This paper investigates the dynamic behaviour of a single rotor-shaft system with nonlinear elastic bearings at the ends mounted on viscoelastic suspensions. A Timoshenko shaft model is utilized to incororate the flexibility of the shaft; the rotor is considered to be rigig and located at the mid-span of the shaft. A nonlinear bearing pedestal model is assumed which has a cubic nonlinear spring and linear damping characteristics. The viscoelastic supports of the bearings are modeled as Kelvin-Voigt model. Free vibration analysis is performed on the linear system including the damping of the bearings. Forced vibration analysis is performed on the nonlinear system. Equations of motion are derived for the nonlinear system based on the direct multiple scale method of one-to-one frequency-to-amplitude relationship using third order perturbation expansion. The effects of stiffness and loss coefficients of the viscoelastic supports on the complex natural frequencies are identified for the linear system. The results show that optimum values of the viscoelastic stiffness and loss coefficient can be achieved for a specific rotating shaft system to reduce vibrations and increase the operating regions. In addition, the frequency response of the nonlinear system indicates that a jump phenomenon takes place for high values of the bearing nonlinear elastic coefficient.

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