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Modal effective mass fraction versus Modal effective mass

Modal effective mass fraction versus Modal effective mass

Modal effective mass fraction versus Modal effective mass

(OP)
I have a very simple model described as follows:
- A 300lb mass and a 100lb mass
- Masses connected via a "soft" spring
- The 100lb mass is connected to "ground" via a "stiff" spring
- The entire model therefore consists of two lumped masses and two springs.
- Element are arranged vertically so the model, from bottom up, is node connected to ground, stiff spring, node + 100lb conm2, soft spring, node + 300lb conm2
- The masses are constrained so that the can only translate in vertical direction

I run a modal analysis and get two modes naturally.  A very low frequency mode corresponding to the top-most 300lb mass "bouncing" and a high frequency mode corresponding to the lower 100lb mass "bouncing".

When I examine the "modal effective mass fraction" I get 0.75 for the first mode (300/400) and 0.25 for the second mode (100/400).  However when I look at the "modal effective mass" I get 0.776 for the first mode and 0.259 for the second mode.

Why is there a small discrepancy between the two? What is the difference between "modal effective mass fraction" and "modal effective mass"?

Any advice is greatly appreciated...

RE: Modal effective mass fraction versus Modal effective mass

You need to read the technical literature for whatever application you are using.  My guess is that the MEM calculation makes some allowance for the motion of the 'other' mass in each mode. MEMF looks almost meaningless, at first sight.


 

Cheers

Greg Locock

SIG:Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of Eng-Tips.

RE: Modal effective mass fraction versus Modal effective mass

Modal effective mass indicates the mass participation of each mode in each of the 6 rigid body motions (T1 to R3). It's only useful under constrained conditions (i.e no Rigid Body modes).

Participation Factors can be negative, and the other outputs - Fraction, MEFF Wt, & MEFF Mass - are positive, related to the square of Participation Factors.

i) Fraction is generally the most useful output - Modal Effective Mass divided by total Rigid Body Active Mass - and adds to 1.0 when all modes are included. You're often looking for mode participations > 0.10 Fraction, and often want to calculate enough modes such that cumulative Modal Effective Mass Fraction > 0.9 in each direction. Essentially the mass fraction is an indicatoer which modes are more readily excited by base vibration.

ii) Modal participation factors are actually the "raw" cofficients of each mode which linearly combine to equal the rigid body vector in each direction. A high absolute value indicates a high participation in that direction. These values are squared & divided by modal mass to give the Modal Effective Mass values. Modal Effective Mass values are in turn divided by total Rigid body Mass in each respective direction to give Modal Effective Mass Fraction's.
 

RE: Modal effective mass fraction versus Modal effective mass

40818, Perfect !!!

RE: Modal effective mass fraction versus Modal effective mass

"However when I look at the "modal effective mass" I get 0.776 for the first mode and 0.259 for the second mode."

The modal effective mass should add up to the total system mass.  0.776*386.4 = 299.85 Lb and 0.259*386.4 = 100.08 Lb.  You problem is a question of units.  Make sure if you input pounds as are on your bathroom scale to use PARAM WTMASS = .00259 to convert to slugs.

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