Nonlinear free vibration of a rotor shaft system with viscoelastically supported bearings

This paper investigates the dynamic analysis of a single-rotor shaft system with nonlinear elastic bearings at the ends mounted on viscoelastic suspension. A Timoshenko shaft model is utilized to incorporate the flexibility of the shaft; the rotor is considered to be rigid 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 are modeled using the Kelvin-Voigt model. Free vibration is investigated based on the direct multiple scales method of one-to-one frequency-to-amplitude relationship using third order perturbation expansion. The results of the nonlinear analysis show that a limiting value of the internal damping coefficient of the shaft exists where the trend of the frequency-response curve switches.