Nonlinear Dynamic Modeling, Instability and Post-buckling Analysis of A Rotating Beam With A Flexible Support

By employing the modeling method of flexible multi-body systems, the linear and nonlinear dynamic models of a rotating Euler-Bernoulli beam with a flexible support are established, in which the deformation is coupled with the overall motion resulting from the flexibility of the support. The flexural vibration equation in the linear coupling model can be linearly transformed into the classical model of a rotating beam with a flexible support. The nonlinear model is applicable to rotating beams with different flexible supports. Based on the nonlinear model, the global bifurcation behavior of the rotating beam with supports of different stiffnesses is investigated by applying assumed modes method, and the results including the critical rotary speeds, the diversely buckled-equilibria, and the bifurcation type are verified by the shooting method.