## 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)

2)

3)

4)

Any help would be greatly appreciated!

Thanks

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

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

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

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

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

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/