Unbalance response and stability analysis of a rotor shaft system, with the rotor mounted in the middle of a massless shaft, having linear elasticity and internal damping, with bearings having nonlinear restoring force characteristics at the ends mounted on viscoelastic support, has been carried out, taking the effect of gravity into account. The restoring force characteristics of the bearing has been linearized, by the method of effective linearization, thereby enabling an approximate stability analysis using simple techniques. It is found that, unlike the case with a bearing having linearly varying restoring force characteristics, gravity not only affects the unbalance response but also causes a decrease in the stability limits when the restoring force characteristics are nonlinear.

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