Model formulation and modal analysis of a rotating elastic uniform Timoshenko beam with setting angle

Based on a six degree-of-freedom model, the dynamics of a rotating and elastic uniform Timoshenko beam at a prescribed setting angle is investigated. A mathematical model with complete formulation has been derived by considering the beam cross section Euler angle in a 3D space. The nonlinear partial differential equations that govern the displacements and rotation angles are obtained by referring to exact geometric relations. The proposed analytical model may be reduced to the common simplified models by discarding some relevant terms in the formulation. The power series method is used to analyze contributions of the centrifugal and gyroscopic forces. Using analytical and numerical means, the complex modal analysis is applied, to examine the phase difference in all directions due to gyroscopic coupling. From the analytical and numerical results, significant dynamics characters of the rotating beam structures are discussed.