OrcaFlex - What is 'nodal period'

There is a complex interaction and a somewhat regular period on the pull of a boat on a mooring. Is that what OrcaFlex is suppose to calculate?

 

OrcaFlex is usually used for moored offshore structures with long mooring lines underwater. If the natural frequency of the wave exciting the moored vessel/buoy is close to the natural frequency of vibration of the mooring lines, then large oscillations can develop - this is bad...

 

That makes sense. The problem must be to try to use it to calculate a mooring line 2.5 meters long. It must be beyond the accuracy of the software.

 

I'm still struggling to understand why should the integration time interval be related to the natural frequency of a single element (say, 1-2 m length and 100 Hz frequency), when you actually have to deal with the harmonic modes of the whole line (say, 30 m length and around 5-10 Hz). I can't believe that the numerical algorithm used requires such a terrific computational cost.

Single elements should be treated like rigid bodies with only 6 degrees of freedom, imho, and no vibratory motions. The sum of their rigid body motions give the oscillatory motion of the line.

 

If your mooring line is 1.5 meters, you are in 40cm of water. I think the vibration of the line, regardless of length, is irrelevant. A cyclic pulling always happens, as anyone on a moored boat knows. Seems that using the program for such a short line is like using a yardstick to measure a hair's width.

 

The very short time step needed comes from the use of the simple explicit solver. Explicit solvers are very simple and efficient for an individual increment. They are also generally robust provided the increment is small enough. The tradeoff is the increment has to be small. The maximum size of the time increment is related to the size of the elements and the time scales inherent in the equations for the elements. In this case the relevant time scale can be considered as the natural period of the element.

Implicit solvers allow much longer time steps, and frequently will automatically adjust the time increment to run as fast as possible. The tradeoffs of implicit schemes is they are more computationally intense per time step, and they have parameters which need to selected. Wrong selection of the parameters can either cause longer run times or, in some cases, the solution can be incorrect.

The choice of an explicit or implicit solver depends on the problem to be solved. As floating noted in a previous message in this thread, OrcaFlex has both explicit and implicit solvers and the user can select which one to use. Apparently his experience is that the implicit solver ran much faster for his problem.

 

Natural period, ok. But what natural period? Not the natural period of vibratory modes of single elements imho, because it is an overkill (100 Hz !), but the natural period of single-element's rigid-body modes. Which (imho imho imho) should be several times higher, and hence the frequency lower.

 

The approriate type of elements depend on the physics of the problem and what information is sought.

1) Consider a guitar string and the time history of the guitar strong is desired. If a guitar string is modeled a string of rigid elements, then the string can't vibrate. Probably the simpliest way to model a guitar string is using simple spring-mass elements. Each element has a spring in one direction which exerts a force proportional to the elongation in the axial direction, and a mass lumped at one point. These elements can be assembled in a string and the equations of motion in the time domain derived.

Either an explicit or an implicit solver can be used to solve the equations of motion. If an explicit solver is used then the time step will need to be proportional to the square root of the (stiffness divided by the mass) of the smallest element. That can be considered as the natural period of the element. It is not related to the natural period of the guitar string.

If an implicit solver is used the time increment can be much longer, and this is the reason implicit solvers are generally prefered for complicated problems.

2) Consider the catenary problem of a suspended thin cable, tensioned only by gravity, being buffeted by wind gusts. In this case modeling the cable as rigid elements with mass is probably appropriate since elastic stretch of the cable will have only a second (or higher) order effect on the solution. If an explicit solver is used there will still be a limit to how long the time increments can be. My guess it would be proportional to the square root of the (acceleration of gravity divided by the length) of the smallest element. This could be considered as the natural period of the element if it was a pendulum even though the elements are not pendulums.

3) The question should be asked as to how many elements and how small elements are needed to obtain a solution with the desired accuracy. More and smaller elements improve accuracy but at computational cost.

4) Back to the mooring lines for the buoy. A question when modeling such a system is whether the elasticity of the lines needs to be considered, or whether they can be treated as suspended catenary. It probably depends in part of whether the line ever will become straight enough that the tension in the line depends significantly on the elastic stretch of the line.

 

You have several things to consider:
*the tension is always changing
*the distance between ends is always changing (in direct relation to above)
*it is dampened by water
*elasticity of the line
*weight and shape of the buoy( to calculate inertia, wave resistance and wind resistance)

 

It depends on the type of element. If it's a simple spring-mass type then the time scale will be that of the vibration of the simple spring-mass system. If it's a higher order element with more degrees of freedom than it will be the the shortest vibratory mode of the higher order element system.

 

That's why an analysis tool such as OrcaFlex is used rather than paper and pencil. OrcaFlex should be able to include for all of the factors which gonzo mentioned by modeling the system as a large number of elements, calculating the location and velocity of each element at each instant in time, calculating the intantaneous forces, and then solving for the motion at that instant in time.

 

DCockey, looks like we don't speak the same language here... So, I'll use graphics to express myself.
What I am saying is this: (see the attached picture). Considering the uncertainities in every single factor involved in the mooring design, I think that any more complex model than one in the pic would be an overkill.
So if ones' analysis of mooring lines involve elements with 0.01 s (100 Hz) natural periods, I really have to agree with Gonzo's last phrase in the post #20.

 

I believe floating is calculating the motions of buoy moored in deep water. The 1 to 2 m is the size of an segment of the bridle model. Floating said in post #7 above: "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'm considering a single element to to have both a spring and a mass, draw a box around one spring and one mass in your illustration and that's what I was considering to be an element. An alternative which I think is what you are suggesting would be to model the system as alternating mass-less springs and point masses, which would also work. The resulting sets of equations would be equivalent, assuming the same number and sizes of spring-mass combinations. The time interval limitation for an explicit solver would be the same.

The time interval limitation is driven by the period of the highest natural frequency mode of the discret system model. In most, but not all, cases this corresponds to the natural period of a single element. With the springs and masses considered as separate elements it would be shortest natural period of adjacent spring-mass combinations.

Mathematicians would be using a different terminology of eigenvalues and eigenmodes of the system of equations. Eigenvalues correspond to natural frequencies, with the time step limitations proportional to the inverse of the largest eigenvalue.

 

I understand what you are saying. However, I believe it would be interesting to see some numbers, in order to understand where does 100 Hz natural frequency comes from. The string equation in my first post here can explain that, but it implies that every single 1-2 meters long discretized element is treated as a vibrating string. That's where my doubts come from, because that would be a real mathematical excess.

Could you please provide a numerical example of discretization with point-mass-spring system of a, say, 10 meters mooring line broken into 1 meter segments, so we'll see if it gives such short natural periods (0.01 s).
Please, let me not be misunderstood. It is not a challenge, it's my curiosity. If you don't feel like doing it or don't have time, I might give it a try myself, but not now.

Cheers!