Spectral element model for the vibration of a spinning Timoshenko shaft

A spectral element model for a spinning uniform shaft is developed.The spinning shaft supported by bearings is represented by the uniform Timoshenko beam model and the bearing-supports are represented by equivalent springs.The variational approach is used to formulate the spectral element model by using the frequency-dependent shape functions derived from exact wave solutions on the frequency-domain governing differential equations.The conventional finite element model is also formulated for evaluating the accuracy of the present spectral element model through some example problems.