Figure 6.36 The mode shape and the node location in the actual geared system

Alternative way to obtain the natural frequency is to consider the equivalent two-disc rotor system (Figure 6.34) as two single-DOF systems (one such system is shown in Figure 6.37).

Figure 6.37 A single DOF system

The stiffness and polar mass moment of inertia properties of the system is given as

It gives the natural frequency as

 

which is same as obtained earlier. The whole free vibration torsional analysis can be done by taking the speed of shaft A as the reference and converting shaft B by an equivalent system. For completeness some of the basic steps are given as follows.