Model reduction for an internally damped n-particle chain in a potential well under polyharmonic excitation

The study focuses on the model reduction of an internally damped chain of particles confined within a weakening potential well subjected to polyharmonic excitation to investigate the chain’s escape dynamics. The chain features strong linear coupling between particles and nonnegligible viscous damping forces arising from their relative motion. The potential well is modeled to have no energy dissipation, which means that damping arises solely from the internal interactions among particles and not from their motion through a resisting medium. Polyharmonic excitation frequencies are chosen to excite both the center of mass of the chain and at least one of the internally resonant frequencies, which are significantly higher than the linearized angular eigenfrequency of the center of mass within the well. The relative motion of the particles quickly reaches a steady state because of the non-small internal damping, allowing for the derivation of an efficient force field for the center of mass. Eliminating fast dynamics reduces the system’s degrees of freedom to one, employing a probabilistic approach based on the relative motion’s probability density function. The reduced 1 DoF model is appropriate for further investigation using various methods established in the literature.