- 1) Newman (1994, Applied ocean research) provided the formula which is widely referred, and the component due to gravity is missing from the paper.
- 2) Senjanovic (2008, Ocean Engineering) shows a complete one where gravity is included. Though the term due to pressure variation is assumed to be identical to the one given in Huang (2000), it is actually shown as they are transpose to each other and Huang (2000) is in agree with Newman (1994)
- 3) Senjanovic (2012, Journal of Engineering Mathematics) gives a revised form which it is believed to be more correct one. It shows that the C_p+C_nh is now in agree with Newman (1994), but again, transpose to each other. The gravity components is the transpose as the version given in Senjanovic (2008)
The question is then any conclusion on which form is the correct one? Since the formulation should be able to apply on the rigid modes. A test on C42 and/or C24 can be perormed. With 1) we can get C42 (due to hydropressure)=-ROU*g*Displacement, this can be balannce out with the gravity component given in 2) as m*g. Seems, neither the formulation in 2) or 3) can get such a concellation so that the total C24 and C42 are both zeros.
Anyone has been noticed this and any reflections?
Hi Peter,
There is a more recent publication with some clarifications on the definition of hydrostatic restoring. You can find the paper here: https://mhl.snu.ac.kr/iwwwfb35/documents/abstracts/IWWWFB35-035.pdf
A discussion between different formulations can be found here: http://www.iwwwfb.org/Abstracts/iwwwfb24/iwwwfb24_37.pdf
It is still unclear if one should include only the variation in the hydrostatic pressures due to a change in the vertical position or as well the shrinking of elements, among others.
Let's talk more about this soon :).
Kind regards,
George
George Jagite Thanks for the answer. I am making a Python code to evaluate matrices (mass, stiffness, restoring) from a panel model and its corresponding FE model, as input to Wadam/Wamit (putting them into .FRC and .mod) for analyses on flexible modes. I am starting with the monopile example. It would be interesting to test it out with more cases. Let me know in case you are also into this, we may work out together.
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