Nonlinear Dynamic Analysis of a Rotor Shaft System With Viscoelastically Supported Bearings

Abstract

This research investigates the dynamic analysis of a single-rotor shaft system with nonlinear elastic bearings at the ends mounted on viscoelastic suspension. 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 Kelvin-Voigt model. Free and forced 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. Also, the primary resonance peak shifts to higher frequencies with the increase of the bearing nonlinear elastic characteristics, but with a flattened curve and hence lower peak values. A jump phenomenon takes place for high values of the bearing nonlinear elastic characteristics.

Analytical solution for primary resonances of a rotating shaft with stretching non-linearity

“…In addition, for slender shafts, the longitudinal inertia mü may be negligible [17]. Therefore, equation (11) and boundary conditions u(0…”

“…To solve the system, the Galerkin and continuation methods were used. The dynamic analysis of a rotor shaft system with non-linear elastic bearings mounted on a viscoelastic suspension was analysed by Shabaneh and Zu [11]. Non-linear bearing pedestal was modelled by a cubic non-linear spring and linear damper.…”

Nonlinear Frequencies and Unbalanced Response Analysis of High Speed Rotor-Bearing Systems

“…Villa et al [8] used invariant manifold approach to numerically investigate the responses of a nonlinear rotor-bearing system. Shabaneh and Zu [9] investigated the dynamic analysis of a single-rotor shaft system with nonlinear elastic bearings at the ends mounted on visco-elastic suspension.…”

Nonlinear dynamic analysis of a rotor-porous air journal bearing system with O-rings mounted

“…performed the linear perturbation and the nonlinear transient methods to analyze the effect of support stiffness and damping of O-rings on the stability characteristics of herringbone-grooved aerodynamic journal bearings. Shabaneh et al[21] analyzed the nonlinear dynamic characteristics of the rotor-bearing system with O-rings mounted. Dult[22] presented the development of preliminary equations by using differential operator algebra to analyze the motion of a simple viscoelastic rotor-shaft-system.…”