The vibration analysis of rotating structure is an emerging topic in the era of structural dynamics. When the rotational speed of the shaft is approaching towards the natural frequency of the structure, there may be the occurrence of resonance which leads to vibrate vigorously. The present work is based on the transverse vibration analysis of a rotating shaft. The natural frequencies and mode shapes of the rotating shaft are determined at various modes. The critical speed and resonance analysis on the response of vibrated rotating shaft are also discussed in this work. The mathematical model for the rotating shaft has been considered first to obtain the generalized equation of the proposed structure in theoretical way. Later, the Finite Element Analysis (FEA) was carried out to validate the proposed theoretical method. Numerical analysis has been carried out to compare the exactness of the two methods and found to be very fine convergent.

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