Free-Free Preloaded Modal Analysis

[nicomedian]

Hello,

It might sound weird but I would like to make a free-free preloaded modal analysis. Imagine that a rocket flies with its pressurized propellant tanks. I want to include the stiffening effect of the pressure. I tried two things:

1. Restrain the structure during static (preload) load step. Refer to first load step and have no SPC definition in modal analysis.
2. Do an unrestrained analysis (inertia relief). Refer to first load step and have no SPC definition in modal analysis.

In both cases, I end up with only 3 rigid modes - very close to zero. The remaining 3 modes are actually rigid modes when I visualize them, but their frequency value are way high. Can anyone think of how to approach such problem?

I am actually doing trial analysis with a representative tank structure; standard steel properties with 50 mm diameter, 0.4 mm wall thickness, 6 mm cap thicknesses, 250 mm length, internal pressure of 0.7 MPa.

Any help would be highly appreciated.

 

[FEA way]

Which software are you using ? How many modes have you requested ? Can you say what kind of structure you want to analyze ?

 

[nicomedian]

Thanks for your reply. I am using Hypermesh as pre/postprocessor and Optistruct as solver. I requested 10 modes. I am attaching .fem file too.

It is a tank cyclindrical tank as follows: Standard steel properties with 50 mm diameter, 0.4 mm wall thickness, 6 mm cap thicknesses, 250 mm length, internal pressure of 0.7 MPa.

 

[FEA way]

Maybe you could try with symmetry or minimum constraint approach (3-2-1 method). Those are typically used for models like this.

 

[nicomedian]

I tried this and ended up with the 4-6 modes are finite, although they seem rigid.

 

[nicomedian]

I tried again to check my constraints. They were improper. After properly constraining the structure by 3-2-1 rule, it worked perfectly fine.

I have now 6 rigid modes and they are all very close to zero.

Edit: I was wrong. Essentially, this gave similar results with Inertia Relief. I still have 4 to 6 modes as finite, but seem rigid.

 

[nicomedian]

After spending my months to this problem, my research and trials lead me some conclusion. The differential stiffness matrix is definitely grounding the rigid body rotational modes. This can be easily verified by simple differential stiffness matrix of a beam. When you give rigid displacements, K*x gives you zero forces, as expected. However, when you give rotations, you end up with reactions, which is spurious.

NX Nastran even mentions about this problem in its Dynamics User Guide. Despite my sincere efforts, I was unable to solve this problem. If anyone has similar experience, and managed to solve this issue, I would be really appreciated.

I also tried to ground the structure by very soft springs and then doing the analysis, but still, I got only 3 rigid modes...

 

[dmapguru]

Take a look at PARAM,KDMFILT,1 in MSC Nastran.

DG

 

[jball1]

I'm not sure I fully understand the details of your problem. But you should be able to do a free-free modal analysis in Abaqus and get 6 rigid body modes. I've done it many times. I'm surprised that you can't do it in any program, which makes me think I'm not understanding the specifics of your problem.

 

[nicomedian]

@dmapguru Thank you for your suggestion. Unfortunately, I use Optistruct and this card does not exist in the solver.

@jball1 The question is not about pure free-free, but a preloaded free-free analysis. In other words, you apply a loading to structure and then perform modal analysis to stiffened structure with free-free condition.

Apparently, as suggested by dmapguru, PARAM,KDMFILT seems to be the only option. However, the details of this card is not given anywhere.

 

[GregLocock]

" Imagine that a rocket flies with its pressurized propellant tanks. I want to include the stiffening effect of the pressure. "

So, you are using a non linear solver (otherwise the preload would have no effect)? There is no such thing as a true modal analysis of a non linear structure, at best you get operating deflection shapes (ODS) for a particular excitation force.

One approach might be to inflate the fuel tank statically, model the deformed geometry, and do a modal on that. You might need mass loading as well.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[nicomedian]

I am using linear solver. The linear solution followed by modal analysis will have the effect of preload. The solver calculates first the element forces, then by using them, it calculates differential stiffness matrix. In the end, the modal solver uses total stiffness matrix.

 

[GregLocock]

Can you get a simple structure that does solve, and try it with different inflation pressures, to check that that is a viable method?

It seems to me there are several confounding effects (1) dimensional changes due to gas pressure (2) mass loading of the skin by the gas and (c) the effect of the skin stress due to pressurisation.

You seem to be hanging your hat on (c).

https://link.springer.com/article/10.1007/s42452-019-1916-z

has some REAL data and an equation that seems to work quite nicely. For air even in a thick walled tank the mass loading effect is significant.



Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[GregLocock]

With a bit of fudging here's the fit of the equation and the test results in that paper


Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[nicomedian]

Hi,

Sorry to respond so late. However, despite my sincere efforts of reading, I still have not managed to understand how the authors was able to do it, as it is acknowledged as a common problem.

Due to the formulation of differential stiffness matrix, we get only 3 rigid modes, the remaining 3 rigid modes are grounded. The author's of the paper do not mention this, which surprises me.