# Vibratory System

Discussion in 'Hydrodynamics and Aerodynamics' started by gonzo, Jul 25, 2018.

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### gonzoSenior Member

A shock absorber functions by dissipating energy, which makes it a damper by definition. There are many types of dampers, of which a shock absorber is one.

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### gonzoSenior Member

A fundamental concept:
A oscillating system is one that with a cyclical transformation of energy.

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### MikeJohnsSenior Member

A step input is just the simplest math function to describe two steady states. It's perfectly normal usage. Feel free to change it anything you like providing there a steady state force eventually.

We are just considering the simplest mooring model for a start, that's under the action of a constant tide or wind. Keeping the model in the realm of simple static kinematics to illustrate a few fundamental basics that you are having trouble comprehending.

No Gonzo, you are getting confused again. A damper might be part of a shock absorbing system or a even shock absorber in it's own right.

Analysis must differentiate clearly what energy remains in the system and what energy is removed permanently from the system. In particular you must understand that damping by definition is Removal Of Energy From The System. It's a component of the system and has it's own function that produces the damping factor (that we term Zeta).

There's a huge margin of difference between a linear vibratory system and a dynamic system with possible oscillatory components.
As soon as we introduce dynamics (rather than statics) to even a simple ideal mooring model (say with a spring line rather than a chain catenary) we are going to get a 2nd order DE.
Do you understand how the poles of the transfer function move on the complex plane in response to Zeta ? That explains very well how the damping factor relates to oscillatory behavior.

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### gonzoSenior Member

A step impulse may or may not be the simplest, but can't be used to model an anchoring system. That would mean that the boat pull with full force or not at all.

Every shock absorber is a damper. If it dissipates energy of a system, and the system vibrates, then it is what we define as a damper. You can't arbitrarily change definitions in physics.

Poles are used in controls, and I do understand what they are and their use. On the left of the y-axis we get stable systems, on the axis are marginally, and to the right have positive feedback and usually break. There are several ways to analyze vibrations and that is useful for some applications, but is not the only one. A mooring system has the same level of complication whether it uses a chain or a rope. There is no difference on the model, only on the values.

Further, linear vibratory systems are dynamic. If they were static, there would be no vibrations.

A vibrating system has 3 elementary components, of which only two are necessary: a mas and a spring.
The components are:
*Means of storing potential energy (spring or elasticity)
*Means of storing kinetic energy (mass)
* Means of dissipating energy (damper)
Everything else is extraneous to the system.

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### rwatsonSenior Member

This definition stuff is irrelevant.

It boils down to "can Vibration analysis be used to calculate the effects or outcomes of the behaviors of an anchoring system."

If not, then there is no point to saying that Anchor Systems can be regarded as Vibratory Systems.

If anyone could come up with ONE example, using one of several methods of Vibratory calculus, in certifying Anchor Systems, they might have a point
Even IF anyone has actually done a study of anchoring systems using any calculations involving Vibration analysis, that would useful.

I haven't found one yet. eg.
https://www.ocimf.org/media/8922/Estimating The Environmental Loads On Anchoring Systems.pdf

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### MikeJohnsSenior Member

But what you have just precisely said is that there are two steady states that we are modelling !

Both static cases presented are perfectly valid and occur often in the real world and are good illustrations of the fundamentals.

I'm asking you to consider a mooring under a steady static force, at equilibrium that isn't oscillating. I don't think a vibratory system isn't a dynamic system it's just that a mooring is a complex dynamic system and NOT a vibratory system.
Anyway forget Vibration for a moment.

Vibrate doesn't feature in the definition of those terms. Shock’s a bit of a colloquial term anyway and it’s not actually defined in physics. By the time you get to a term like Shock Absorber it’s certainly not defined . Most of us are happier using Shock than Jerk. Which is probably why we don't have a more accurate commonly used term.

It’s too easy to get into semantic arguments about what defines Absorb and whether it’s to Store or Dissipate energy. I’d argue both are valid but it doesn't matter except in argumnts over semantics that aren't helpful .

Anyway this is why I introduced Jerk (defined as ROCOA). Reduction of jerk is a more accurate term for what we are calling shock. It’s just such a horrible term.

So maybe it would help to redefine the discussion to make it clearer. For example:

Consider a Ball Bearing falling into a tub of silicon gell as a simple example. There is both damping and Jerk reduction from viscous action.

Now consider the Ball Bearing being arrested by a well matched perfect rubber band. Jerk is reduced by the rubber band without any damping. A damper is then required to remove energy and allow the system motion to decay. But even without any damping, Jerk and hence peak force are still reduced.

When the nylon rode is stretched it just stores strain energy and releases it again the same as the rubber band. It's the spring in the spring mass damper system. Not the damper.

We're getting to that claim, slowly with lots of diversions.

Back to the diagram I posted, and back to the fundamentals. There is one force input into the system it's a steady state, all the vectors are steady forces. We're not considering any dynamics.

Where does the vertical force component that lifts the chain originate? And it's not from buoyancy as you suggested before, that's just a reaction.

