Modal participation factors

[huffte]

Good points, morello. You can really come up with almost anything for modal mass - as you say, it depends on the normalization procedure used on the mode shapes (eigenvectors). Things still work out in the end because the participation factor for a given mode is linearly proportional to the mode shape for that mode. One common approach is to normalize such that:

SUM{M(i)Phi(i,m)^2}, i = 1....N is equal to 1.00 for each mode, m. This slightly simplifies the participation factor, Gamma, which is now:
Gamma = SUM{M(i)Phi(i,m)}, i = 1....N, for each mode, m.

Now, with the normalized mode shapes and corresponding participation factor, the displacement at DOF i for a given mode, m is:
Delta(i,m) = Gamma(m) x Phi(i,m) x SD(m), where SD(m) is the spectral displacement for mode m. The modes are then combined using SRSS or CQC or . . . .

So you really can normalize to virtually anything. The normalization affects the Gamma values, so the response in the end comes out the same regardless.

Maybe your articular problem is best solved by using the mentioned normalization?
SUM{M(i)Phi(i,m)^2}, i = 1....N is equal to 1.00 for each mode, m.

Best of luck, morello.