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Technical Brief

Periodic Motions With Overshooting Phases of a Two-Mass Stick–Slip Oscillator

[+] Author and Article Information
Madeleine Pascal

Laboratoire IBISC,
Universite d'Evry Val d'Essonne,
Evry 91000, France
e-mail: madeleine.pascal3@wanadoo.fr

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 13, 2016; final manuscript received January 10, 2017; published online February 8, 2017. Assoc. Editor: Sotirios Natsiavas.

J. Comput. Nonlinear Dynam 12(4), 044504 (Feb 08, 2017) (3 pages) Paper No: CND-16-1428; doi: 10.1115/1.4035786 History: Received September 13, 2016; Revised January 10, 2017

We investigate the dynamics of a two degrees-of-freedom oscillator excited by dry friction. The system consists of two masses connected by linear springs and in contact with a belt moving at a constant velocity. The contact forces between the masses and the belt are given by Coulomb's laws. Several periodic orbits including slip and stick phases are obtained. In particular, the existence of periodic orbits involving a part where one of the masses moves at a higher speed than the belt is proved.

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References

Galvanetto, U. , and Bishop, S. , 1999, “ Dynamics of a Simple Damped Oscillator Undergoing Stick-Slip Vibrations,” Meccanica, 34(5), pp. 337–347. [CrossRef]
Pascal, M. , 2008, “ Dynamics of Coupled Oscillators Excited by Dry Friction,” ASME J. Comput. Nonlinear Dyn., 3(3), p. 031009. [CrossRef]
Teufel, A. , Steindl, A. , and Troger, H. , 2007, “ Rotating Slip Stick Separation Waves,” IUTAM Symposium on Dynamics and Control of Nonlinear Systems With Uncertainty, Springer, Berlin, pp. 257–266.
Pascal, M. , 2011, “ New Events in Stick Slip Oscillators Behaviour,” J. Appl. Math. Mech., 75(3), pp. 283–288. [CrossRef]
Chowdhury, I. , and Dasgupta, S. P. , 2003, “ Computation of Rayleigh Damping Coefficients for Large Systems,” Electron. J. Geotech. Eng., 43, pp. 6855–6868.

Figures

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Fig. 1

Description of the model

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Fig. 2

Symmetrical orbits of the system

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Fig. 3

Phase portrait of m1 with overshooting of m2

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Fig. 4

Phase portrait of m2 with overshooting part

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Fig. 5

Phase portrait of m1 with overshooting part

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Fig. 6

Phase portrait of m2 with overshooting of m1

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