Jerzy Wojewoda

Hysteretic effects of dry friction: modelling and experimental studies.

In this paper, the phenomena of hysteretic behaviour of friction force observed during experiments are discussed. On the basis of experimental and theoretical analyses, we argue that such behaviour can be considered as a representation of the system dynamics. According to this approach, a classification of friction models, with respect to their sensitivity on the system motion characteristic, is introduced. General friction modelling of the phenomena accompanying dry friction and a simple yet effective approach to capture the hysteretic effect are proposed. Finally, the experimental results are compared with the numerical simulations for the proposed friction model.

Imperfect chimera states for coupled pendula.

The phenomenon of chimera states in the systems of coupled, identical oscillators has attracted a great deal of recent theoretical and experimental interest. In such a state, different groups of oscillators can exhibit coexisting synchronous and incoherent behaviors despite homogeneous coupling. Here, considering the coupled pendula, we find another pattern, the so-called imperfect chimera state, which is characterized by a certain number of oscillators which escape from the synchronized chimeras cluster or behave differently than most of uncorrelated pendula. The escaped elements oscillate with different average frequencies (Poincare rotation number). We show that imperfect chimera can be realized in simple experiments with mechanical oscillators, namely Huygens clock. The mathematical model of our experiment shows that the observed chimera states are controlled by elementary dynamical equations derived from Newtons laws that are ubiquitous in many physical and engineering systems.

Chaotic mechanics in systems with impacts and friction

Chaotic phenomena in applied mechanics - nonlinearities in mechanical systems properties of a dry friction force chaos in systems with dry friction basic theory of impact coefficient of restitution chaos in impact oscillator impact oscillator with dry friction -experimental observation of intermittency dynamics of impact oscillator with dry friction an investigation of the dynamical system with impacts systems with impacts - some aspects of the dynamical behaviour of the impact force generator operation of the multifender generator systems with friction - chaotic behaviour of friction force complex behaviour of a quasiperiodically forced experimental system with dry friction.

Attractors of Quasiperiodically Forced Systems

Attractors of Dynamical Systems Strange Nonchaotic Attractors, Inhibition of Chaotic Behaviour in Coupled Geophysical Models Experimental System with Dry Friction.

Chaos caused by non-reversible dry friction

Abstract In this short communication we investigate how the non-reversible dry friction characteristics will alter the non-linear responses of a simple mechanical oscillator. The presented approach is based on a certain mathematical description of the experimentally determined non-reversible dry friction characteristics, which causes chaotic and irregular motion of the studied system. A novelty of our idea is an introduction of the relative acceleration in description of the dry friction model.

Chaos-hyperchaos transition

Abstract We discuss properties of an attractor in the neighbourhood of chaos-hyperchaos transition. The intermittency like model and a scaling law for the transition based on the features of the Poincare map are developed. We investigate the properties of the Lyapunov and correlation dimensions in the neighbourhood of the transition point.

Synchronous rotation of the set of double pendula: experimental observations.

We study the occurrence of the synchronous rotation of a set of four uncoupled nonidentical double pendula arranged into a cross structure mounted on a vertically excited platform. Under the excitation, the pendula can rotate in different directions (counter-clockwise or clockwise). It has been shown that after a transient, many different types of synchronous configurations with the constant phase difference between pendula can be observed. The experimental results qualitatively agree with the numerical simulations.

Complex Behaviour of a Quasiperiodically Forced Experimental System with Dry Friction

A mechanical experiment is described in which dry friction provides a nonlinear coupling between forced linear oscillators. Interpretation of the aperiodic behaviour of the system suggests that the friction force is a chaotic function of the relative velocity; the chaotic behaviour may be understood in terms of a degree of freedom of motion normal to the surfaces in friction contact. Spectral analysis showed a specific structure of power spectra characteristic of quasiperiodically forced systems which has already been known from numerical experiments. A new method of predicting power spectra components is proposed.

The smallest chimera state for coupled pendula

Chimera states in the systems of coupled identical oscillators are spatiotemporal patterns in which different groups of oscillators can exhibit coexisting synchronous and incoherent behaviors despite homogeneous coupling. Although these states are typically observed in large ensembles of oscillators, recently it has been suggested that chimera states may occur in the systems with small numbers of oscillators. Here, considering three coupled pendula showing chaotic behavior, we find the pattern of the smallest chimera state, which is characterized by the coexistence of two synchronized and one incoherent oscillator. We show that this chimera state can be observed in simple experiments with mechanical oscillators, which are controlled by elementary dynamical equations derived from Newton’s laws. Our finding suggests that chimera states are observable in small networks relevant to various real-world systems.

Experimental and numerical analysis of self-excited friction oscillator

Abstract A self-excited friction oscillator has been designed and manufactured to carry out experimental analysis of dry friction phenomenon. A mathematical model of this oscillator has been formulated. The influence of the different types of classical friction characteristics on the dynamical behaviour of the model is investigated by way of numerical analysis. A comparison with dynamics of real oscillator is presented and some reasons of observed differences are explained. A particular analysis of experimental data leads to the confirmation of non-reversible friction characteristics and allows to formulate a hypothesis that a course of such characteristics also depends on value (not only on the sign) of acceleration.