Chaotic Motion of a Two-Frequency Forced Oscillator With Dry Friction

2003 ◽  
Author(s):  
Gong Cheng ◽  
Jean W. Zu
Keyword(s):  
Dry Friction ◽  
Periodic Motions ◽  
Bifurcation Diagrams ◽  
External Excitation ◽  
Forced Oscillator ◽  
Friction Oscillator ◽  
Frequency Excitation ◽  
Simulation Results ◽  
Excitation Frequencies ◽  
Insight Into

In this paper, the dynamic behavior of a dry friction oscillator subjected to simultaneous self- and external excitations is studied. The dry friction in the system follows the classical Coulomb’s law, and the external excitation consists of two harmonic forces with different frequencies. The focus of the paper is laid on bifurcation analysis to gain insight into the influence of the two-frequency excitation upon the qualitative features of system dynamics. Numerical simulations are performed and the simulation results are visualized by means of bifurcation diagrams, Poincare´ sections and Lyapunov exponents. New and interesting conclusions are reached from the study. It is shown that small excitation frequencies and amplitudes tend to cause chaos in the system, whereas large excitation amplitudes can induce only periodic motions. Furthermore, it is found that the probability of the occurrence of periodic motions increases, as the ratio between the two excitation frequencies increases.

Two-Frequency Oscillation With Combined Coulomb and Viscous Frictions

2002 ◽  
Vol 124 (4) ◽  
pp. 537-544 ◽  
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.

Periodic Motions in a Periodically Forced Oscillator Moving on the Oscillating Belt With Dry Friction

2005 ◽  
Author(s):  
Albert C. J. Luo ◽  
Brandon C. Gegg
Keyword(s):  
Relative Motion ◽  
Efficient Method ◽  
Periodic Motion ◽  
Dry Friction ◽  
Displacement Velocity ◽  
Eigenvalue Analysis ◽  
Analytical Prediction ◽  
Periodic Motions ◽  
Mapping Structures ◽  
Forced Oscillator

In this paper, periodic motion in an oscillator moving on a periodically vibrating belt with dry-friction is investigated. The conditions of stick and non-stick motions for such an oscillator are obtained in the relative motion frame, and the grazing and stick (or sliding) bifurcations are presented as well. The periodic motions are predicted analytically and numerically, and the analytical prediction is based on the appropriate mapping structures. The eigenvalue analysis of such periodic motions is carried out. The periodic motions are illustrated through the displacement, velocity and force responses in the absolute and relative frames. This investigation provides an efficient method to predict periodic motions of such an oscillator involving dry-friction. The significance of this investigation lies in controlling motion of such friction-induced oscillator in industry.

On the Mechanism of Stick and Non-Stick, Periodic Motions in a Forced Linear Oscillator Including Dry Friction

2004 ◽  
Author(s):  
Albert C. J. Luo ◽  
Brandon C. Gegg
Keyword(s):  
Dry Friction ◽  
Local Stability ◽  
Displacement Velocity ◽  
Linear Oscillator ◽  
Periodic Motions ◽  
Friction Forces ◽  
Stability And Bifurcation ◽  
Mapping Structures ◽  
Linear Friction ◽  
Friction Oscillator

In this paper, the dynamics mechanism of stick and non-stick motion for a dry-friction oscillator is discussed. From the theory of Luo in 2004, the conditions for stick and non-stick motions are achieved. The stick and non-stick periodic motions are predicted analytically through the appropriate mapping structures. The local stability and bifurcation for such periodic motions are obtained. The stick motions are illustrated through the displacement, velocity and force responses. This investigation provides a better understanding of stick and nonstick motions of the linear oscillator with dry-friction. The methodology presented in this paper is applicable to oscillators with non-linear friction forces.

On the Mechanism of Stick and Nonstick, Periodic Motions in a Periodically Forced, Linear Oscillator With Dry Friction

2005 ◽  
Vol 128 (1) ◽  
pp. 97-105 ◽  
Author(s):  
Albert C. J. Luo ◽  
Brandon C. Gegg
Keyword(s):  
Dry Friction ◽  
Local Stability ◽  
Displacement Velocity ◽  
Linear Oscillator ◽  
Nonlinear Friction ◽  
Periodic Motions ◽  
Friction Forces ◽  
Stability And Bifurcation ◽  
Mapping Structures ◽  
Friction Oscillator

In this paper, the dynamics mechanism of stick and nonstick motion for a dry-friction oscillator is discussed. From the theory of Luo in 2005 [Commun. Nonlinear Sci. Numer. Simul., 10, pp. 1–55], the conditions for stick and nonstick motions are achieved. The stick and nonstick periodic motions are predicted analytically through the appropriate mapping structures. The local stability and bifurcation conditions for such periodic motions are obtained. The stick motions are illustrated through the displacement, velocity, and force responses. This investigation provides a better understanding of stick and nonstick motions of the linear oscillator with dry friction. The methodology presented in this paper is applicable to oscillators with nonlinear friction forces.

