 ## General Mechanical

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#### AQWA Eigenvalue vs Free Decay Test Resulting in Different Heave Natural Period?

• riyanto.r
Subscriber

Hi all,

I am trying to find the heave natural period of a simple cone using the AQWA Eigenvalue module and a free decay test. I also calculated that manually so that I could confirm that the results were matching. However, the results are all different:

*** AQWA Eigenvalue: 3.77 sec

*** AQWA Free Decay: 4.04 sec (below is my setting):

*** My eigenvalue calculation with added mass & critical damping coefficient from the .LIS file from RAO Calculation: 4.78 sec

Do you have any tips on how I can get the calculation correct? Or were any settings that I should have calculated the natural period accurately? I believe my analysis (4.78 sec), but I fear it will not be reflected in the model and would interfere with the seastate peak period I would put into the structure.

Thank you!

Danu Riyanto

• Mike Pettit
Ansys Employee

Hello,

The Natural Modes result uses the linear hydrostatic stiffness matrix at the cone's equilibrium position to find the natural periods of the system. On the other hand, in your time domain analysis the Aqwa solver calculates the nonlinear hydrostatics over the instantaneous wetted surface of the cone at each time step.

In the time domain Analysis Settings, try setting the 'Use Linear Stiffness Matrix to Calculate Hydrostatic' option to 'Yes'. This should give you a better agreement between the Natural Modes result and your estimated natural period in the time domain.

You can also try setting the 'Convolution' option to 'No', which causes the Aqwa solver to use the acceleration RAOs to calculate the radiation forces/moments (rather than a convolution integral method). This may give you a better match with your own eigenvalue calculation.

I should point out that the natural period from your original time domain analysis (with nonlinear hydrostatics and convolution method for radiation terms) should be the most accurate estimate of the real system behaviour.

I hope this helps!

Mike

• riyanto.r
Subscriber

Hi Mike, thank you for your clear explanation! I am surprised that AQWA can process the non-linear stiffness from the structure; I should read the documentation more deeply!

However, I have several follow-up questions:

1. How can the solver get the non-linear hydrostatic stiffness above the waterline of the structure if we only included the wetted area during the hydro-diffraction analysis? I excluded the freeboard structure above the waterline (to avoid error). Is there any setting(s) that I should have included here?
2. During the time-domain analysis of the no-wave decay test, how does the solver calculate the added mass & damping ratio? Is this term fixed? Therefore they read the added mass coefficient from the diffraction analysis at its respective natural period? Because added mass & damping is dependent on the wave period. I would like to know what coefficient the solver chose if no wave is included in the simulation.

Thank you!
Danu Riyanto

• Mike Pettit
Ansys Employee

Hi Danu,

No problem, I'm happy to help.

Just to clarify, Aqwa has two types of time domain solver:

• when the 'Analysis Type' is 'Irregular Wave Response with Slow Drift' or 'Slow Drift Only', the calculation includes drift forces, but only uses linear hydrostatic/incident/diffracted/radiated wave pressures;
• when the 'Analysis Type' is 'Irregular Wave Response' or 'Regular Wave Response', the calculation does not include drift forces, but the hydrostatic and incident wave pressures are calculated under the instantaneous water surface (diffracted/radiated pressures are still linear).

1. Ideally you should model at least some of the structure above the waterline, unless you are only going to run a Hydrodynamic Diffraction analysis. In the diffraction calculation the solver will ignore any non-diffracting panels, so they do not make a difference to the calculation time. Otherwise, in your Hydrodynamic Response analysis the solver will assume that the cut waterplane area is constant above the cone as it becomes fully submerged.
2. This is what the convolution method does for us - rather than using frequency-dependent added mass/radiation damping terms in the equation of motion, instead it calculates the acceleration impulse function matrix for the structure, then we have: Where m is structural mass; A_inf is added mass at infinite frequency (estimated by Aqwa); X is position, X˙ is velocity, X¨ is acceleration; c is damping excluding radiation damping; K is stiffness; F is the total force; h is the acceleration impulse function, which is calculated by Aqwa from the frequency-dependent added mass/radiation damping.

If you turn off convolution, the Aqwa solver will use an RAO-based method to calculate radiation forces, then you will find that there is no damping (because you have defined no wave). 