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.

Issue Section:
Research Papers
Keywords:
friction, nonlinear dynamical systems, oscillations, coupled oscillators, dry friction, periodic motions, analytical method, stick-slip motion
Topics:
Dry friction, Friction, Oscillations, Stick-slip, Dynamics (Mechanics)
1.
Awrejcewicz
,
J.
, and
Delfs
,
J.
, 1990, “
Dynamics of a Self-Excited Stick-Slip Oscillator With Two Degrees of Freedom, Part I. Investigation of Equilibria
,”
Eur. J. Mech. A/Solids
0997-7538,
9
(
4
), pp.
269
–
282
.
2.
Liu
,
C. S.
, and
Chang
,
W. T.
, 2002, “
Frictional Behavior of a Belt-Driven and Periodically Excited Oscillator
,”
J. Sound Vib.
0022-460X,
258
(
2
), pp.
247
–
268
.
Crossref
Search ADS
 
3.
Andreaus
,
U.
, and
Casini
,
P.
, 2001, “
Dynamics of Friction Oscillators Excited by a Moving Base and∕or Driving Force
,”
J. Sound Vib.
0022-460X,
245
(
4
), pp.
685
–
699
.
Crossref
Search ADS
 
4.
Awrejcewicz
,
J.
,
Dzyubak
,
J.
 and
Grebogi
,
C.
, 2005, “
Estimation of Chaotic and Regular (Stick-Slip and Slip-Slip) Oscillations Exhibited by Coupled Oscillators With Dry Friction
,”
Nonlinear Dyn.
0924-090X,
42
, pp.
383
–
394
.
Crossref
Search ADS
 
5.
Pascal
,
M.
, 2006, “
Dynamics and Stability of a Two Degrees of Freedom Oscillator With an Elastic Stop
,”
ASME J. Comput. Nonlinear Dyn.
1555-1423,
1
(
1
), pp.
94
–
102
.
Crossref
Search ADS
 
6.
Luo
,
A. C. J.
, and
Gegg
,
B. C.
, 2006, “
Stick and Non-Stick Periodic Motions in Periodically Forced Oscillators With Dry Friction
,”
J. Sound Vib.
0022-460X,
291
(
1–2
), pp.
132
–
168
.
7.
Khizgiyaev
,
S. V.
, 2007, “
Stick-Slip Self Oscillations of Mechanical System With Two Degrees of Freedom
,”
PMM
,
71
(
4
), pp.
40
–
57
.
Copyright © 2008
 by American Society of Mechanical Engineers
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