Can anyone correct this passage please ? Since the importance of dynamic problems of beams in the design of mechanical structures, the analysis of vibration and stability of no-rotating and rotating shafts under axial loading have been widely investigated. Many structures, such as rotating shafts, satellite booms and spacecraft arms can be modelled as flexible beams. Natural frequencies and mode shapes of such systems are indispensable in the design of such structures. In the vibrational analysis of rotating shafts, the axial load, the rotational speed, geometric aspects, rotary inertia and shear deformation have a considerable effect on the dynamic responses. Generally, based on the Euler-Bernoulli and Timoshenko beam theory, the vibrational behavior of beam structures has been analyzed. It is essential to point out such structural properties in the analysis of structural dynamics and the cancellation of undesirable levels of vibrations.