Natural frequencies and normal modes of a spinning Timoshenko beam with general boundary conditions

The free vibration analysis of a spinning, finite Timoshenko beam is described. The solutions for the frequency equations and modes shapes for six boundary conditions are also derived. Numerical simulation results show that the simply supported beam exhibits free vibrations behavior different from the other five boundary conditions. The varying forward and backward precessions considered in the study also indicated that each natural frequency corresponds to a single normal mode.