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Lyapunov Stability of a Fractionally Damped Oscillator with Linear (Anti-)Damping.
- Source :
- International Journal of Nonlinear Sciences & Numerical Simulation; Aug2020, Vol. 21 Issue 5, p425-442, 18p
- Publication Year :
- 2020
-
Abstract
- In this paper, we develop a Lyapunov stability framework for fractionally damped mechanical systems. In particular, we study the asymptotic stability of a linear single degree-of-freedom oscillator with viscous and fractional damping. We prove that the total mechanical energy, including the stored energy in the fractional element, is a Lyapunov functional with which one can prove stability of the equilibrium. Furthermore, we develop a strict Lyapunov functional for asymptotic stability, thereby opening the way to a nonlinear stability analysis beyond an eigenvalue analysis. A key result of the paper is a Lyapunov stability condition for systems having negative viscous damping but a sufficient amount of positive fractional damping. This result forms the stepping stone to the study of Hopf bifurcations in fractionally damped mechanical systems. The theory is demonstrated on a stick-slip oscillator with Stribeck friction law leading to an effective negative viscous damping. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15651339
- Volume :
- 21
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- International Journal of Nonlinear Sciences & Numerical Simulation
- Publication Type :
- Academic Journal
- Accession number :
- 147040214
- Full Text :
- https://doi.org/10.1515/ijnsns-2018-0381