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 b eam, the equilibrium solution of the steadily rotating beam is stable if th e effect of its shearing stress (i.e. the beam belongs to the Euler-Bernoul li type) is not considered. But for the deep beam, if is necessary to consi der the effect of the shearing stress (i. e. the beam belongs to the Timosh enko type:). In this case, the tension buckling of the equilibrium solution of the steadily rotating beam may occur. In the present work, using the ge neral 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 Timos henko beam is investigated by using numerical methods. Furthermore, the cri tical rotating velocity is also obtained.