The Basin Stability of Bi-Stable Friction-Excited Oscillators

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 sta...

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Bibliographic Details
Published inLubricants Vol. 8; no. 12; p. 105
Main Authors Stender, Merten, Hoffmann, Norbert, Papangelo, Antonio
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.12.2020
Subjects
Approximation
basin of attraction
Basins
bi-stability
Dry friction
Dynamic stability
Dynamical systems
Eigenvalues
Friction
Mechanical oscillators
multi-stability
nonlinear dynamics
Nonlinear systems
self-excitation
Stability analysis
Velocity
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Summary: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 was 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.
ISSN:2075-4442
2075-4442
DOI:10.3390/lubricants8120105