We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Stochastic stability of variable-mass Duffing oscillator with mass disturbance modeled as Gaussian white noise.
- Authors
Qiao, Yan; Xu, Wei; Jia, Wantao; Liu, Weiyan
- Abstract
The stochastic asymptotic stability with probability one of the stochastic variable- mass Duffing oscillator under weakly parametric excitation is investigated by using the largest Lyapunov exponent, in which the small disturbance of mass is modeled as Gaussian white noise. First, the original system is replaced by an approximate system without mass disturbance based on an equivalent transformation. Then the averaged Itô equation of the approximate system is derived by applying the stochastic averaging method based on the generalized harmonic function. Finally, the Lyapunov exponent of the linearized averaged Itô equation is derived and a necessary and sufficient condition for the stability of the trivial solution is obtained approximately by letting this Lyapunov exponent be negative. The effects of mass disturbance on system stability are explored adequately. It turns out that mass disturbance deteriorates system stability remarkably. It is remarkable that the influences of linear stiffness on the stability of a variable-mass system are significantly different from that of an associated invariable-mass system.
- Subjects
STOCHASTIC processes; STABILITY theory; VARIABLE mass systems; DUFFING oscillators; RANDOM noise theory
- Publication
Nonlinear Dynamics, 2017, Vol 89, Issue 1, p607
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-017-3474-5