Hamiltonian dynamics and targeted energy transfer of a grounded bistable nonlinear energy sink

Abstract

A two-degree-of-freedom nonlinear mechanical system describing a damped linear oscillator weakly coupled to a lightweight grounded bistable nonlinear energy sink is proposed to investigate the targeted energy transfer (TET) under asymmetric local nonlinear potentials. The bifurcations of equilibria are discussed to reflect the bistable and asymmetric characteristics of the system. Through projections of isoenergetic manifolds, the topological features of the Hamiltonian dynamics under 1:1 internal resonance have been investigated, which induces conditions for energy localization and exchange. In the general case, the topological features of the Hamiltonian dynamics related to the nonlinear normal modes (NNMs) are classified by the Poincaré map, the relations between the NNMs and the Hamiltonian dynamics have been interpreted through the frequency energy plots. The results show that introducing the asymmetric characteristics may enhance the TET and realize the complete TET.