SOURCE: Journal of Applied Mechanics, Transactions ASME v 62 n 2
Jun 1995. p 496-504.
PUBLICATION: JA (Journal Article).
noise-induced transitions between the oscillatory steady states of a class
of weakly nonlinear oscillators excited by
resonant harmonic forcing is investigated. A set of
equations is derived governing slow variables of the
when the latter is perturbed by both additive white
noise and by random phase fluctuations of the resonant
excitation. The behaviour of the reduced system in the
of cubic stiffness and viscous damping forces is
investigated including the case of weak damping, the case
near bifurcation and the more general case when neither
the first two situations apply. In each case, the
quasi-stationary probability density of the response and
mean time taken by the trajectories to pass from one basin
of attraction to the other is predicted based on averaging
of a near-Hamiltonian system in the weak damping limit,
center-manifold theory in the near-bifurcation case, or
Wentzell-Kramers-Brillouin (WKB) singular perturbation
expansions in the more general case. These predictions
compared with digital simulations which show excellent
agreement. 19 Refs.