  The dynamics of mechanical systems such as turbomachinery with multiple
blades are often modeled by arrays of periodically driven coupled nonlinear
oscillators. It is known that such systems may have multiple stable vibrational
modes, and transitions between them may occur under the influence of random
factors. A methodology for finding most probable escape paths and estimating
the transition rates in the small noise limit is developed and applied to a
collection of arrays of coupled monostable oscillators with cubic nonlinearity,
small damping, and harmonic external forcing. The methodology is built upon the
action plot method (Beri et al. 2005) and relies on the large deviation theory,
optimal control theory, and the Floquet theory. The action plot method is
promoted to non-autonomous high-dimensional systems, and a method for solving
the arising optimization problem with discontinuous objective function
restricted to a certain manifold is proposed. The most probable escape paths
between stable vibrational modes in arrays of up to five oscillators and the
corresponding quasipotential barriers are computed and visualized. The
dependence of the quasipotential barrier on the parameters of the system is
discussed.
