Chaos of a Dry Friction Oscillator with Periodic Excitation

AbstractThe responses of a simple harmonically excited dry friction oscillator are analysed in the case when the coefficients of static and kinetic coefficients of friction are different. One- and two-parameter bifurcation curves are determined at suitable parameters by continuation method and the largest Lyapunov exponents of the obtained solutions are estimated. It is shown that chaotic solutions can occur in broad parameter domains—even at realistic friction parameters—that are tightly enclosed by well-defined two-parameter bifurcation curves. The performed analysis also reveals that chaotic trajectories are bifurcating from special asymmetric solutions. To check the robustness of the qualitative results, characteristic bifurcation branches of two slightly modified oscillators are also determined: one with a higher harmonic in the excitation, and another one where Coulomb friction is exchanged by a corresponding LuGre friction model. The qualitative agreement of the diagrams supports the validity of the results.

Download Full-text

Two-Frequency Oscillation With Combined Coulomb and Viscous Frictions

Journal of Vibration and Acoustics ◽

10.1115/1.1502670 ◽

2002 ◽

Vol 124 (4) ◽

pp. 537-544 ◽

Cited By ~ 6

Author(s):

Gong Cheng ◽

Jean W. Zu

Keyword(s):

Steady State ◽

Dry Friction ◽

Single Frequency ◽

Friction Oscillator ◽

One Stop ◽

Frequency Excitation ◽

Stop Motion ◽

The One ◽

Coulomb Dry Friction ◽

Mass Spring

In this paper, a mass-spring-friction oscillator subjected to two harmonic disturbing forces with different frequencies is studied for the first time. The friction in the system has combined Coulomb dry friction and viscous damping. Two kinds of steady-state vibrations of the system—non-stop and one-stop motions—are considered. The existence conditions for each steady-state motion are provided. Using analytical analysis, the steady-state responses are derived for the two-frequency oscillating system undergoing both the non-stop and one-stop motions. The focus of the paper is to study the influence of the Coulomb dry friction in combination with the two frequency excitations on the dynamic behavior of the system. From the numerical simulations, it is found that near the resonance, the dynamic response due to the two-frequency excitation demonstrates characteristics significantly different from those due to a single frequency excitation. Furthermore, the one-stop motion demonstrates peculiar characteristics, different from those in the non-stop motion.

Download Full-text

Dynamics of a dry friction oscillator under two-frequency excitations

Journal of Sound and Vibration ◽

10.1016/j.jsv.2003.06.027 ◽

2004 ◽

Vol 275 (3-5) ◽

pp. 591-603 ◽

Cited By ~ 15

Author(s):

G Cheng ◽

J.W Zu

Keyword(s):

Dry Friction ◽

Friction Oscillator

Download Full-text

Analysis of a dry-friction oscillator driven by a stochastic base motion

10.20906/cps/usm-2016-0011 ◽

2015 ◽

Cited By ~ 3

Author(s):

Roberta Lima ◽

Rubens Sampaio

Keyword(s):

Dry Friction ◽

Friction Oscillator

Download Full-text

Experiments in Control and Anti-Control of Chaos in a Dry Friction Oscillator

Journal of Vibration and Control ◽

10.1177/107754603030777 ◽

2003 ◽

Vol 9 (3-4) ◽

pp. 387-397 ◽

Cited By ~ 4

Author(s):

Francis C. Moon ◽

Anil J. Reddy ◽

William T. Holmes

Keyword(s):

Dry Friction ◽

Normal Force ◽

Control Method ◽

Unstable Periodic Orbits ◽

Mechanical Oscillator ◽

Chaotic State ◽

Control Of Chaos ◽

Magnetic Actuator ◽

Friction Oscillator ◽

Proportional Feedback

We describe a mechanical oscillator with a dry friction nonlinearity and feedback control. It is shown to exhibit both control of chaos, i.e., the stabilization of unstable periodic orbits in a strange attractor, as well as anti-control of chaos. Anti-control of chaos is the use of feedback to drive a nonlinear system into a chaotic state near a periodic motion. The addition of noise or dither onto periodic oscillations can often be useful in engineering devices. The control and anti-control method is based on “ occasionally proportional feedback” developed by Hunt as an extension of the well-known OGY theory of the control of chaos. In this work, the control is effected by changing the normal force of the dry friction element using a magnetic actuator.

Download Full-text