Dynamics analysis of a bistable 2-DOF coupled oscillator with nonlinear damping

Abstract

This paper investigates the dynamics of a novel bistable 2-DOF coupled oscillator with nonlinear damping. The system is based on a conventional bistable nonlinear energy sink (NES), with nonlinear damping introduced to enhance the vibration absorption efficiency and reduce the threshold for a strongly modulated response (SMR). Initially, the slow invariant manifold (SIM) of the system is derived using complexification-averaging and multiple scales methods. The characteristics of saddle-node (SN) bifurcation and Hopf bifurcation at the periodic fixed point are then analyzed, identifying the ranges of stiffness, damping, and other parameters that influence the SMR. Subsequently, the SIM is examined in detail across different timescales, and the amplitude thresholds of external excitation that trigger SMR are derived. Finally, the system's maximum amplitude is optimized to reduce it while ensuring the generation of SMR. A numerical analysis of the energy spectrum near the resonance frequency is also conducted to compare the vibration suppression efficiency between the conventional NES and the bistable NES with nonlinear damping. The results demonstrate that the bistable NES with nonlinear damping effectively lowers the external excitation threshold for SMR, offering a wider threshold range and higher vibration suppression efficiency. Key parameters such as the mass ratio, linear and nonlinear stiffness, and nonlinear damping significantly influence the occurrence of SMR.