Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Basin Stability of Bi-Stable Friction-Excited Oscillators

Version 1 : Received: 5 November 2020 / Approved: 6 November 2020 / Online: 6 November 2020 (09:21:32 CET)

How to cite: Stender, M.; Hoffmann, N.; Papangelo, A. The Basin Stability of Bi-Stable Friction-Excited Oscillators. Preprints 2020, 2020110234 (doi: 10.20944/preprints202011.0234.v1). Stender, M.; Hoffmann, N.; Papangelo, A. The Basin Stability of Bi-Stable Friction-Excited Oscillators. Preprints 2020, 2020110234 (doi: 10.20944/preprints202011.0234.v1).

Abstract

Stability considerations play a central role in structural dynamics to determine states that are robust against perturbations during the operation. Linear stability concepts, such as the complex eigenvalue analysis, constitute the core of analysis approaches in engineering reality. However, most stability concepts are limited to local perturbations, i.e. they can only measure a state’s stability against small perturbations. Recently, the concept of basin stability has been proposed as a global stability concept for multi-stable systems. As multi-stability is a well-known property of a range of nonlinear dynamical systems, this work studies the basin stability of bi-stable mechanical oscillators that are affected and self-excited by dry friction. The results indicate how the basin stability complements the classical binary stability concepts for quantifying how stable a state is given a set of permissible perturbations.

Subject Areas

nonlinear dynamics; basin of attraction; self-excitation; bi-stability; multi-stability

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