Breaking reciprocity to realize extreme energy isolation in coupled oscillators

Abstract

This research investigates the isolation achieved by breaking the reciprocity of between two coupled oscillators. The two oscillators have equal mass and the first one is linearly grounded and called the linear oscillator (LO). The second oscillator is nonlinearly coupled to the LO and is termed the nonlinear oscillator (NO). By breaking dynamical reciprocity using asymmetry and nonlinearity, the LO–NO system is shown to exhibit regimes of extreme energy isolation in only one of the oscillators as well as regimes where energy is exchanged between them. These regimes are shown to arise under both impulsive and harmonic excitation. The resulting system is governed by two nonlinear normal modes (NNMs), which can interact with each other under internal resonance of different ratios. Under different loading scenarios, different energy isolations are illustrated. This research starts with analytical study using numerical simulations that assess how energy distributes in the structure under varying loads. The analytical predictions are validated experimentally for both impulsive and harmonic excitations. The results of this research demonstrate that there remains much to learn about energy transfer in general and the breaking of dynamic reciprocity may lead to new types of acoustic and vibrational metamaterials.