Vibratory System

There has been some arguments on other threads about vibrations in a system. A vibratory system requires two main components: a spring (means to store potential energy) and a mass (means for storing kinetic energy). The third element in the system is a damper which dissipates energy. Anything else is not part of the system and an external influence.

 

Completely true!
What do we do with this?

 

This is to move the discussion into its own thread. Someone hijacked a thread arguing that I am wrong about that statement.

 

That is not strictly correct.

A vibrating system must have 4 elements:

1) Mass
2) Restoring force
3) Damping force
4) Driving force (spring force)

If imagine you have a mass attached to spring of stiffness 'k', and it is hanging from a solid object like a ceiling. If i pulled down on the weight by a distance , x, and then released it, there is now a displacement towards the spring owing to the 'stiffness' or the spring force of kx and it continues past the equilibrium position it was first at....but once it has reached its maximum amplitude, what then?...it is pulled back down, this is owing to gravity forces. It is this force that brings a mass back to its equilibrium position is called a restoring force. It is very important, not just the non-rigid connection of a 'spring'.

Also, take an example of a solid rod. It is fixed to the ceiling, a solid object. It is fixed via a pin, that allows it to rotate in one plane. ...generally called a compound pendulum. Where is the 'spring' in the sense you mean above..?
Instead of an 'elastic restoring force', there is a restoring moment due to gravity. Same for a simple U-tube....with liquid inside that oscillates, the restorce force is also because of gravity.

All basic vibration.

 

That is not correct. A vibratory system does not need to be damped or excited; it only needs two elements.
The mass of the pendulum stores potential energy and is the spring. As long as it fulfills F = kx it is modeled as a spring.
An ideal spring (with no damping) would continue to move up and down indefinitely if displaced from its resting position.

 

A vibration cannot start "on its own", so even if we look into a damped system that was set into movement by a single pulse, you have to include the input energy in order to understand the process. That done, you may have a system with declining amplitudes (=damping destroying the trigging pulse energy), or a continuous swinging system with a final amplitude depending on the ratio (input frequency/system resonance frequency) and on the damping.

So, to describe the complete vibration over the time domain, the fourth dimension "driving force" has to be included (even if only a stepwise pulse), otherwise you are only studying the "dissipation side".

 

I think there is no disagreement between your various points of view, just a semantic issue. The usual frame for the study of any mass dynamic motion is the second degree dynamic equation, itself directly derived from the Newton law :
m X°° + d X° + k X = Fd
, which can be describe as :
Inertia force + damping force + restoring force = driving (external) force(s)

From this general frame, 3 particular cases :
m X°° + k X = 0 : free undamped oscillating system ("free ideal spring" of which period is T = 2 pi (m/k)^0,5 )
m X°° + k X = Fd : forced undamped oscillating system
m X°° + d X° + k X = 0 : free damped oscillating system
, with here a usual difficulty : the physical damping phenomena usually involved is not linear, cannot be reduced to just d coefficient.

The study of the dynamic of marine vehicles is certainly one of the most difficult thing because :
- you have to consider the 6 degrees of freedom (x, y, z, pitch, roll, yaw) in the most general case,
- the expression of Fd forces are extremely complexed even within linear approaches, and the real response of a hull on real waves cannot always be reduced to the domain where the linear approach is valid. That means that the most extreme forces to consider for a design can be (are) usually outside the linear domain.

For a lot more on that subject, a quite old but reference document is the "Bhattacharya Dynamic of Marine Vehicles"
Bhattacharya Dynamics of Marine Vehicles https://fr.scribd.com/doc/44416872/Bhattacharya-Dynamics-of-Marine-Vehicles

 

There's been no such argument, you've been posting misinformation and have been corrected. I told you finally :

Particularly the issue I want you (Gonzo) to understand is that a mooring system is not a vibratory system, it's dynamic system with a transfer function of higher order DE's. And as I said it's quite a complex analysis.
And how can you even comprehend something you have no knowledge of ? You even display trouble comprehending basic school level physics.

Anyone remotely interested can read the gist of it from page 2 in this thread Amidships Chain Storage https://www.boatdesign.net/threads/amidships-chain-storage.60722/page-2

 

It would be interesting to see the arguments relating to perhaps the most perfect vibratory system yet devised, an electrical oscillator.

 

I started a thread about vibrations so this discussion stops hijacking the thread. You are describing what is called "disturbance".

 

Mike, it is the same MO here too, not understanding the definitions and the basics of material science.

 

Who causes the unnecessary thread drift by posting ignorant statements ? Do you think technical posts that are absurd should go unchallenged?

Come on, you’ve stated that there’s no such thing as Gravitational Energy. That gravity is a force. That a chain is a spring, that a complex dynamic system has simple trivial analysis and that complex dynamic system can be solved by anyone with introductory college math skills.
Then with this level of ignorance you post absurd statements, ignore corrections and drag an otherwise interesting subject off the rails.

Even when another engineer M Ovenden gives you a link to Gravitiational energy on Wikipedia your response is to damn Wikipedia rather than checking it for yourself.

Now you want to redefine a very complex characteristic equation as a simple vibration. That’s just as absurd as declining to accept forms of energy that you haven’t been taught.

 

There are three sources of excitation a wave spectra, tide and wind. Then there’s the response of the system to the excitation. The governing equation has to consider the full dynamic response and damping factors. There’s a restoring function from either stored gravitational energy in the rode or in strain energy in an elastic element or a combination of both. And the moored craft on a loose single point mooring can be in any position within the circumference of the rode.
Now remember we are looking at force in the rode. It’s nothing even remotely close to being able to be solved as a vibration. It’s a very complex analysis, so complex that we use finite element multi physics methods and tie the results into the real world with empirical data.

Trying to get that into Gonzo's skull is proving to be challenging

 

... then there is Peters total empirical solution on his number 2 mooring, just put such heavy chain in the mud that the holding power of the train wheels will never be tested

(He's boasting about Sydney Sunshine again. I'll have to talk to him about that )

 

I could be out of a job if that ever gets out, the oil industry will just copy Peter's empirical and I'll never do another mooring analysis again !