Den Hartog: equivalence of angle/force and displacement/moment

[electricpete]

This is more a statics question than a vib question, but the context is Den Hartog's "Mechanical Vibrations", so I figure I'd try ask it here.

Page 261:

Alpha12 is the angle theta at the disk from 1 lb force
Alpha12 is also the y at the disk from 1 in-lb moment.

Are these two quantities always the same? It seems like he's assuming they are. Seems plausible that there is some kind of reciprocity/duality that causes this in a linear system. There alpha's would be the off-diagnoal elements in a stiffness matrix K such that:
[Displacment, angle]' = K * [Force,moment]'

I'm a little foggy on the related question: Are stiffness matrices always symmetric for simple linear systems?

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[electricpete]

I think I've got it now. The K matrix certainly is symmetric for simple systems such as I am interested in.

Some related discussion of when may not be symmetric was here:

http://maintenanceforums.com/eve/forums/a/tpc/f/3751089011/m/7571023023?r=9541063223#9541063223

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[MikeyP]

Yes, any linear system has a symmetrical stiffness matrix and obeys reciprocity for force vs displacement and moment vs angle

M

--
Dr Michael F Platten

 

[electricpete]

Thanks Mike.

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