Free vibration of high-speed rotating Timoshenko shaft with various boundary conditions: effect of centrifugally induced axial force

A new analytical solution for free lateral vibration of a rotating Timoshenko shaft with various boundary conditions is presented in this paper. Gyroscopic and rotary inertia effects, as well as the couplings associated with the shear deformation in Timoshenko shaft, are considered in the equation of motion. Both forward and backward undamped natural frequencies can be obtained for simply supported (S-S), clamped-clamped (C-C), clamped-simply (C-S), clamped-free (C-F) and clamped-guided (C-G) boundary conditions using state-space approach. A centrifugally induced axial force, which is produced as a result of Poisson’s ratio, is also included in the equation of motion. The effect of this axial force on the lateral natural frequencies is investigated as the rotational speed increases. Numerical results and illustrative examples are given and comparisons are made between the results of the present method and those of the previous works.