Modal Analysis - LNF above 3 Hz

Hello everybody,

I am doing modal analysis of a 32" Diesel pipeline, wt 9.52 mm. There are expansion loops 8 m height and 9 m lenght every 250 m. The line is about 30 km lenght, but in our scope we have to focus only on a typical section of about 1 km with 3 expansion loops. There are rest supports every 12 m and guides support every 24 m.

Now, here's my problem. As you know, is good engineering practice to keep the lowest natural frequency above 3 Hz. But after running modal analysis, the LNF is only 0.4 Hz! Wathcing the animation for the 1st mode, I can see that there is lateral displacement at the expansion loops. Then I put guides at the center of the loops and LNF increases up to 2.7 Hz. But still is not acceptable...

Any other ideas?

Note that the line is already under construction, so keep this in mind when you think about some ideas to make the system more rigid! (So forget about snubbers)

Thank you

I noticed that by not considering any gap on the guides, the stiffness increases a lot. This is because as long as you input even 1 mm gap to the restraints, Caesar won't add any extra stiffness to the dynamic model (this can be verified looking at the dynamic output, Active Boundary Condition Report).

Now, how far from reality is not considering any gap on the guides support?

Dynamics in c2 are linear - that means no one-direction restraints, no gaps, and no friction. Since most models include these items, c2 linearizes the model for dynamic analysis.

The linearization is based on the Static Load case you reference in they Dynamic Input, on the Control Parameters dialog. That 1st option "Static Load Case for Non-Linear Supports" specifies which static load case to reference.

The static results from this referenced load case are used to linearize the non-linear restraints. So in the static case, if a gap closes (the pipe moves to the restraint), the gap is removed and the dynamic model has a restraint with no gap. If the gap remains open (the pipe moves but doesn't close the gap), the restraint is removed completely.

You can read the "help text" on this item for more information. This is also explained in the Documentation.

Thank you Richard, now I have very clear picture of how Caesar behave.

Now I can give explanation to my poor 0.4 Hz.

In the Control Parameter Tab I was considering the operating case as the static load case for the non-linear restraint status. In the operating case, uplift occurs at the expansion loops. Hence, the +Y support on the expansion loops were on an "open" condition, not contributing at all to the pipe stiffness.

If I consider the sustained case as the static load case for the non-linear restraint status, LNF reaches the more than acceptable value of 8.1 Hz. This is because in the sustained case temperature is not considered and uplift doesn't occur at expansion loops. +Y support are then on a "closed" conditions, contributing this time to the stiffness of the pipe.

For your information, I am considering 100 as stiffness factor for friction.

Now, this bring me to another question: how correct is considering sustained case instead of the operating case for the linearization of the dynamic model?

You might check out what source of vibration may cause resonance in your pipe.

Do you have fluid induced vibration ?

What wind speed would cause vortex shedding of any concern ?

Is there any other risk to consider ?

If there are no perceived risks, are you possibly wasting your time ?

I am doing dynamic analysis because of surge pressure coming from the closure of an ESD valve.

Anyway, client is asking to satisfy the 3 Hz requirement.

Now, this bring me to another question: how correct is considering sustained case instead of the operating case for the linearization of the dynamic model?

Answer: Modal analysis has been performed to check the possibility of vibration when line is in operating condition. So, if you consider sustain case and satisfy LNF of system is more than 3Hz is meaning less.