Page 230 - Steam Turbines--Design, Applications, and Rerating by Heinz-Bloch, Murari-Singh

Campbell, Goodman, and SAFE Diagrams for Steam Turbine Blades 209

Figure 11.23 Some mode shapes (for eight packets) and their harmonic
contents. (Dresser-Rand Company, Wellsville, N.Y.)

The 1-packet and 40-packet constructions are two limits; any other
packeting, such as eight groups of five blades, will fall in between these
two extremes.

11.6 Mode Shapes of a
Packeted Bladed Disk

The mode shapes of a packeted bladed disk are complicated. The
Fourier decomposition of the displacements of each blade does not lend
to only one component (e.g., sin θ or sin 5θ) but other components as
well.
For the example problem of a 40-bladed disk with eight packets, four
mode shapes are plotted together with plots of different harmonic con-
tents in Fig. 11.23.
In general, the mode shape of a packeted bladed disk can be writ-
ten as:

Y(M) =ΣA L sin(Lθ+θ L) (11.4)

for M nodal diameter mode shape