Abstract
In this paper a co-rotational finite element formulation combined with the rotating frame method is proposed to derive the equations of motion for a rotating inclined Euler beam with constant angular velocity. The steady state deformation and natural frequency of the infinitesimal free vibration measured from the position of the corresponding steady state deformation are investigated for rotating inclined Euler beams with zero setting angle. The element deformation nodal forces, inertia nodal forces, stiffness matrix, centripetal stiffness matrix, mass matrix and gyroscopic matrix are systematically derived by consistent linearization of the fully geometrically non-linear beam theory using the d'Alembert principle and the virtual work principle in the current rotating element coordinates. Numerical examples are studied to investigate the steady lateral deformation and the natural frequency of rotating inclined beams with different inclined angle, angular velocities, radius of the hub, and slenderness ratios.
