On nonlinear energy flows in nonlinearly coupled oscillators with equal mass

Abstract

Due to the near monopoly held by nonlinear energy sinks in the study of targeted energy transfer, little research has been done on the flow of mechanical energy between oscillators with comparable mass. The goal of the present paper is to investigate the flow of mechanical energy between two nonlinearly coupled oscillators with comparable mass that arise due to the breaking of dynamic reciprocity. The first oscillator represents the prototypical linear oscillator (LO), whereas the second oscillator represents a nonlinear oscillator (NO) that is nonlinearly coupled to the LO only. By breaking dynamic reciprocity, one-way energy propagation is achieved in the system, such that energy can only be irreversibly transferred from the NO to the LO. As such, the NO is isolated from the LO for physically reasonable energies whenever it is not directly excited. Moreover, when the NO is directly excited, there exist regimes where the LO, despite being linear and of comparable mass to the NO, behaves like a nonlinear energy sink and parasitically and irreversibly absorbs energy from the NO. The theoretical portion of this works employs direct numerical simulation of the structure to explore the strongly nonreciprocal dynamics and resulting energy transfers. The theoretical results are then verified through experimental measurements of a comparable structure. The present study promotes a new paradigm for investigating energy transfer in mechanical structures and opens the way for passively controlling the flow of energy in complex mechanical systems.