Calculating of structure natural frequencies

[TomekZeWschodu]

Hello all,

Do anyone know a tool, that will help with quick calculations of natural frequencies of: plates / stiffened panels / frame system?
The key is that I need a tool that will include damping of the liquid that may be adjacent to the particular structural elements.

thanks for help

Naval Architect/ Structural Engineer

 

[JStephen]

Short answer, No, I don't know.
One of the standard reference papers for seismic tank design was by a Dr. Veletsos, and as I recall, his tank work was based on prior work relating to dams subject to seismic action. The point of the paper was figuring out what mass of contents in the tank moved with the tank in calculating natural frequencies and responses of the tank. That wouldn't be directly applicable to anything else, but the methods might be of interest if you don't already have a better reference available. It didn't address damping effects, but rather the effective masses involved.

 

[bkal]

Have a look at Blevins, R.D., Formulas for Natural Frequency and Mode Shape. It has expressions for various types of beams and plates, and also addresses effects of fluid.

 

[helfreco]

TomekZeWschodu, is the element you are trying to find the natural frequency or submerged in water, or does it constrain water. If it is simply submerged in water, and the water is not sloshing, the natural frequency would be independent of the fluid it resides in. When you do the Structural analysis, you would have to consider an appropriate damping value, but that would not impact the natural frequency.

If the element is something that restrains a liquid, like the walls of a tank, or a brace that supports a sea wall, then you need to consider hydrodynamic effects. See ASCE 4-98 Section 3.1.6.3. You need to consider the impulsive and convective water mass, more how to calc those in ASCE 4. Once you have them figured out, you can apply the mass to your model and then use whatever structural analysis software (RISA, STAAD, ANSYS, etc) to compute the natural frequency.

 

[JStephen]

I believe that if you submerge an element in water, there will be a change in the natural frequency due to a certain amount of the water moving with the element, changing the effective mass.

 

[TomekZeWschodu]

@helfreco - I am looking for a tool that will be able to consider both, for initial design evaluation ship structures. There are both elements constraining liquids and submerged in them.

As @JStephen mentioned, there is no doubt - fully submerged elements resonance frequencies will different from those exposed on air due to influence of added mass of the liquid. The key issue is to calculate how much. When it comes to sloshing it is not so much important for me at the moment. I am rather looking for some theory to avoid resonance with the rotating machinery installed onboard the vessel.
As I can see all the standards refer to round tanks for oil on the shore. On ships almost all tanks are always rectangular / cuboid - type.



Naval Architect/ Structural Engineer

 

[elreedyman]

For every structure elemen by knowing the structure element end joint constrain and the shape of load (distribute, concentrate...) it is in blast resistance design book. Depends on Bigs formula there are a tables to provide the stifness, and the mass can be calculated then by knowing mass and stifness can obtain the natural frequency.

http://www.elreedyman.com

 

[TomekZeWschodu]

@elreedyman

Thanks for help I will review it once I get it somewhere It looks that simple cases may be calculated by hand with use of formulas that can be found in: MR. Blevins's book: Formulas for natural frequency. It's quite powerfull book. I recommend
For sure cases are simplified and margins of uncertainty must be applied to the results.

However Still there is not so much theories about vibrations in fluids. Issue of calculation of addedd mass is quite... black hole. In above book there are some formulas, but there must be some second source for comparison to proove its reliability.



Naval Architect/ Structural Engineer