Vibration reduction mechanism of Van der Pol oscillator under low-frequency forced excitation by means of nonlinear energy sink

Van der Pol (VDP) oscillator under forced excitation has complicated vibration modes, and its harm to the system cannot be ignored. The vibration reduction mechanism of VDP oscillator by means of nonlinear energy sink (NES) is explored under low-frequency forced excitation. Firstly, a mechanical model of VDP oscillator coupled NES is established by utilizing Newton's law. Then the time history diagrams under different excitation amplitudes are compared to measure the vibration reduction effect of the coupled system. Finally, the stability and Hopf bifurcation behavior of the corresponding autonomous system are discussed, and the mechanism of cluster phenomenon and the mechanism of vibration reduction are revealed. It is interesting that, the vibration reduction effect is optimal when cluster phenomenon occurs, which is a typical vibration model in slow-fast system. The real part of eigenvalues and hysteresis time are critical factors affecting vibration reduction. These researches provide a theoretical basis for the vibration reduction of VDP oscillator coupled NES.