Bifurcation and chaos of a linear structure with a nonlinear energy sink

A nonlinear energy sink (NES) is an effective device to reduce structural vibration while keeping the system frequency unchanged. However, a nonlinear energy sink may leads to complex dynamics such bifurcation and chaos. The investigation treats bifurcation and chaos in forced vibration of a harmonically excited linear structure coupled with a nonlinear energy sink. The bifurcations with the varying NES mass and NES nonlinear stiffness are numerically examined via the Poincaré map. Dynamical behaviours are identified by phase trajectories amplitude spectrums and Poincaré maps. The bifurcation diagrams reveal that the responses of the structure and the energy sink are periodic except a few bursts of chaotic motions. In addition, the dynamic behaviours of the structure may be different from those of the nonlinear energy sink for appropriate parameters.