# FEM modal analysis scaling

Hi all,

I have an FEM model that I am doing a modal analysis of. I wanted to check that how I am computing the physical displacement is the correct way, as I've read a lot of about normalising modes, participation factors, effective masses, etc. and I'm not 100% sure on it.

I've got the various mode shapes and frequencies but now I want to compute how much actual displacement I get if I apply a harmonic force to it. However, I don't want to compute this using the FEM tool as I want to compute a displacement in another tool.

So if I have made my FEM model using units m/kg/N/s and computed a set a modal mass normalised modes, {\phi_i}, whose respective amplitudes are q_i. The physical displacement of my model would then be:

$$U(x,y,z) = \sum_i q_i \phi_i(x,y,z)$$

Does this have units of meters as my modes are mass normalised or do I need another scaling factor here?

The actual mode amplitudes I compute with:

$$q_i = F_i / (-w^2 + j\,C\,w - w_i^2)$$

Here w is the frequency I'm looking at, C some damping constant, w_i the resonance frequency of the mode. The actual force I apply in my other tool is some factor of the generalised modal force, F_i. Which is just a projection of the forces I choose to apply in units of Newtons into the various modes.

Does the above sound correct?

If so, do FEM models typically output using modal mass normalisation just because the calculations of displacements are straight forward like this?

Thanks for any help!