Multibody systems with many friction contacts not being decoupled by some force laws afford a special treatment with respect to the uniqueness of the solution after a contact event. This problem can be solved by an optimization technique including unequality constraints which corresponds exactly to the physical properties of stick-slip vibrations. The theoretical background to this complementarity problem is presented and illustrated by examples from machine dynamics.

Issue Section:
Research Papers
Topics:
Stick-slip, Vibration, Friction, Machine dynamics, Multibody systems, Optimization
1.
Be´ghin, H., 1924–1925, “Sur l’inde´termination de certains proble´mesde frottement,” Nouvelles Annales. 5e se´rie, No. 3, pp. 343–347.
2.
Brandl
H.
, and
Hajek
M.
,
1988
, “
Mechanische Systeme mit Trockenreibung
,”
ZAMM 68
, Vol.
4
, pp.
59
–
61
.
3.
Cottle
R. W.
, and
Dantzig
G. B.
,
1968
, “
Complementary Pivot Theory of Mathematical Programming
,”
Linear Algebra and Its Applications
, Vol.
1
, pp.
103
–
125
.
4.
Glocker
Ch.
, and
Pfeiffer
F.
,
1992
, “
Dynamical Systems with Unilateral Contacts
,”
Nonlinear Dynamics
, Vol.
3
, pp.
245
–
259
.
5.
Hajek, M., 1990, “Reibungsda¨mpfer fu¨r Turbinenlaufschaufeln,” Fortschr.-Ber. VDI., Reihe 11, Nr. 128, Du¨sseldorf, VDI Verlag.
6.
Karamardian
S.
,
1969
, “
The Nonlinear Complementarity Problem with Applications
,” Parts 1, 2.
J. of Optimization Theory and Apllication
, Vol.
4
, No.
3
, pp.
167
–
180
.
7.
Lemke, C. E., 1970, “Recent Results on Complementarity Problems,” Rosen, J. B. et al., eds., Nonlinear Programming. Academic Press, New York, pp. 349–384.
8.
Lo¨tstedt, P., 1981, “Coulomb Friction in Two-Dimensional Rigid Body Systems,” ZAMM 61, pp. 605–615.
9.
Lo¨tstedt
P.
,
1982
, “
Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints
,”
SIAM J. Appl. Math.
, Vol.
42
, No.
2
, April, pp.
281
–
296
.
10.
Moreau, J. J., 1988, “Nonsmooth Mechanics and Applications, Chapter: Unilateral Contact and Dry Friction in Finite Freedom Dynamics,” CISIW Courses and Lectures, Springer-Verlag, Wien-New York.
11.
Moreau, J. J., 1985, “Unilateral Problems in Structural Analysis, Chapter: Standard Inelastic Shocks and the Dynamics of Unilateral Constraints,” CISM Courses and Lectures, Springer-Verlag, Wien-New York.
12.
Moreau
J. J.
,
1979
, “
Application of Convex Analysis to some Problems of Dry Friction
,”
Trends in Applications of Pure Mathematics to Mechanics
, Vol.
2
, London, pp.
263
–
280
.
13.
Panagiotopoulos, P. D., 1982, “Ungleichungsprobleme und Differentialinklusionen in der analytischen Mechanik,” Aristoteles Universita¨t, Thessaloniki.
14.
Panagiotopoulos, P. D., and Antes, H., 1992, “The Boundary Integral Approach to Static and Dynamic Contact Problems,” Birkha¨user Verlag, Basel, Boston, Berlin.
15.
Pfeiffer
F.
,
1991
, “
Dynamical Systems with Time-Varying or Unsteady Structure
,”
ZAMM 71
, Vol.
4
, pp.
6
–
22
.
16.
Pfeiffer, F., 1990, “Dynamical Systems with Impact and Stick-Slip Phenomena,” CSME Mechanical Engineering Forum, Toronto, Canada.
17.
Pfeiffer
F.
, and
Hajek
M.
,
1992
, “
Stick-Slip Motion of Turbine Blade Dampers
,”
Phil. Trans. R. Soc. London A
, Vol.
338
, pp.
503
–
517
.
18.
Pfeiffer, F., 1992, “On Stick-Slip Vibrations in Machine Dynamics,” Machine Vibration, pp. 20–28.
19.
Seyfferth, W., and Pfeiffer, F., 1992, “Dynamics of Assembly Processes with a Manipulator,” Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, Vol. 2, pp. 1303–1310.
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