On the vibration and stability of spinning axially loaded pre-twisted Timoshenko beams

Two sets of lateral vibration equations for a spinning axially loaded twisted Timoshenko beam have been studied. The compressed axial load is assumed to be normal to the shear force and tangential to the axis of the beam for the two systems, respectively. A quadratic eigenvalue problem of a real gyroscopic system is formulated and utilized to investigate the free vibration and buckling stability of various twisted Timoshenko beams. Some typical results are compared with numerical results in the published literature to validate the accuracy of the presented analysis. The influence of thickness-to-width ratio, twist angle, spinning speed and axial load on the natural frequency and buckling load of Timoshenko beams has been investigated and discussed. Comparisons between the results of the two sets of system equations are also made to justify the effect of the axial load for various Timoshenko beams.