Escape dynamics in engineering systems

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The project aims at theoretical and experimental assessment of escape phenomena in engineering systems. The concepts of potential well, and escape from it, are crucial in physics, chemistry and engineering. Very incomplete list of research topics in physics, that are related to the escape processes includes dynamics of molecules and absorbed particles, celestial mechanics and gravitational collapse, energy harvesting and physics of Josephson junctions. In mechanical engineering, the escape dynamics commonly exhibits itself in transient resonance responses of oscillatory systems, buckling in discrete and continuous structures, and even in capsize of ships. The escape dynamics poses double analytic challenge – it is both transient and strongly nonlinear. Previous work and additional preliminary results demonstrate that at least for simple benchmark potential wells and harmonic forcing one can quantitatively predict the dependence of the escape threshold on the excitation frequency in the framework of isolated resonance approximation. Moreover, some promising preliminary results concern the safe zones in the space of initial conditions, paving way to an efficient control and monitoring of the escape-related phenomena. The project aims to extend the method for more generic settings in terms of the dimensionality, subharmonic/superharmonic and combined external forcing, and prediction of detailed structure of the safe basins in the space of initial conditions. It is proposed to develop new methods for exploration of the escape dynamics in the systems where the isolated resonance approximation is irrelevant, in particular for one- and multi-degree-of freedom (DOF) models with general/partial strong damping. In order to verify the validity and limitations of the approximate analytic methods, we suggest to design and perform benchmark experiments on forced buckling in simple single – and two - DOF systems. Successful accomplishment of the project will allow better understanding, design and control of the escape phenomena in a plethora of engineering systems.