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# Combining Modal Effective masses in the 6 degrees of freedom into a single value

## Combining Modal Effective masses in the 6 degrees of freedom into a single value

(OP)
Hello,

I have spent a couple of days fruitlessly searching forums for the answer, but I haven't found it yet so I thought I was ask it here.

I have seen that in modal analyses, often there is a percentage for each mode which tells you how much of the overall mass is participating in that mode. I am using NASTRAN and have an output for the modal effective mass fraction but it is listed in each degree of freedom (x, y, z, rx...). See attachment

I am very confused as to how to combine these into a useful total effective mass fraction. Currently I have these 3 approaches:
1) Calculate the magnitude by doing sqrt(x^2 + y^2 ... +rz^2). This seems to be the most sensible, but does it make sense to do all degrees of freedom at once?
2) Simply sum all the values. I am sure this will give an answer that is too high, as mass that is rotating, can also be translating, so this mass would be double accounted for?
3) Select the highest value in any of the 6 degrees of freedom?. This feels wrong because changing the co ordinate system would give you the a different answer.
4) What I'm asking for doesn't exist Potentially the most likely. Why would NASTRAN not provide you with a total effective mass percentage for each mode, if it was a simple calculation? And why would I be struggling so much to find an answer.

Any help would be greatly appreciated!
Thanks

### RE: Combining Modal Effective masses in the 6 degrees of freedom into a single value

Hi
What is the purpose of the calculation?

For example, for a seismic analysis I would check the mass participation in three perpendicular directions. So, to summarize three components into a single value, what is the purpose?

Thomas

### RE: Combining Modal Effective masses in the 6 degrees of freedom into a single value

(OP)
Hi Thomas,

Thanks for the reply. I am analysing an aerospace structure, and I have a requirement that states that all modes with a total effective mass fraction of >10% have to be above X Hz. I have no idea how to calculate this total effective mass fraction from the data from NASTRAN.

Does the question I'm asking even make mathematical sense?

### RE: Combining Modal Effective masses in the 6 degrees of freedom into a single value

Hi

Since I don't work with aerospace structures I probably shouldn't be to persistent regarding the requirements .

But I have not seen a requirement like that before. But I have seen requirements stating that all modes with an effective mass >X% of total should be included. And the effective mass was measured in three perpendicular directions. Perhaps it is possible to calculate a total effective mass based on the total mode shape instead of the components.

Thomas

### RE: Combining Modal Effective masses in the 6 degrees of freedom into a single value

I second Thomas' remarks - I have not seen a requirement like this before. My advice would be to return to those stating the requirement and ask them to clarify what they mean.

Thomas also introduces an important notion with seismic analysis, where the structure under consideration is subject to base motion. If your structure has a statically determinate boundary condition (base motion is one such condition), then the effective mass output is giving you the same information as the modal participation factors (to a factor). If the boundary condition of your structure is NOT statically determinate (e.g. it is free-free or statically indeterminate), the modal effective mass is meaningless (at least in the way it is computed in MSC Nastran).

DG

### RE: Combining Modal Effective masses in the 6 degrees of freedom into a single value

Dear Owheel,
This is done pretty well in NASTRAN & FEMAP where you can compute & plot the effective modal mass fraction.
The plot of MODAL MASS vs. mode number will tell how many modes you need to extract when performing a modal dynamic frequency response (SOL111) to account for a good accuracy on the response, minimum 85%: in the following picture of a FEMAP project I had to compute a minimum of 200 modes to account for the 90% of modal mass in the three directions of excitation:

To learn more please visit my blog, I have a few examples of the use of modal mass, for instance:
https://iberisa.wordpress.com/2020/01/07/analisis-...
Best regards,
Blas.

~~~~~~~~~~~~~~~~~~~~~~
Blas Molero Hidalgo
Ingeniero Industrial
Director

IBERISA
48004 BILBAO (SPAIN)
WEB: http://www.iberisa.com
Blog de FEMAP & NX Nastran: http://iberisa.wordpress.com/

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