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### DolfimanSenior Member

As it was said previously, there are tons of research and papers on the mooring lines dynamic issue within the requirements of the oil&gas industry. But of course more focused on full synthetic cables and deep sea moorings than for the classic nylon+ chain mooring line in shallow waters.
To address your question, I think that what you called Vibration analysis could be the one named LM in this paper and used as a simplified alternative of FEA or FD for the dynamic representation of a mooring line, excerpts :
"Mooring line dynamic theories are categorized into two main groups: FEA (Finite Element Analysis) models and FD (Finite Difference) models. A third subcategory, the LM (Lumped-Mass) model, can be derived from the FEA process, so it is regarded as a simplification of a higher-order model. It is valuable, however, to describe the distinct features of all three models to understand the capabilities and cost each bring to a dynamics simulation. "
If I well understand the paper, that simplified approach lights a lot the computation duties, as there is no longer FEA from the cable side of the global system (Matrix size limitation). See Figures 3 and 4 of this paper :
https://www.nrel.gov/docs/fy14osti/61159.pdf

Also this another older approach from the 1970's , for a full nylon rope using for a deep sea mooring, modelling the cable with a non linear strain-stress diagram and a 2 parameters damping, and using 4 parameters for its description : the tension, the angle with the horizontal, axial and radial speeds :
http://www.dtic.mil/dtic/tr/fulltext/u2/715788.pdf

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### MikeJohnsSenior Member

Only for small cyclic variations around an otherwise steady state. But the model in it's entirety isn't even in the same realm as vibration, it has too many degrees of [I'll change that to too much] freedom and far too much complexity.

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### gonzoSenior Member

Anchoring is never a steady state. If it was, it wouldn't be as complicated as you claim and actually is. Vibrations are not restricted b complexity or degrees of freedom. Vibratory systems with 6 degrees of freedom can be observed in a car suspension.

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### MikeJohnsSenior Member

You are right, never simplify anything. Degrees of unconnected freedom indeterminate static locations and responses unable to be modeled by a system of interconnected spring mass damper elements and not having a defined rest position. Might be better.

I'll change that to a condensed "too much freedom" as in undefined equilibrium positions.

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### MikeJohnsSenior Member

Go and look at some anchored ships.

Even if it didn't occur in practical applications there's nothing wrong in modelling a hypothetical situation. All the parameters still relate properly and it's a very useful way of determining the basic system parameters.
In the case of a Chain Catenary the parameters are not trivial and you need to consider the perfectly valid static condition to derive the basic functions. That's before you can go near complicated excitation functions and dynamic responses.

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### gonzoSenior Member

There is a lot wrong with using the wrong model.
Shock is an engineering term and is well defined.
In your previous post you say: "You are right, never simplify anything. " and then in this you claim it is valid to make oversimplified models. Which one is it?

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### MikeJohnsSenior Member

What’s that got to do with modelling the Chain Catenary response sketched ? I'll come back to this at the end.

You are very keen to argue minor points of definition that seem to go around in endless self contradiction. A short time ago you were implying Shock was clearly defined in Physics :

I said we use Shock colloquially in engineering instead of Jerk but that shock is not actually defined in Physics nor is a Shock Absorber defined in Physics.

Without fundamental definitions it’s important to define terms. So I sensibly defined the issue, I said we use Shock for Jerk. I suggested why the undefined term Absorb should include Storage of energy as well as Dissipation. And I gave examples of why your terminology and definitions could be misleading. And all of that because you mix and define terms such as Absorb and Damp at whim.
A good example being your claim that a Nylon Rode is a Damper because it Absorbs Shock.

And your response now is to give me one of my statements back as a one liner, as though it’s some form of argument .

Lastly
Sorry but I mean never simplify my posts. I incorrectly wrote a term that had a specific meaning when I should have used more general term or typed a paragraph that couldn’t be misrepresented in any way.

Anyway back to the diagram. If that represents an oversimplified model of the forces of a boat at rest, in a current or constant wind ,then can you state what you think is wrong with it . Don't just contradict with some one liner.

Then we can objectively address some of the claims you've made, show that the system is definately not linear and address some of the more creative Claims such as: that Nylon and chain act in identical ways, can be both be modeled by a simple spring or a even a balloon and that there's no such thing as Catenary Action in the mooring chain.

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### MikeJohnsSenior Member

Gonzo

I guess if you have never even encountered a Tension vector before, that you probably can’t proceed anyway. ( I'm interested in how that was ommited from your course)

The model is actually a bit of a challenge, which is why it’s so interesting. The tension vector is a function of both the input force and the Catenary equation. This is for the static case alone. As soon as you consider a change in input the Catenary length and touchdown point change too. It’s non linear and actually quite complicated. That’s why we resort to numerical methods and discretisation.

I mentioned frequency domain solutions before and you said you understood them. There’s a bit of an irony in using those methods that you should be aware of. We get around it in creative ways. There are even expert conferences on how to best represent the non linearity of catenary action using lumped linear discretisation.

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### gonzoSenior Member

I would love to have a discussion with no personal comments.
The vector has a vertical component. Where does it come from?

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