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# Large Mass Method

## Large Mass Method

(OP)
Hi,

Could anyone please give me some idea about using the "large mass method" to calculate the structural dynamic response to random or sinusoidal excitations? Why this method is used and what are the advantages?

If I understand it correctly, a paper in my hand says that acceleration excitations are not applied to the corresponding DOFs of the structure directly, instead, a large mass (*10^6 of the mass of the structure) is rigidly connected to these DOFs and a equivalent force (force=largeMass*accerlaration)is applied to the large mass. Why is that?

It seems to me that this is quite a common technique in NASTRAN to calculate the steady state or random responses (to base excitation?) but in the ABAQUS it is not mentioned at all, I am not a Nastran user, but I would expect that implementing such a technique in abaqus should be straight forward, am I on the right track? I notice that in abaqus acceleration can be applied directly to the DOFs, then under what situation that the “large mass method” can be used?

Thanks

John

### RE: Large Mass Method

Hi John,

The large mass method is easy to emplement but there
are a few cautions.

1. You must define a large mass.  Large is a relative
term.  This mass magnitude needs to produce an
inertia force which is significantly larger than
and load in the attached members.

2. If you make the mass too large it will create
numerical overflow problems which will produce
unexpected results.

3. To guarantee a good simulation. Compute the fixed
base frequency and compare it to the large mass
model frequency.  The first mode of course is zero
but the second mode should be the equivalent
fixed base mode.

Have fun
Warren Hoskins
warren_hoskins@yahoo.com

Warren Hoskins
warren_hoskins@att.net

### RE: Large Mass Method

(OP)

A further question that is still puzzling me. If I know excitations in terms of accelerations, say, acceleration time histories, on one hand, I can applied such excitations directly onto the corresponding nodes(DOFs), and will get the calculated response, which I think this is what I can do in ABAQUS.

One the other hand, if the large mass method is to be used, what I need to do is that first attach a large mass to the node(DOF) on which the excitation is going to be applied, then convert the acceleration history to force history by F=LargeMass*acceleration, then applied the force history to the node(DOF) attached with the large mass, which seems to be a method recommended by NASTRAN.

Both ways can get structural response, but it seems to me that the first method is more straightforward and free of assumptions, but why Nastran uses the second method? Am I misunderstanding something here?

Thank you again for your time

regards

John

### RE: Large Mass Method

If memory serves me right, the primary reason the large mass method was used was that Nastran and some other older FEA codes did not originally have base excitation capability and thus it was approximated with the structure attached to a large mass with force excitation (to the large mass).

### RE: Large Mass Method

I believe what is going is that you need to realize the difference between an applied force and an applied displacement.  If a force is applied to a structure, the structure will respond and deform according to the structural properties.  If a displacement is applied, then at the application point, the structure has to displace that amount, regardless of the structure.  In the analysis, a large mass is used to represent a base excitation.  Essentially, the structure has to move the applied displacement in both approaches.  I know ABAQUS has native base excitation approach and so you do not need a large mass to mathematically represent a base excitation by a large mass.

### RE: Large Mass Method

(OP)
Thanks very much, KSWpe and FeaGuru,

In ABAQUS, when subspace projection method is to be used then again boundary conditions need to be approximated by the "Large Mass Method". As described in its users' manual, "in the subspace projection method it is not currently possible to specify nonzero boundary conditions directly".

Does it mean that it is "theoretically currently unavailable" or it is actually theoretically available but has not yet been implemented in abaqus.

It seems to me that when transforming the EOM from the physical space to the modal space will not affect excitation if the excitation is forces. But if the excitation is disp, velo or acc. then I have the problem. How to enforce the known acceleration from the physical space in the modal space, or do I need to? Is this the reason why the nonzero boundary conditions can not be directly applied when subspace technique is used?

### RE: Large Mass Method

(OP)
I have a problem similar to what has been discussed here.  I am running I-DEAS here.  As some of you will know in I-DEAS you can define DOFs and connect them to any node and then apply any excitations.  This did not worked for my model as I have 42 different excitation spectrum. (software limitations)  My next approach is to use the large mass method.  I have added masses of 1E6 to my nodal points and run the model for the normal mode generations.  The results are frequencies, ranging from 1.05 Hz - 1.50 Hz.  I run the model with fixed BCs at the excitation points and it gave me eigen modes ranging from 1800 Hz - 3500 Hz.
My questions is:
1)  Whether the assumptions made for the lumped mass selection are correct.  In other word, do I need to change the masses to get better frequency results.

2) The next step for my analysis is to apply the excitations.  These are in a format of acceleration.  My second question is whether they are needed to be downscaled for removing the artificial effects of the large mass added to the model.

Any suggestions will be highly appreciated.

Thanks,

Moss

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