. Mech.
,
24
(
2
), pp.
251
254
.10.1016/j.probengmech.2008.06.005
5.
Pennestri
,
E.
,
1998
, “
An Application of Chebyshev's Min-Max Criterion to the Optimal Design of a Damped Dynamic Vibration Absorber
,”
J. Sound Vib.
,
217
(
4
), pp.
757
765
.10.1006/jsvi.1998.1805
6.
Zuo
,
L.
, and
Nayfeh
,
S. A.
,
2004
, “
Minimax Optimization of Multi-Degree-of-Freedom Tuned-Mass Dampers
,”
J. Sound Vib.
,
272
(
3–5
), pp.
893
908
.10.1016/S0022-460X(03)00500-5
7.
Brown
,
B.
, and
Singh
,
T.
,
2011
, “
Minimax Design of Vibration Absorbers for Linear Damped Systems
,”
J. Sound Vib.
,
330
(11), pp.
2437
2448
.10.1016/j.jsv.2010.12.002
8.
Sinha
,
A.
,
2007
,
Linear Systems: Optimal and Robust Control
,
CRC Press
, Boca Raton.
9.
Nishihara
,
O.
, and
Asami
,
T.
,
2002
, “
Closed-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers (Minimization of the Maximum Amplitude Magnification Factors)
,”
ASME J. Vib. Acoust.
,
124
(
4
), pp.
576
582
.10.1115/1.1500335
10.
Asami
,
T.
, and
Nishihara
,
O.
,
2003
, “
Closed-Form Exact Solution to HOptimization of Dynamic Vibration Absorbers (Application to Different Transfer Functions and Damping Systems)
,”
ASME J. Vib. Acoust.
,
125
(
3
), pp.
398
405
.10.1115/1.1569514
11.
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
.10.1016/j.jsv.2011.03.027
12.
Korenev
,
B. G.
, and
Reznikov
,
L. M.
,
1993
,
Dynamic Vibration Absorbers: Theory and Technical Applications
,
Wiley
, New York, pp.
32
38
.
13.
Kuo
,
B. C.
,
2000
,
Automatic Control Systems
,
Prentice-Hall
, Englewood Cliffs, NJ.
You do not currently have access to this content.