Investigation on dynamic stability of Timoshenko beam using axial parametric excitation

Vibration mitigation has been an important research interest in the past decades. In this paper, the enhancement of vibration suppression of thick beams is investigated. The Timoshenko beam is considered, and finite element method is used to discretize governing equations for the beam consisting of axial load. The stability of the system is studied both numerically by using Floquet theory, and analytically by employing averaging perturbation method. Effects of the thickness change, also boundary conditions are provided. The results demonstrate that, by adding extra boundary condition, the stability of the beam increases under the same circumstances. It means that, boundary condition can play important role in mitigating the vibration. Moreover, considering the thick beam reveals that the equivalent damping of the beam enhances. In this case, the excitation amplitude as well as the excitation frequency will increase. Therefore, under the same condition, the thicker the beam is, the more stable it will be.