Dynamics of A Single Elastic Bodies under Large Rigid Rotation

The generalized elasticity is presented where a modified constitutive relation for the couple stress is proposed. A rigid-flexible coupled model is set up where three types of additional inertia forces along with their increments are elucidated in the model. The finite element formulation is developed with the use of the constrained variational principle. As an example, a dynamic analysis on a rotating cantilever is numerically carried out. The dynamical responses of the displacement and rotational angle at the free end, the stress and couple stress at the fixed end of cantilever are presented. An idea of critical angular velocities is proposed to insure system stability. The displacement trajectory of the free end of cantilever is approached and the dynamic stiffening problem is discussed.