Abstract
In this work, the asymptotic stability bounds are identified for a class of linear quasi-periodic dynamical systems with stochastic parametric excitations and nonlinear perturbations. The application of a Lyapunov–Perron (L-P) transformation converts the linear part of such systems to a linear time-invariant form. In the past, using the Infante’s approach for linear time-invariant systems, stability theorem and corollary were derived and demonstrated for time periodic systems with variation in stochastic parameters. In this study, the same approach is extended toward linear quasi-periodic with stochastic parameter variations. Furthermore, the Lyapunov’s direct approach is employed to formulate the stability conditions a for quasi-periodic system with nonlinear perturbations. If the nonlinearities satisfy a bounding condition, sufficient conditions for asymptotic stability can be derived for such systems. The applications of stability theorems are demonstrated with practical examples of commutative and noncommutative quasi-periodic systems.
Original language | English (US) |
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Article number | 051010 |
Journal | Journal of Vibration and Acoustics |
Volume | 144 |
Issue number | 5 |
DOIs | |
State | Published - Oct 2022 |
Externally published | Yes |
Keywords
- dynamics
- nonlinear vibration
- random vibration
- stability
ASJC Scopus subject areas
- Acoustics and Ultrasonics
- Mechanics of Materials
- Mechanical Engineering