Research Papers

Dynamics of Coupled Oscillators Excited by Dry Friction

[+] Author and Article Information
Madeleine Pascal

Laboratoire IBISC, FRE 2873,  Universite d’Evry Val d’Essonne, 40 rue du Pelvoux, 91020 Evry cedex, Francempascal@iup.univ-evry.fr

J. Comput. Nonlinear Dynam 3(3), 031009 (May 05, 2008) (6 pages) doi:10.1115/1.2908272 History: Received July 02, 2007; Revised November 15, 2007; Published May 05, 2008

In this paper, we present an analytical method to investigate the behavior of a two-degree-of-freedom oscillator excited by dry friction. The system consists of two masses connected by linear springs. These two masses are in contact with a driving belt moving at a constant velocity. The contact forces between the masses and the belt are obtained assuming Coulomb’s friction law. Two families of periodic motions are found in closed form. The first one includes stick-slip oscillations with two switches per period, the second one is also composed of stick-slip motion, but includes three switches per period. In both cases, the initial conditions and the time duration of each kind of motions (stick or slip phases) are obtained in analytical form.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Coupled oscillators with dry friction

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Figure 2

Phase portrait of the slip-stick orbit (first mass)

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Figure 3

Phase portrait of the slip-stick orbit (second mass)

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Figure 4

Constraint x1′−V<0

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Figure 5

Constraints z1<0,z2>0

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Figure 6

Phase portrait of the first mass (Solution II)

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Figure 7

Phase portrait of the second mass (Solution II)

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Figure 8

Constraints p1>0,p2>0

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Figure 9

Constraints q1>0,q2>0



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