Abstract: In this paper, a rotating Timoshenko beam is investigated. The effect of shear deformation is included into flexural deflection. Then, considering the coupling effects of deformations in the extensional and flexural deflection, the second-order coupling terms of deformations in two displacement fields are developed. At the same time, the axial inertial force and transverse distributed force are considered. The new governing differential equations of the beam in the geometrically non-linear kinematics of deformation are derived using finite element technique and Hamilton’s principle. Numerical examples of a rotating Timoshenko beam are studied to analysis the frequency and tip deflection of the proposed methods, and to investigate the effect of axial inertial force and transverse distributed force and the 'softer effects’ resulting form the coupling effect, with different angular velocities and high-length ratios.

Key words: Timoshenko beam, coupling terms, nonlinear