OrcaFlex - What is 'nodal period'

[floating]

I am using the software OrcaFlex to model the motions of a moored buoy in waves. The manual says to pick the integration time step based on the "shortest natural nodal period" of the system, which for my model is 0.01 seconds for one of the lines in the mooring bridle.
1) What is the definition of the "nodal period" for a line? Is it the period of strumming? I can't think of many real processes that have such a small period (model doesn't include eddy shedding, for example).
2) Does 0.01 seconds sound like a realistic nodal period for an elastic line (Spectra) under tension?

[Boat Design Net Moderator]

Humorous replies split to http://www.boatdesign.net/forums/ope...iod-36750.html

[daiquiri]

0.01 s period corresponds to 100 Hz. Now, I don't know if you play guitar... If you do, you'll understand this example: the "A" string of a guitar (the 2nd string) vibrates at a fundamental frequency of 110 Hz. So, you are talking here of a buoy line which vibrates like a gutar string, which sounds quite unlikely to me. I'm really not an expert in mooring systems but I've seen some of them, neither of which would vibrate at such a high frequency.

Anyways, you can make a quick check of that value if you know the line tension and material. The fundamental frequency of a vibrating string is given by the equation

f = ( square.root ( Tension / LineicDensity ) ) / ( 2 * Length )

where LineicDensity is mass per unit length.

That's for a string vibrating in air. In water, the density is apparently bigger since there's an added mass of water to be considered - so the frequency will be much lower. How much lower - I don't know.
Hope this helps at least a bit.

Cheers!

P.S.
And if you don't play guitar, I suggest you to try to learn it. It's such a wonderful, versatile and funny instrument.

[daiquiri]

I've found some data for Spectra ropes here: http://www.machovec.com/rope/spectra_12strand.htm

Don't know what diameter are your lines, but consider an example of a 40 mm rope. Its lineic density (from the data sheet in that webpage) is 98 kgs/100 ft = 3.2 kg/m. If you put that number in the above equation, and assume frequency equal to 100 Hz, you get that a 40 mm spectra rope could vibrate at 100 Hz only if its tension is equal to, circa:
T = 129.6 * Length^2
where Length is in meters and T in kN (kilonewtons).

But since the maximum tensile load of the rope is 828 kN (from the rope data sheet), you get the maximum length of 2.5 meters.

So, considered that particular rope, it can vibrate (in air) at 100 Hz frequency only if its length is less than 2.5 meters. You decide if that's your case.

Cheers!

[DCockey]

daiquri, you are not using a proper analysis program but rather relying on the outdated stuff that is/was taught in engineering school. Don't you know that such knowledge is no longer needed with modern computer codes. Plug in the data and the answer pops out.


Thoughts for "floating":

The time step needs to be appreciably shorter than the natural periods of the components of the system inorder to resolve the detaoils of the motions of the components.

On the other hand a very small time step can take too long to converge. What you need to decide is what needs to be included in your model. Is resolving the 100 Hz vibrations of a piece of the bridle important for the information you need? If it's the motion of the buoy which is over concern than the answer is probably not.

[gonzo]

I'm with Daiquiri on this. Understanding the principle allows you to know if the answer makes sense. There are a lot of undereducated people that can push keys on a computer or a calculator and believe themselves engineers. Garbage in=garbage out. Calculating the frequency of a vibration is very simple. Also, the formula is not outdated, unless you have any information about the Laws of physics having changed. A line vibrating under water is dampened and will have a longer period than in air.

[floating]

Thanks for the equation for frequency as a function of line length, which explains why I am getting such high frequencies. Lines in OrcaFlex are broken into short segments, as if they were a series of rods connected by spring joints. The segments should be short enough so that the resulting line shape looks right (makes a smooth catenary), but not so short that the simulations take days to run. In my model, the bridle's line segments are around 1-2m (actually too long). While the resulting high-frequency behavior (0.01s) isn't relevant to a real buoy in real seas, it must be resolved by a very small time step or else the simulations crash.

I can get around this in OrcaFlex by modeling each leg of the bridle as a Link (massless spring/damper) which I believe doesn't require segmentation. The rest of the mooring will be modeled more accurately as a Line. Will report back whether this produces reasonable results. Thanks for the engineering insights!

[daiquiri]

Thank you Gonzo, but I read DCockey's words as a sarcastic way of telling the same thing you are saying (and which I endorse).

Of course the formula is not outdated, because the physics is still the same as always - as you've said . It is being commonly used by makers of string musical instruments to determine the distance between nut, frets and bridge. And it works, I can assure that. My guitar works.

Cheers!

[DCockey]

daiquiri understood my attempt at humor. I should have added a smilely face which I'll do.

