Phase Portraits of the Autonomous Duffing Single-Degree-of-Freedom Oscillator with Coulomb Dry Friction

Nikola Jakšić

doi:10.1155/2014/465489

Abstract

The paper presents phase portraits of the autonomous Duffing single-degree-of-freedom system with Coulomb dry friction in its δ-γ-ε parameter space. The considered nonlinearities of the cubic stiffness (ε) and Coulomb dry friction (γ) are widely used throughout the literature. It has been shown that there can be more than one sticking region in the phase plane. It has also been shown that an equilibrium point occurs at the critical combinations of values of the parameters γ and ε which gives rise to zero eigenvalue of the linearised system. The unstable limit cycle may appear in the case of negative viscous damping (δ); δ<0.

Highlights

It is beneficial, if not essential, to know the system behaviour prior to using it in any other application or analysis
The unstable limit cycle may appear in the case of negative viscous damping (δ); δ < 0
Negative viscous damping is normally associated with self-exciting systems

Summary

Introduction

If not essential, to know the system behaviour prior to using it in any other application or analysis. Negative viscous damping is normally associated with self-exciting systems. They are most commonly found in solid-fluid interactions with the fluid induced vibrations [3, 4], but certainly not exclusively [5, 6]. There are two main reasons for using the self-excited model: either the excitation itself is too difficult to model or only the consequences of the energy-input mechanism are important for the problem under consideration. It was shown that separating the viscous damping and frictional damping from the system response is possible, but difficult [10, 11]. The mixed model (power law damping) has received some attention [12, 13]

Equilibrium Points

Sticking Regions

Phase Portraits and Basins of Attraction

Conclusions

Conflict of Interests