Nonlinear Oscillations of Structures Induced by Dry Friction

Hysteretic effects of dry friction: modelling and experimental studies

“…For example, if one considers the dynamics of a system where the relative velocity practically remains constant, there is no need for sophisticated dry friction models and even the simplest one described by the Coulomb law will suffice. However, the systems with dry friction can often exhibit more complex dynamical behaviour, such as chaotic or even stochastic responses (Den Hartog 1931;Tolstoi 1967;Shaw 1986;Popp & Stelter 1990;Wojewoda 1992;Feeny & Moon 1994;Wiercigroch 1994;Oestreich 1998;Bogacz & Ryczek 2003). Then, the chosen model must account for the transition from static to dynamic friction and should provide a means of guiding the system through zero relative velocity.…”

Qualitative bifurcation analysis of a non-smooth friction-oscillator model

“…We remark that, contrary to the related results in e.g. [31,32], our aim is to localize the various different regions in {(η, γ) : η, γ ≥ 0} which correspond to qualitatively different behaviour of the system. In this way we will obtain a more complete picture of the dynamics instead of particular examples.…”

“…Compared to related results on this example as obtained e.g. in [31,32,37,19,20], we identified a lot of new and interesting bifurcation structures by reducing the analysis of the whole excited 3-dimensional system to the study of a suitable 1-dimensional Poincaré-map. We determined the various ranges of frequency and amplitude of the external forcing which correspond to differentiability and/or monotonicity of this Poincaré-map.…”

Asymptotic Behaviour of an Oscillator Excited by Dry Friction Forces

“…It is well known that dry friction forces always have non-linear characteristics and can cause very complex behaviour of a given system: e.g., non-linear excited (stick±slip) oscillations [2,3] or a chaotic motion and bifurcations [1,4,5].…”