This paper involves the development of mathematical model of multilayered viscoelastic rotor using beam finite element and at the same time studying their modal analysis. The operator based constitutive relationship is used to obtain the equations of motion. The FE formulation contents higher order system where the number of order increases with the number of layers exists in the rotor shaft. Under these conditions, the complex modal behaviour of the rotor-shaft is studied to get an insight of the dynamic characteristics of the system, in terms of Modal Damping Factors, Stability Limit of Spin-speed (SLS), the directional Frequency Response Function (dFRF) as well as the direction of whirl of the shaft in different modes. Many researchers adopted this methodology for obtaining the dynamic behaviour of a second order system. This work is started by motivation of the absentia of work for higher order system.

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