Periodic Motions in a Periodically Forced Oscillator Moving on an Oscillating Belt With Dry Friction

2006 ◽  
Vol 1 (3) ◽  
pp. 212-220 ◽  
Author(s):  
Albert C.J. Luo ◽  
Brandon C. Gegg
Keyword(s):  
Relative Motion ◽  
Efficient Method ◽  
Periodic Motion ◽  
Dry Friction ◽  
Displacement Velocity ◽  
Eigenvalue Analysis ◽  
Analytical Prediction ◽  
Periodic Motions ◽  
Mapping Structures ◽  
Forced Oscillator

In this paper, periodic motion in an oscillator moving on a periodically oscillating belt with dry friction is investigated. The conditions of stick and nonstick motions for such an oscillator are obtained in the relative motion frame, and the grazing and stick (or sliding) bifurcations are presented as well. The periodic motions are predicted analytically and numerically, and the analytical prediction is based on the appropriate mapping structures. The eigenvalue analysis of such periodic motions is carried out. The periodic motions are illustrated through the displacement, velocity, and force responses in the absolute and relative frames. This investigation provides an efficient method to predict periodic motions of such an oscillator involving dry friction. The significance of this investigation lies in controlling motion of such a friction-induced oscillator in industry.

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

Meccanica ◽  
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.

Tribometer for Dry Friction Measurement

1999 ◽  
Author(s):  
Marc Brandl ◽  
Friedrich Pfeiffer
Keyword(s):  
Coefficient Of Friction ◽  
Dry Friction ◽  
Stribeck Curve ◽  
Body System ◽  
Friction Measurement ◽  
Detailed Model ◽  
The Coefficient Of Friction ◽  
Simulation Results ◽  
Multi Body

Abstract This paper deals with the measurement of dry friction. A tribometer was developed in order to identify both the sticking and the sliding coefficient of friction. The aim was to determine the so called Stribeck-curve of any material in contact. The design of the plant is presented. Avoiding errors in recalculating the coefficient of friction, a detailed model of the plant as a multi body system with motor feedback was generated. Advantages of the tribometer are shown in simulations. Some results of measurements in comparison with simulation results are presented.

scholarly journals Maximization of Eigenfrequency Gaps in a Composite Cylindrical Shell Using Genetic Algorithms and Neural Networks

2019 ◽  
Vol 9 (13) ◽  
pp. 2754 ◽  
Author(s):  
Bartosz Miller ◽  
Leonard Ziemiański
Keyword(s):  
Genetic Algorithm ◽  
Neural Networks ◽  
Genetic Algorithms ◽  
Excitation Frequency ◽  
Algorithm Optimization ◽  
External Excitation ◽  
Excitation Frequencies ◽  
Objective Function Values ◽  
Using Data ◽  
Laminated Structures

This paper presents a novel method for the maximization of eigenfrequency gaps around external excitation frequencies by stacking sequence optimization in laminated structures. The proposed procedure enables the creation of an array of suggested lamination angles to avoid resonance for each excitation frequency within the considered range. The proposed optimization algorithm, which involves genetic algorithms, artificial neural networks, and iterative retraining of the networks using data obtained from tentative optimization loops, is accurate, robust, and significantly faster than typical genetic algorithm optimization in which the objective function values are calculated using the finite element method. The combined genetic algorithm–neural network procedure was successfully applied to problems related to the avoidance of vibration resonance, which is a major concern for every structure subjected to periodic external excitations. The presented examples illustrate a combined approach to avoiding resonance through the maximization of a frequency gap around external excitation frequencies complemented by the maximization of the fundamental natural frequency. The necessary changes in natural frequencies are caused only by appropriate changes in the lamination angles. The investigated structures are thin-walled, laminated one- or three-segment shells with different boundary conditions.

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