Article (Scientific journals)
Average first-passage time of a quasi-Hamiltonian Mathieu oscillator with parametric and forcing excitations
Vanvinckenroye, Hélène; Denoël, Vincent
2017In Journal of Sound and Vibration
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Keywords :
stochastic stability; Pontryagin equation; first passage time; stochastic averaging; parametric oscillator
Abstract :
[en] A linear oscillator simultaneously subjected to stochastic forcing and parametric excitation is considered. The time required for this system to evolve from a low initial energy level until a higher energy state for the first time is a random variable. Its expectation satisfies the Pontryagin equation of the problem, which is solved with the asymptotic expansion method developed by Khasminskii. This allowed deriving closed-form expressions for the expected first passage time. A comprehensive parameter analysis of these solutions is performed. Beside identifying the important dimensionless groups governing the problem, it also highlights three important regimes which are called incubation, multiplicative and additive because of their specific features. Those three regimes are discussed with the parameters of the problem.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Vanvinckenroye, Hélène ;  Université de Liège > Département ArGEnCo > Analyse sous actions aléatoires en génie civil
Denoël, Vincent  ;  Université de Liège > Département ArGEnCo > Analyse sous actions aléatoires en génie civil
Language :
English
Title :
Average first-passage time of a quasi-Hamiltonian Mathieu oscillator with parametric and forcing excitations
Publication date :
July 2017
Journal title :
Journal of Sound and Vibration
ISSN :
0022-460X
eISSN :
1095-8568
Publisher :
Elsevier, United Kingdom
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 31 March 2017

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