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# Modal Analysis - modal matrices export

## Modal Analysis - modal matrices export

(OP)
Hello.

I have question regarding the NX Nastran modal analysis. I am working on project which takes Nastran results from modal analysis for further post processing/computation. However, the values which I am interested in are modal mass matrix(Mhh), modal matrix(Phi) and matrix of eigenvalues(omega). Modal mass matrix should be NxN (N-number of DOF) diagonal matrix of ones so thats no problem. The modal matrix Phi is NxN and its columns consists of N eigenvectors. However, I a bit confused since the real eigenvectors listed in output are of AxB dimensions, where A-number of nodes in FEM model and B-number of directions(3 translations,3 rotations) therefore by using these eigenvectors the modal matrix won't be NxN. Can anyone explain how can I build the modal matrix from these eigenvalues so the dimensions would agree? Or, is there any option to directly export these matrices from nastran?

I've also attached a figure which describes the derivation of problem and variables I am interested in. Is there an option to directly obtain some of these (sub)matrices from Nastran?
Thanks.

Mat

### RE: Modal Analysis - modal matrices export

The snip you provided does not tell you how to get the eigenvectors. Typically when you run modal analysis you would not request all possible modes of the model. If the model has N degrees of freedom (DOF), and stiffness and mass are defined at all these DOF (rarely the case), and there are no boundary conditions and no rigid elements or MPCs, then technically you could obtain N eigenvectors and your Mhh, omega and Phi matrices would all be NxN. However, this transformation to modal coordinates is not just for fun; the main reason for doing it is to restrict the computation to the first M important modes, or perhaps the M important modes in a frequency range. Which are the important modes rather depends on what you are trying to achieve, and this is a subject of a different discussion.

So let's assume you have decided that the first M modes ( where M<<N ) are important. If you chose mass normalisation of the eigenvectors, then by definition, as you pointed out the Mhh (modal mass) matrix is an identity matrix and will have dimensions MxM. Likewise, the omega matrix will be a diagonal matrix MxM with the eigenvalues along the diagonal. The eigenvectors in Phi, one for each of the M modes, will have N rows (one row for each DOF) and M columms (one for each mode).

If you have an eigenvector matrix AxB, where B=N and A=number of GRID points, the most likely explanation is that either you requested the number of modes equal to the number of GRID points or you requested a very large number of modes, which the eigensolver has restricted to the number of DOF with mass, and this happens to correspond to the number of GRID points.

You already have these outputs from Natran. The EIGENVALUE SUMMARY TABLE shows you Mhh and omega in the columns GENERALIZED MASS and GENERALIZED STIFFNESS respectively. The eigenvectors may be obtained by requesting DISP=ALL (VECTOR=ALL will do the same thing). These outputs are available in formatted tables (known as OFP tables), but you can also obtain any of these quantities (and others you choose to compute) at the matrix level using the DMAP language, which is again a subject of a different discussion.

DG

### RE: Modal Analysis - modal matrices export

(OP)
Thank you for reply.I've already requested DISP=ALL. You're right, the generalized mass,stiffness,eigenvalues are printed in the eigenvalue summary table, thats no problem. But lets consider simple 2DOF spring-mass system. The system has obviously 2 DOF, so Mhh is 2x2, Phi(modal matrix) should be also 2x2. However, when I look at the printed eigevectors,those are in this case in shape 5x6 where 5 is number of grid points(nodes) and 6 is number of directions. Since Phi is matrix of eigenvectors, than resulting shape would be 5x12 and not 2x2. Ofc, if I ignore all the zeros in those eigenvectors I get the desired shape and result but in general 3D problems,there will be no zeros. So my main confusion is how to obtain the Phi matrix from printed eigenvectors since those eigenvectors are in shape AxB, A-no. of grid points,B-no. of directions(6). I've attached the results file for this particular case.

Mat

### RE: Modal Analysis - modal matrices export

That's not a 2 DOF problem, it is a 30 DOF problem where you have computed the first 2 modes.
Mhh and Khh (omega) are 2X2 because you have 2 modes
Phi is 30 rows (DOFs) by 2 columns (modes).

Remember that in Nastran, all GRID points have 6 DOF whether you use them or not. If GRID points 5,8 and 9 are not doing anything, then remove them from the model. Then you will have a 12 DOF problem where perhaps you are using only the first DOF of each GRID point (the other 5 DOF are restrained either by direct action through an SPC or by the auto-restraint mechanism of AUTOSPC). The eigenvector will always show you all 6 DOF per GRID point, just zero values at the DOF you are not using.

DG

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