[MBDyn-users] How to perform a direct eigenanalysis of a curved beam with MBDyn

Resch Reinhard Reinhard.RESCH at accomp.it
Fri Mar 4 14:59:49 CET 2011

Dear Mr. Masarati,

In the attached file you can find an updated version of the curved beam model to be included in the examples. I have added some comments and fixed the error of the mass distribution.

The input file for the finite element model is also included in this file.
It uses straight two node Euler Bernoulli beam elements in order to model the curved beam.
I used a simple in house FE software for beam structures and rigid bodies with eccentric nodes written in GNU octave which is not included in this file.


Reinhard Resch
Research & Development
ACC Austria GesmbH
Jahnstrasse 30
8280 Fürstenfeld, Austria
Tel: ++43 3382 5010-434
Fax: ++43 3382 5010-355
www: http://www.the-acc-group.it/
mail: reinhard.resch at accomp.it

-----Ursprüngliche Nachricht-----
Von: Pierangelo Masarati [mailto:masarati at aero.polimi.it]
Gesendet: Freitag, 4. März 2011 12:18
An: Resch Reinhard
Cc: 'mbdyn-users at mbdyn.org'
Betreff: Re: [MBDyn-users] How to perform a direct eigenanalysis of a curved beam with MBDyn

Pierangelo Masarati wrote:
> Resch Reinhard wrote:
>> Dear Mr. Masarati,
>> Thanks a lot for your help!
>> I've found the reason for the different eigenvalues. There was an
>> error in the mass distribution of the MBDyn model.
>> The difference between the eigenvalues computed by MBDyn and the
>> reference solution is listed in the following table now:
>> f [Hz] MBDyn  f [Hz] FEM    difference [%]
>>      0.14335     0.14358    -0.16094
>>      0.14776       0.148    -0.16205
>>      0.69233      0.6937    -0.19799
>>      0.71231     0.71372    -0.19716
>>       2.2217      2.2258    -0.18499
>>       2.2504      2.2545    -0.18375
>>       4.5724      4.5806    -0.17848
>>       4.6026      4.6109     -0.1796
>>       7.7172       7.731      -0.178
>>       7.7489      7.7626    -0.17677
>> The eigenvalues computed by MBDyn are always a little bit smaller than
>> the reference solution. I think the reason for this difference is that
>> MBDyn uses a lumped mass matrix whereas the reference solution was
>> computed by means of a consistent mass matrix.
> Yes, that's probably one of the reasons; another could be that MBDyn's
> beams are C0, so the shear stiffness is not infinite.
>> I suggest to add the formula lambda = 1/dCoef * (LAMBDA - 1)./( LAMBDA
>> + 1) to the MBDyn input manual.
> I'll do :)  Actually, there's an octave script that's supposed to do
> some post-processing to the raw output, including that operation and
> more; however, it's far from general, so I've never released it, it's on
> the TODO list.

On a related note: you may want to turn this model into an example, I'd
be more than happy to put it in the contributed examples
<http://www.mbdyn.org/documentation/examples/>.  What FEM did you use?
If allowed by the license, you could also post that code's input file.

Cheers, p.

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