Resonance in Balded Disk

[Domainpower]

i would highly appreciate if someone could clear my doubt regarding resonance condition of a cyclic structure (say Bladed disk). Most of the articles mention two conditions to be respected:
matching frequency ( excitation force and natural frequency)
matching nodal diameter of the structure with force shape (m=k).
My question is linked with the second condition
i have found in some papers this condition more completely mentioned in the form
k = Nn + m and k = Nn- m.
where N is the number of blades and n = 0,1,2,3...

which shows that a positive work can be done on a bladed disk even when the shape of the force is larger than N/2 on a
lower nodal diameter.Can someone explain this?

Is this applicable to a particular kind of bladed disk (say packeted bladed disk) or it is applicable in general to any configuration of bladed disk?

Regards
Rajesh Kachroo
Alstom Power

 

[turb1]

I'm not familiar with the equations that you posted, maybe the referenced paper was specific to a particular kind of bladed disc.

My experience is that the nodal diameters are calculated using modal analysis (FEA), then plotted versus the forcing function (nozzle/vanes and operating speed) via a safe diagram to see which mode shapes align with the forcing function in the operating range. Even though the mode shapes/frequencies change with the blade count, they are not directly related to the modal frequencies to the point that a simple equation as listed above could be used.

Maybe you could link the paper referenced?