ANALYTICAL DYNAMICS OF A FRICTION OSCILLATOR UNDER TWO-FREQUENCY EXCITATIONS WITH FLOW BARRIERS

This paper presented a methodology to determine the analytical dynamics of the periodically forced friction oscillator. The friction force is modeled by a piecewise linear, kinetic friction model with the static force. The input and output force concepts in the vicinity of the discontinuous friction force boundary are introduced. The force criteria for the onset and vanishing of stick and non-stick motions are presented through the input and output forces. The periodic motion of such an oscillator is determined through the corresponding mapping structure. The local stability of the periodic motions is presented. Illustrations of the periodic motions in such a piecewise friction model are given for better understanding the stick motion with static friction. The force responses are presented, which agreed very well with the force criteria.

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Asymmetric and chaotic responses of dry friction oscillators with different static and kinetic coefficients of friction

Meccanica ◽

10.1007/s11012-021-01382-8 ◽

2021 ◽

Author(s):

Gábor Csernák ◽

Gábor Licskó

Keyword(s):

Dry Friction ◽

Continuation Method ◽

Friction Model ◽

Lugre Friction Model ◽

Kinetic Coefficients ◽

Friction Oscillator ◽

Lugre Friction ◽

Friction Parameters ◽

Two Parameter ◽

Parameter Bifurcation

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.

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COULOMB FRICTION OSCILLATOR: MODELLING AND RESPONSES TO HARMONIC LOADS AND BASE EXCITATIONS

Journal of Sound and Vibration ◽

10.1006/jsvi.1999.2594 ◽

2000 ◽

Vol 229 (5) ◽

pp. 1171-1192 ◽

Cited By ~ 45

Author(s):

H.-K. HONG ◽

C.-S. LIU

Keyword(s):

Coulomb Friction ◽

Friction Oscillator

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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.

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SINGULARITY, SWITCHABILITY AND BIFURCATIONS IN A 2-DOF, PERIODICALLY FORCED, FRICTIONAL OSCILLATOR

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127413300097 ◽

2013 ◽

Vol 23 (03) ◽

pp. 1330009 ◽

Cited By ~ 5

Author(s):

ALBERT C. J. LUO ◽

MOZHDEH S. FARAJI MOSADMAN

Keyword(s):

Dynamical Systems ◽

Bifurcation Analysis ◽

Degrees Of Freedom ◽

Eigenvalue Analysis ◽

Analytical Dynamics ◽

Periodic Motions ◽

Stability And Bifurcation ◽

Mapping Structures ◽

Stability And Bifurcation Analysis ◽

The Stability

In this paper, the analytical dynamics for singularity, switchability, and bifurcations of a 2-DOF friction-induced oscillator is investigated. The analytical conditions of the domain flow switchability at the boundaries and edges are developed from the theory of discontinuous dynamical systems, and the switchability conditions of boundary flows from domain and edge flows are presented. From the singularity and switchability of flow to the boundary, grazing, sliding and edge bifurcations are obtained. For a better understanding of the motion complexity of such a frictional oscillator, switching sets and mappings are introduced, and mapping structures for periodic motions are adopted. Using an eigenvalue analysis, the stability and bifurcation analysis of periodic motions in the friction-induced system is carried out. Analytical predictions and parameter maps of periodic motions are performed. Illustrations of periodic motions and the analytical conditions are completed. The analytical conditions and methodology can be applied to the multi-degrees-of-freedom frictional oscillators in the same fashion.

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