Free vibration of axially loaded, rotating Timoshenko shaft systems by the wave-train closure principle

A systematic approach for the free vibration analysis of a rotating Timoshenko shaft system subjected to axial forces is presented in this paper[ The system has multiple point discontinuities such as elastic supportsrotor masses\ and cross!sectional changes[ Wave re~ection and transmission matrices are employed to characterize the wave motions between the sub!spans of the shaft system[ These matrices are combined with the _eld transfer matrices expressed in wave forms to obtain the characteristic equation in a straightforward manner[ The solutions are exact since e}ects of attenuating wave components are included in the formulation[ The wave propagation!based matrix algebra leads to recursive algorithms which are suitable for computer coding[ Three examples are presented to illustrate the numerical procedure