Dynamics of 1-dof and 2-dof energy sink with geometrically nonlinear damping: application to vibration suppression

Nonlinear energy sink (NES) refers to a lightweight nonlinear device that is attached to a primary linear or weakly nonlinear system for passive energy localization into itself. In this paper, the dynamics of 1-dof and 2-dof NES with geometrically nonlinear damping is investigated. For 1-dof NES, an analytical treatment for the bifurcations is developed by presenting a slow/fast decomposition leading to slow flows, where a truncation damping and failure frequency are reported. Existence of strongly modulated response (SMR) is also determined. The procedures are then partly paralleled to the investigation of 2-dof NES for the bifurcation analysis, with particular attention paid to the effect of mass distribution between the NES. To study the frequency response for 2-dof NES, the periodic solutions and their stability are obtained by incremental harmonic balance method and Floquet theory, respectively. Poincare map and energy spectrum are specially introduced for numerical analysis of the systems in the neighborhood of resonance frequency, which in turn are used to compare the efficiency of the NESs to the application of vibration suppression. It is demonstrated that a 2-dof NES can generate extra SMR by adjusting its mass distribution and hence to a great extent reduces the undesired periodic responses and provides with a more effective vibration absorber.