This work presents a new strategy in design optimization of nonlinear vibration absorbers with continuous and discontinuous motions. A cluster-based harmonic balance aided optimization technique using force balance or energy balance as the basis is generalized and adapted for nonlinear systems. It is found that optimal design parameters form a cluster in the parameter space and points from the parameter space inside the cluster satisfies design considerations. One of the main disadvantages of using existing optimization methods in nonlinear systems is that the parameter regimes, which provide periodic solutions, are not known beforehand, so one has to first do bifurcation studies to arrive at periodic regimes and optimization has to be conducted in the range. Proposed method combines these two steps as it converges to periodic clusters alone. Since the method admits only periodic solutions, occurrence of conditions such as chaos and quasi periodicity can be eliminated from the dynamics of the system. The proposed method can also be used to find the optimal parameters of both linear and nonlinear dynamical systems.

References

References
1.
Watts
,
P.
,
1883
, “
On the Method of Reducing the Rolling of Ships at Sea
,”
Trans. Inst. Naval Archit.
,
24
, pp.
165
190
.http://mararchief.tudelft.nl/catalogue/entries/16328/
2.
Frahm
,
H.
,
1911
, “
A Device for Damping Vibrations of Bodies
,” U.S. Patent No. 989,958.
3.
Den Hartog
,
J. P.
, and
Ormondroyd
,
J.
,
1928
, “
The Theory of Dynamical Vibration Absorber
,”
ASME J. Appl. Mech.
,
50
(
7
), pp.
9
22
.
4.
Den Hartog
,
J. P.
,
1985
,
Mechanical Vibrations
,
Dover Books on Engineering
,
McGraw Hill, New York
.
5.
Hunt
,
J.
, and
Nissen
,
J. C.
,
1982
, “
The Broadband Dynamic Vibration Absorber
,”
J. Sound Vib.
,
83
(
4
), pp.
573
578
.
6.
Soom
,
A.
, and
Lee
,
M.
,
1983
, “
Optimal Design of Linear and Nonlinear Vibration Absorbers for Damped Systems
,”
ASME J. Vib. Acoust., Stress, Reliab. Des.
,
105
(
1
), pp.
112
119
.
7.
Burton
,
T. D.
,
1994
,
Introduction to Dynamic System Analysis
,
McGraw-Hill
, New York.
8.
Narayanan
,
M. D.
,
Narayanan
,
S.
, and
Padmanabhan
,
C.
,
2007
, “
Nonlinear System Identification Using Multiple Trials
,”
Nonlinear Dyn.
,
48
(
4
), pp.
341
360
.
9.
Balaram
,
B.
,
Narayanan
,
M. D.
, and
Rajendra
,
P. K.
,
2012
, “
Kumar. Optimal Design of Multi-Parametric Nonlinear Systems Using a Parametric Continuation Based Genetic Algorithm Approach
,”
Nonlinear Dyn.
,
67
(
4
), pp.
2759
2777
.
10.
Thothadri
,
M.
,
Casas
,
R. A.
,
Moon
,
F. C.
,
D'Andrea
,
R.
, and
Johnson, Jr.
,
C. R.
,
2003
, “
Nonlinear System Identification of Multi-Degree-of-Freedom Systems
,”
Nonlinear Dyn.
,
32
(
3
), pp.
307
322
.
11.
Den Hartog
,
J. P.
,
1930
, “
Forced Vibrations With Combined Viscous and Coulomb Damping
,”
Philadelphia Mag.
,
9
(
59
), pp. 801–817.
12.
Fang
,
J.
, and
Wang
,
Q.
,
2012
, “
Min-Max Criterion to the Optimal Design of Vibration Absorber in a System With Coulomb Friction and Viscous Damping
,”
J. Nonlinear Dyn.
,
70
(1), pp. 393–400.
13.
Ricciardelli
,
F.
, and
Vickery
,
B. J.
,
1999
, “
Tuned Vibration Absorbers With Dry Friction Damping
,”
Earthquake Eng. Struct. Dyn.
,
28
(
7
), pp.
707
723
.
14.
Marcus
,
A. L.
, and
Roitman
,
N.
,
2005
, “
Vibration Reduction Using Passive Absorption System With Coulomb Damping
,”
Mech. Syst. Signal Process.
,
19
(3), pp.
537
549
.
15.
Hundal
,
M. S.
,
1979
, “
Response of a Base Excited System With Viscous and Coulomb Damping
,”
J. Sound Vib.
,
64
(
3
), pp. 371–378.
16.
Leine
,
R. I.
,
van Campen
,
D. H.
,
de Kraker
,
A.
, and
van den Steen
,
L.
,
1998
, “
Stick-Slip Vibrations Induced by Alternate Friction Models
,”
Nonlinear Dyn.
,
16
(
1
), pp.
41
54
.
17.
Liang
,
J.
, and
Feeny
,
B.
,
2011
, “
Balancing Energy to Estimate Damping in a Forced Oscillator With Compliant Contact
,”
J. Sound Vib.
,
330
(
9
), pp.
2049
2061
.
18.
Liang
,
J.
, and
Feeny
,
B.
,
2006
, “
Balancing Energy to Estimate Damping Parameters in Forced Oscillators
,”
J. Sound Vib.
,
295
(
3–5
), pp.
988
998
.
19.
Rao
,
S. S.
,
2012
,
Engineering Optimization, Theory and Practice
,
3rd ed.
,
Wiley Interscience
,
New York
.
20.
Inaudi
,
J. A.
, and
Kelly
,
J. M.
,
1995
, “
Mass Damper Using Friction Dissipation Devices
,”
Eng. Mech.
,
121
(
1
), pp.
142
149
.
21.
Gordon
,
C. K. Y.
,
1966
, “
Forced Vibrations of a Two Degree of Freedom System With Combined Couloumb and Viscous Damping
,”
J. Acoust. Soc
.,
39
(
1
), pp.
14
24
.
22.
Hoffman
,
J.
,
1992
,
Numerical Methods for Scientists and Engineers
,
McGraw-Hill
,
New York
.
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