Vibration Analysis of a Viscoelastic Beam Equipped with a Resilient Impact Damper

In this paper, the impact damper is used to illustrate that the vibration of all modes of viscoelastic beams can be effectively suppressed. Hertz contact theory is used to model the collision process as a form of stiffness and damping. In addition, viscous damping added between the main mass and the small mass is also studied to increase the consumption of vibration energy of the cantilever beam. Because the collision is discontinuous, the equations with collision and without are established. The Runge-Kutta algorithm is used to solve the differential equation. Taking the first- and second-order mode vibration of the cantilever beam as an example, numerical results show that the multiple-order mode displacement response of the cantilever beam is reduced by the impact damper. Moreover, the mass of the vibrator and the collision gap is very sensitive to the vibration suppression effect of the cantilever beam.