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The dynamics of mechanical systems such as turbomachinery with multipleblades are often modeled by arrays of periodically driven coupled nonlinearoscillators. It is known that such systems may have multiple stable vibrationalmodes, and transitions between them may occur under the influence of randomfactors. A methodology for finding most probable escape paths and estimatingthe transition rates in the small noise limit is developed and applied to acollection of arrays of coupled monostable oscillators with cubic nonlinearity,small damping, and harmonic external forcing. The methodology is built upon theaction plot method (Beri et al. 2005) and relies on the large deviation theory,optimal control theory, and the Floquet theory. The action plot method ispromoted to non-autonomous high-dimensional systems, and a method for solvingthe arising optimization problem with discontinuous objective functionrestricted to a certain manifold is proposed. The most probable escape pathsbetween stable vibrational modes in arrays of up to five oscillators and thecorresponding quasipotential barriers are computed and visualized. Thedependence of the quasipotential barrier on the parameters of the system isdiscussed.

Most probable escape paths in periodically driven nonlinear oscillators