Bifurcation analysis of linear oscillator coupled to nonlinear energy sink with harmonic forcing

The system under investigation comprises a linear oscillatorcoupled to a nonlinear energy sink (NES) under harmonicforcing. The NES is a small mass which is attached to theprimary system via a linear damper and nonlinear spring.Nonlinear energy sinks (NES) have been shown to beeffective for vibration attenuation under certain conditions.We study periodic and quasiperiodic response regimes ofthe system via complex averaging method and evaluate theabilities. In this paper, one parameter and two parameterbifurcations diagrams are presented to show instabilities ofsolutions. The obtained results give guideline on the effectof NES on dynamic behavior of system.