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# Physical meaning of generalized mass in normal modes?

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## Physical meaning of generalized mass in normal modes?

(OP)
I've always normalized so that the generalized mass is 1, but the Nastran lesson here (http://www.aerospacengineering.net/?p=2652) mentions that MAX normalization can lead to developing more intuition for what's going on based on the generalized mass. Can anyone explain what generalized mass physically means in more detail? I always thought the normalization of mode shapes was completely arbitrary.

### RE: Physical meaning of generalized mass in normal modes?

I agree with you the mode shapes are arbitrary so doubling the eigenvector would quadruple the modal (generalized) mass.

I don't know exactly how it's done in NASTRAN but if "MAX" normalizes the vector such that the largest component is 1.0, that would interesting. Imagine a twisting mode of a starship, the mass matrix will be weighed by their respective modal displacement so the generalized mass would be large. On the other hand, a mode with the captain's chair going into local resonance will have the tiny mass of the chair weighed high while the rest of the starship's mass would be weighed to small fractions squared. The generalized mass here is thus much smaller.

Though it could provide good insights, I disagree with the linked page comment that it can be "useful in the determination of the relative participation of an individual mode". The participation depends on how the structure is excited. The captain's chair could still be excited despite scoring a low generalized mass.

Best regards,
Jason

### RE: Physical meaning of generalized mass in normal modes?

(OP)
I think they may have been confusing generalized mass with modal effective mass. Part of finding effective mass is the general mass, right? Maybe they just meant that general mass helps lead to the effective mass.

### RE: Physical meaning of generalized mass in normal modes?

I think the author uses the terms "generalized mass" and "modal mass" interchangeably.

Modal effective mass is a different beast altogether. 40818 describes it eloquently in this thread: http://www.eng-tips.com/viewthread.cfm?qid=236820

Best regards,
Jason

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