Journal ArticleDOI
Dynamics of oscillators with impact and friction
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In this paper, two types of nonsmooth oscillators are investigated: an impact oscillator and a self-sustained friction oscillator with harmonic external excitation, and two different formalisms for the calculation of the Lyapunov exponents are applied.Abstract:
In the present paper two types of nonsmooth oscillators are investigated: an impact oscillator and a self-sustained friction oscillator. Both are nonsmooth one degree of freedom oscillators with harmonic external excitation. Here the different types of motion, bifurcation diagrams and Poincare maps are determined from experiments. These results will be compared with numerical results on the basis of the identified impact and friction models. The nonsmooth third-order systems show rich bifurcational behaviour which is analysed by numerical simulations but also using mapping approaches. Two different formalisms for the calculation of the Lyapunov exponents are applied. The latter one requires special considerations in the given case of nonsmooth systems. Furthermore, the embedding dimension is gained applying the method of false nearest neighbours. In the case of coexisting solutions further analysis is done by means of bifurcation and stability analysis and the cell-mapping approach.read more
Citations
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Friction modeling for dynamic system simulation
TL;DR: It is clear that multi-scale effects can dominate performance of friction contacts, and as a result more research is needed into computational tools and approaches capable of resolving the diverse length scales present in many practical problems.
Journal ArticleDOI
Experimental observation of nonlinear vibrations in a rub-impact rotor system
Fulei Chu,Wenxiu Lu +1 more
TL;DR: In this article, a special structure of stator is designed to simulate the condition of the full rotor-to-stator rub of the rotor system, which can be used to analyze nonlinear responses and bifurcation characteristics of the system when the rub-impact occurs.
Journal ArticleDOI
Analysis of Dynamic Systems With Various Friction Laws
Jan Awrejcewicz,Paweł Olejnik +1 more
TL;DR: In this paper, a survey devoted to a significant role of various dry friction laws in engineering sciences is presented, with an emphasis on new approaches (Bay-Wanheim, Dahl, Bliman-Sorine, LundGrenoble, as well as atomic scale and fractal model s, among others).
Journal ArticleDOI
Experimental study of impact oscillator with one-sided elastic constraint
TL;DR: Different bifurcation scenarios under varying the excitation frequency near grazing are shown for a number of values of the excited amplitude and a good correspondence between them is shown for different stiffness ratios.
Journal ArticleDOI
Chaos in brake squeal noise
TL;DR: In this paper, the authors analyzed the brake squeal data obtained from a full brake system on a noise dynamometer with nonlinear analysis techniques and showed that lower dimensional attractors are isolated and quantified by dynamic invariants such as correlation dimension estimates or Lyapunov exponents.
References
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Journal ArticleDOI
Determining Lyapunov exponents from a time series
TL;DR: In this article, the authors present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series, which provide a qualitative and quantitative characterization of dynamical behavior.
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Independent coordinates for strange attractors from mutual information.
TL;DR: In this paper, the mutual information I is examined for a model dynamical system and for chaotic data from an experiment on the Belousov-Zhabotinskii reaction.
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Determining embedding dimension for phase-space reconstruction using a geometrical construction
TL;DR: The issue of determining an acceptable minimum embedding dimension is examined by looking at the behavior of near neighbors under changes in the embedding dimensions from d\ensuremath{\rightarrow}d+1 by examining the manner in which noise changes the determination of ${\mathit{d}}_{\math it{E}}$.