Inplane vibration analysis of rotating beams with elastic restraints

In this paper, the dynamic model of a rotating beam with elastic restraints is constructed by Euler-Bernoulli and Timoshenko beam theories. The study includes the Coriolis effect and the additional effect of dynamic centrifugal stiffness. A modified Fourier series method is used for expanding displacement field functions in the analysis. The standard eigenvalue equation is established and written in terms of the state space for dynamic analysis. Then, the natural frequencies of the rotating beam are calculated. The convergence analysis and the comparison of the results are carried out to verify the applicability of the method. The effects of the rotational velocity and boundary stiffness on the natural frequencies are analysed. The results show that the influence of the linear spring on the frequency is more evident than that of the torsional spring. The boundary can be considered to be elastic restraints when the boundary stiffness is within a certain interval. With the increase in the rotational velocity, the phenomenon of modal exchange appears. The elastic restraints cause the rotational velocity of the modal exchange to lag. Finally, the reason that the fundamental frequency goes to zero with increasing rotational velocity is explained. The Coriolis effect and elastic restraints reduce the critical velocity.