The effect of electromagnetic actuation (EMA) on the dynamic of a single-sided Hertzian contact forced oscillator is studied near primary and secondary resonances. Emphasis is put on the case where two symmetric EMAs are introduced, such that one is driven by a DC actuation and the other is actuated by AC actuation with a fast frequency. An averaging technique and a perturbation analysis are performed to obtain the frequency response of the system. It is shown that for appropriate values of AC, forced Hertzian contact systems are more likely to remain operating in the linear regime without the loss of contact near certain resonances.

References

References
1.
Nayak
,
R.
,
1972
, “
Contact Vibrations
,”
J. Sound Vib.
,
22
(
3
), pp.
297
322
.10.1016/0022-460X(72)90168-X
2.
Hess
,
D.
, and
Soom
,
A.
,
1991
, “
Normal Vibrations and Friction Under Harmonic Loads: Part 1-Hertzian Contact
,”
ASME J. Tribol.
,
113
(
1
), pp.
80
86
.10.1115/1.2920607
3.
Sabot
,
J.
,
Krempf
,
P.
, and
Janolin
,
C.
,
1998
, “
Nonlinear Vibrations of a Sphere-Plane Contact Excited by a Normal Load
,”
J. Sound Vib.
,
214
(
2
), pp.
359
375
.10.1006/jsvi.1998.1582
4.
Soom
,
A.
, and
Chen
,
J. W.
,
1986
, “
Simulation of Random Surface Roughness-Induced Contact Vibrations at Hertzian Contacts During Steady Sliding
,”
ASME J. Tribol.
,
108
(
1
), pp.
123
127
.10.1115/1.3261131
5.
Rigaud
,
E.
, and
Perret-Liaudet
,
J.
,
2003
, “
Experiments and Numerical Results on Nonlinear Vibrations of an Impacting Hertzian Contact. Part 1: Harmonic Excitation
,”
J. Sound Vib.
,
265
(
2
), pp.
289
307
.10.1016/S0022-460X(02)01262-2
6.
Perret-Liaudet
,
J.
, and
Rigaud
,
E.
,
2003
, “
Experiments and Numerical Results on Non-Linear Vibrations of an Impacting Hertzian Contact. Part 2: Random Excitation
,”
J. Sound Vib.
,
265
(
2
), pp.
309
327
.10.1016/S0022-460X(02)01267-1
7.
Perret-Liaudet
,
J.
, and
Rigaud
,
E.
,
2006
, “
Response of an Impacting Hertzian Contact to an Order-2 Subharmonic Excitation: Theory and Experiments
,”
J. Sound Vib.
,
296
(
1–2
), pp.
319
333
.10.1016/j.jsv.2006.03.004
8.
Perret-Liaudet
,
J.
, and
Rigaud
,
E.
,
2007
, “
Superharmonic Resonance of Order 2 for an Impacting Hertzian Contact Oscillator: Theory and Experiments
,”
ASME J. Comput. Nonlinear Dyn.
,
2
(
2
), pp.
190
196
.10.1115/1.2447549
9.
Bichri
,
A.
,
Belhaq
,
M.
, and
Perret-Liaudet
,
J.
,
2011
, “
Control of Vibroimpact Dynamic of a Single-Sided-Hertzian Contact Forced Oscillator
,”
Nonlinear Dyn.
,
63
(
1–2
), pp.
51
60
.10.1007/s11071-010-9784-5
10.
Bichri
,
A.
, and
Belhaq
,
M.
,
2012
, “
Control of a Forced Impacting Hertzian Contact Oscillator Near Sub- and Superharmonics of Order 2
,”
ASME J. Comput. Nonlinear Dyn.
,
7
(
1
), pp.
22
28
.10.1115/1.4004309
11.
Chang
,
S. C.
, and
Ling
,
H. P.
,
2005
, “
Nonlinear Dynamics and Chaos Control for an Electromagnetic System
,”
J. Sound Vib.
,
279
(
1–2
), pp.
327
344
.10.1016/j.jsv.2003.11.033
12.
Gospodaric
,
B.
,
Voncina
,
D.
, and
Bucar
,
B.
,
2007
, “
Active Electromagnetic Damping of Laterally Vibrating Ferromagnetic Cantilever Beam
,”
Mechatronics
,
17
(
6
), pp.
291
298
.10.1016/j.mechatronics.2007.04.002
13.
Fung
,
R. F.
,
Liu
,
Y. T.
, and
Wang
,
C. C.
,
2005
, “
Dynamic Model of an Electromagnetic Actuator for Vibration Control of a Cantilever Beam With a Tip Mass
,”
J. Sound Vib.
,
288
(
4–5
), pp.
957
980
.10.1016/j.jsv.2005.01.046
14.
Sokolov
,
I. J.
,
Babitsky
,
V. I.
, and
Halliwell
,
N. A.
,
2007
, “
Autoresonant Vibro-Impact System With Electromagnetic Excitation
,”
J. Sound Vib.
,
308
(
3–5
), pp.
375
391
.10.1016/j.jsv.2007.04.010
15.
Der Hagopian
,
J.
, and
Mahfoud
,
J.
,
2010
, “
Electromagnetic Actuator Design for the Control of Light Structures
,”
Smart Struct. Syst.
,
6
(
1
), pp.
29
38
.10.12989/sss.2010.6.1.029
16.
Belhaq
,
M.
,
Bichri
,
A.
,
Der Hogapian
,
J.
, and
Mahfoud
,
J.
,
2011
, “
Effect of Electromagnetic Actuations on the Dynamics of a Harmonically Excited Cantilever Beam
,”
Int. J. Nonlinear Mech.
,
46
(
6
), pp.
828
838
.10.1016/j.ijnonlinmec.2011.03.001
17.
Johnson
,
K. L.
,
1979
,
Contact Mechanics
,
Cambridge University
,
Cambridge, MA
.
18.
Ajibose
,
O. K.
,
Wiercigroch
,
M.
,
Pavlovskaia
,
E.
, and
Akisanya
,
A. R.
,
2010
, “
Global and Local Dynamics of Drifting Oscillator for Different Contact Force Models
,”
Int. J. Nonlinear Mech.
,
45
(
9
), pp.
850
858
.10.1016/j.ijnonlinmec.2009.11.017
19.
Nayfeh
,
A. H.
, and
Mook
,
D. T.
,
1979
,
Nonlinear Oscillations
,
Wiley
,
NY
.
20.
Blekhman
,
I. I.
,
2000
,
Vibrational Mechanics—Nonlinear Dynamic Effects, General Approach, Application
,
World Scientific
,
Singapore
.
21.
Thomsen
,
J. J.
,
2003
,
Vibrations and Stability: Advanced Theory, Analysis, and Tools
,
Springer-Verlag
,
Berlin, Germany
.
You do not currently have access to this content.