I have to disagree with gonzo about the uneducated people. There are a lot of educated people with degrees, some advanced, who believe that all which is needed for an engineering analysis is running computer software, and the only knowledge which is required is how to enter input. I do agree about Garbage in=garbage out. But it's even worse than that. Good data into good software which is the wrong software for the job = garbage out.

None of this is intended as a comment on floating and his knowledge or ability. And based on a quick look at the OrcaFlex website it appears to be suitable software, though having to use time steps based on natural period of individual elements is surprising to me. I would have thought there is the ability to add damping to make the calculations stable, though then the amount of damping which stabalizes the calculations without too much impact on the solution has to be determined.

[daiquiri]

Yes, computers have their good sides and advantages, but also one big disadvantage - they tend to make us become overconfident and somewhat lazy.

[floating]

Some more information on high-frequency modes in OrcaFlex, so other users can learn from my 'experience' (mistakes). Numbers refer to sections of the manual.
a) Implicit time integration includes numerical damping, and should be the first choice for stable simulations. For explicit time integration, consider adding numerical damping via 'Line Target Damping'. 6.4.6
b) You can get the natural period of all components of your model by calculating the statics (Calculation > Single Statics), then Results > Full Results > All Objects. The natural periods for each model component is listed in a table.
c) Artificial short period oscillations (0.01s) are likely due to short line segments or high stiffness values in components such as lines, winches, or seabed where lines touch.
d) You can animate any of the modal oscillations in Results > Modal Analysis to get more insight into them, 7.
Sorry for the software-specific info, but hope it helps someone.

[gonzo]

I don't understand the relationship with waves and the vibration of a line at tension. To start with, no mooring line has a constant tension. Also, it would be infinitesimal the possibility of the line vibrating at a harmonic of the wave frequency. Even if they did, what does that affect?

[DCockey]

Originally Posted by gonzo

I don't understand the relationship with waves and the vibration of a line at tension. To start with, no mooring line has a constant tension. Also, it would be infinitesimal the possibility of the line vibrating at a harmonic of the wave frequency. Even if they did, what does that affect?

The stability of the solver algorithm, particularly an explicit one, can be directly related to the time step interval relative to the time scales of the system, and the natural period of the components provide a good way to estimate the time scales of the system. This appears to be what floating encountered.

Also, if the peak dynamic forces in the mooring cables are of interest, say when a cable goes slack and then snaps tight, then resolution at the time scale of that cable may be needed. One way to work around this is to look at the energy being put into the cable rather directly at the forces/strain of the cables themselves.

[gonzo]

How does the vibration of the mooring line affect the calculation? It will change depending on how much is submerged and how much of it is wet.

[DCockey]

Originally Posted by gonzo

How does the vibration of the mooring line affect the calculation? It will change depending on how much is submerged and how much of it is wet.

A disclaimer. I have no experience with or direct knowledge of OrcaFlex beyond reading what's on the website and a quick scan of the manual. I have studied and developed numerical modeling and solution methods in the somewhat distant past, including modeling a wave energy buoy-pump system. The OrcaFlex website is at http://www.orcina.com/SoftwareProduc...Flex/index.php The manual is at http://www.orcina.com/SoftwareProduc...entation/Help/ and the manual section on the dynamic solution method can be found at Theory > Dynamic Analysis > Dynamic Analysis: Calculation Method.

OrcaFlex is a finite element type program in which a complex system is modeled as a network of simplier elements. For time-domain dynamic calculations the equations of motion for the system as modeled are derived, and these equations include first (velocity) and second (acceleration) derivatives with respect to time. The equations are solved by stepping through time.

OrcaFlex has two solution methods. One is a simple, explicit solution method. At a given time instant the forces acting on each element are calculated, then the corresponding accelerations are obtained. These accelerations are then integrated for the time increment to obtain the velocities and displacements at the end of the time increments. The process is then repeated for the next time increment. The approximation made in the explicit solver is that the accelerations are constant for that time increment. This is a reasonable approximation if the time increment is short enough, but can be seriously in error and lead to overshoots if the time increment is too long. In turn the overshoots can lead to even larger overshoots; the calculations go unstable and the solution "blows up". Even a problem with only a few elements which may not be of direct interest as far as the results go can cause the entire system to blow up. The critical question with the explicit method is how short does the time interval need to be to prevent blow ups? It turns out that the length of the time increment which works for this method is directly tied to the shortest natural period of oscillations of the system.

OrcaFlex also has an implicit solver. This solver doesn't assume the accelerations to be constant during the time increment and trys to estimate the changes in the accelerations during the time period. Iteration is required and it's a more complex solution method. The beneficial tradeoff of an implicit method is generally considerably longer time increments can be used.

With either solution method the forces are calculated based on the current state, including the velocities, displacements, tensions in lines, etc.

So the problem with the "vibration" of the mooring line is not a physical phenomena, but rather due to approximations made in the solver.