The planar rotor model is the simplest rotor model. Only
the motion in the plane, which is perpendicular to the
rotating shaft, is considered. The geometric setup of the
planar rotor model is shown in Figure 1.
In this model, the imbalance-induced vibration is
described by the particle motion of the geometric center of
the disk. P is the geometric center of the disk, and G is the
mass center of the disk. The motion is represented by the
vector r. It is well known that the governing equation of
motion is (Childs, 1993)