Suppression of multiple modal resonances of a cantilever beam by an impact damper

Impact dampers are usually used to suppress single mode resonance. The goal of this paper is to clarify the difference when the impact damper suppresses the resonances of different modes. A cantilever beam equipped with the impact damper is modeled. The elastic contact of the ball and the cantilever beam is described by using the Hertz contact model. The viscous damper between the ball and the cantilever beam is modeled to consume the vibrational energy of the cantilever beam. A piecewise ordinary differential-partial differential equation of the cantilever beam is established, including equations with and without the impact damper. The vibration responses of the cantilever beam with and without the impact damper are numerically calculated. The effects of the impact absorber parameters on the vibration reduction are examined. The results show that multiple resonance peaks of the cantilever beam can be effectively suppressed by the impact damper. Specifically, all resonance amplitudes can be reduced by a larger weight ball. Moreover, the impacting gap is very effective in suppressing the vibration of the cantilever beam. More importantly, there is an optimal impacting gap for each resonance mode of the cantilever beam, but the optimal gap for each mode is different.