and

 

Natural frequencies of three-disc rotor system are given as (equation(6.35) )

ω_nf1=0

and

On substituting values of various parameters of the present problem in above equation, it gives

The mode shape (relative angular displacements of various discs) can be obtained as summarised in Table 6.1 (refer equations (6.36) and (6.37)). Fig. 6.15 shows mode shapes with node locations, in drawing T, C and G represent location of the turbine, coupling and generator, respectively.

Table 6.1 Relative angular displacements of various discs

Fig. 6.15 Three mode shapes corresponding to three torsional natural frequencies