Nonsmooth Dynamics of a Double-Belt Friction Oscillator

2006 ◽  
pp. 253-262 ◽  
Author(s):  
P. Casini ◽  
F. Vestroni
Keyword(s):  
Nonsmooth Dynamics ◽  
Friction Oscillator

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.

Nonlinear Dynamics and Bifurcation Analysis of a Boost Converter for Battery Charging in Photovoltaic Applications

2014 ◽  
Vol 24 (11) ◽  
pp. 1450142 ◽  
Author(s):  
Mohammed M. Al-Hindawi ◽  
Abdullah Abusorrah ◽  
Yusuf Al-Turki ◽  
Damian Giaouris ◽  
Kuntal Mandal ◽  
...  
Keyword(s):  
Current Mode ◽  
Solar Irradiation ◽  
Nonsmooth Dynamics ◽  
Pv Systems ◽  
Current Mode Control ◽  
Mode Control ◽  
Pv Panel ◽  
Voltage Variation ◽  
Average Current ◽  
Average Current Mode Control

Photovoltaic (PV) systems with a battery back-up form an integral part of distributed generation systems and therefore have recently attracted a lot of interest. In this paper, we consider a system of charging a battery from a PV panel through a current mode controlled boost dc-dc converter. We analyze its complete nonlinear/nonsmooth dynamics, using a piecewise model of the converter and realistic nonlinear v–i characteristics of the PV panel. Through this study, it is revealed that system design without taking into account the nonsmooth dynamics of the converter combined with the nonlinear v–i characteristics of the PV panel can lead to unpredictable responses of the overall system with high current ripple and other undesirable phenomena. This analysis can lead to better designed converters that can operate under a wide variation of the solar irradiation and the battery's state of charge. We show that the v–i characteristics of the PV panel combined with the battery's output voltage variation can increase or decrease the converter's robustness, both under peak current mode control and average current mode control. We justify the observation in terms of the change in the discrete-time map caused by the nonlinear v–i characteristics of the PV panel. The theoretical results are validated experimentally.

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.

Vibration Damping by Friction Forces: Theory and Applications

2003 ◽  
Vol 9 (3-4) ◽  
pp. 419-448 ◽  
Author(s):  
Karl Popp ◽  
Lars Panning ◽  
Walter Sextro
Keyword(s):  
Three Dimensional ◽  
Friction Damping ◽  
Friction Forces ◽  
Single Degree Of Freedom ◽  
Practical Applications ◽  
Linear Friction ◽  
Solution Methods ◽  
Friction Oscillator ◽  
Contact Models

In this paper, we deal with the vibrational behavior of mechanical structures interconnected by contacts with friction. The focus is set on the utilization of friction forces that are generated in the contact interfaces with the objective to increase damping and to reduce vibration amplitudes in order to prevent structures from failures owing to high resonance stresses. We present a comparison and classification of different contact models that are most commonly used, including the derivation of a three-dimensional contact model under consideration of rough surfaces. We give different solution methods for problems with non-linear friction elements. The effectiveness of friction damping devices is pointed out by a single-degree-of-freedom friction oscillator, beam-like structures with frictional interfaces and different underplatform dampers in turbo-machinery applications. It can be shown that in many practical applications friction damping devices provide a remarkable decrease of vibration amplitudes.

A General Purpose Formulation for Nonsmooth Dynamics With Finite Rotations: Application to the Woodpecker Toy

2020 ◽  
Vol 16 (3) ◽  
Author(s):  
Alejandro Cosimo ◽  
Federico J. Cavalieri ◽  
Javier Galvez ◽  
Alberto Cardona ◽  
Olivier Brüls
Keyword(s):  
Finite Element ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Horizontal Displacement ◽  
General Purpose ◽  
Nonsmooth Dynamics ◽  
Unilateral Constraints ◽  
Simulation Code ◽  
Frictional Contacts ◽  
Large Rotations

Abstract The aim of this work is to extend the finite element multibody dynamics approach to problems involving frictional contacts and impacts. The nonsmooth generalized-α (NSGA) scheme is adopted, which imposes bilateral and unilateral constraints both at position and velocity levels avoiding drift phenomena. This scheme can be implemented in a general purpose simulation code with limited modifications of pre-existing elements. The study of the woodpecker toy dynamics sets up a good example to show the capabilities of the NSGA scheme within the context of a general finite element framework. This example has already been studied by many authors who generally adopted a model with a minimal set of coordinates and small rotations. It is shown that good results are obtained using a general purpose finite element code for multibody dynamics, in which the equations of motion are assembled automatically and large rotations are easily taken into account. In addition, comparing results between different models of the woodpecker toy, the importance of modeling large rotations and the horizontal displacement of the woodpecker's sleeve is emphasized.

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