Analysis of steady-state dynamics and stability of particle dampers considering the friction effect

Abstract

This study analyzes the steady-state dynamics and stability of a structure with a particle damper considering the friction effect between the particle and container, with a focus on whether the system can maintain stable-state motion for an extended period. The determination of friction’s contribution and the maximum allowable gap clearance for steady-state motion is demonstrated through the solution of motion of the primary structure with a particle damper subjected to low-frequency vibration conditions. Additionally, stability analysis is conducted to assess if initial disturbances cause deviations from the original stable state and identify necessary parameters for stability when the system parameters are uncertain. Analytical descriptions for the stability of the system are derived. The effects of friction on the dynamics and stability regions of the particle dampers are systematically revealed, where the theoretical and numerical models are mutually verified and supported by the cases of previous studies. Results show that the inclusion of the rolling friction effect will disrupt the steady-state motion as gap clearance approaches the optimal value. As the coefficient of rolling friction increases, the stability region’s area gradually decreases with a notable leftward shift of its right boundary. This shift ultimately leads to a leftward shift in the optimal vibration reduction curve. In the range of gap clearance variation allowing for steady-state motion with two symmetrical impacts per cycle, the relative velocity of the particle is more effective and intuitive to reveal the vibration reduction mechanism of particle dampers than other perspectives such as momentum, energy, and phase.