Dynamics of flexible beams based on spin softening

A nonlinear dynamic model is developed for a rotating flexible beam. The dynamic equations are derived by using the energy approach and Hamilton's variational principle, in which the effects of the rotating inertia, Coriolis force, stress stiffening, spin softening, acceleration, lateral displacement and bending stiffness are taken into account. Then the finite element dynamic model of the beam is proposed and the effects of the stress stiffening, spin softening etc. are set. Numerical simulation of the beam is carried out and show that the spin softening effect of a beam has significant influence on the bending vibration (swing vibration) frequencies of the rotation plane and the influence on the first order swing vibration frequency is the most significant, which exhibits a nonlinear property, and has little influence on the bending vibration frequencies of non-rotation plane. Results obtained further show the complexity of the dynamic characteristics of rotating flexible beams. To calculate the vibration characteristics of a rotating flexible beam, it must also set both the translational and rotational inertial mass matrices in order to obtain accurate results. The accuracy of the beam model and the solution techniques are demonstrated by comparison with solid model results of commercial software, and the errors less than 5%.