Modeling and bifurcation analysis of the centre rigid-body mounted on an external Timoshenko beam

For the system of the centre rigid_body mounted on an external cantilever beam, the equilibrium solution of the steadily rotating beam is stable if the effect of its shearing stress (i.e. the beam belongs to the Euler_Bernoulli type) is not considered. But for the deep beam, it is necessary to consider the effect of the shearing stress (i.e. the beam belongs to the Timoshenko type). In this case, the tension buckling of the equilibrium solution of the steadily rotating beam may occur. In the present work, using the general Hamilton Variation Principle, a nonlinear dynamic model of the rigid_flexible system with a centre rigid_body mounted on an external Timoshenko beam is established. The bifurcation regular of the steadily rotating Timoshenko beam is investigated by using numerical methods. Furthermore, the critical rotating velocity is also obtained.