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Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

Comparison of TLP Motion and Tendon Fatigue with versus without VIM or VIV Effects in TLP-Tendon
Coupled Analysis
Byoung Wan Kim1,2, Hyun-Sung Kim1,2, Kangsu Lee1,2 and Sa Young Hong1,21Korea Research Institute of Ships & Ocean Engineering (KRISO), Daejeon, South Korea
2University of Science and Technology (UST), Daejeon, South Korea

ABSTRACTThis study numerically compares TLP(Tension Leg Platform) motions
and fatigue lives of tendons with or without including TLP
VIM(Vortex Induced Motion) or tendon VIV(Vortex Induced Vibration)in coupled analysis of TLP with tendons in waves and currents.
Equation of motion was solved by HOBEM(Higher Order Boundary
Element Method) and convolution for the floater part and byFEM(Finite Element Method) for tendon part. The fatigue life oftendon was calculated by Rainflow method with the tension resultsfrom coupled analysis. A cylindrical TLP with tendons was analyzed asa numerical example and the floater motions and tendon tensions were
examined for various current speeds to see the trend versus current
speed. Four analysis cases such as coupled analysis without TLP VIM
nor tendon VIV, coupled analysis without TLP VIM and with tendon
VIV, coupled analysis with TLP VIM and without tendon VIV,
coupled analysis including both TLP VIM and tendon VIV werecompared to discuss which case has larger effects on TLP motion ortendon fatigue.

KEY WORDS: VIM, VIV, TLP motion, tendon fatigue, coupledcoupled analysis of TLP with tendons in waves and currents to see
which case more affects TLP motion or tendon fatigue. A floating windturbine studied by Robertson & Jonkman(2011) was analyzed as anumerical example. The sample sturucture is a TLP structure connectedwith 8 pretensioned tendons. The TLP motions and tendon tensions
were examined for various current speeds to see the trend versus
current speed. Four analysis cases such as coupled analysis withoutTLP VIM nor tendon VIV, coupled analysis with tendon VIV, coupledanalysis with TLP VIM, coupled analysis with both TLP VIM &tendon VIV were compared.

EQUATION OF MOTION
Coupled form of equation of motion for TLP body and tendons inwaves and currents are expressed by (1) and (2).
𝑡

[𝑀𝐵 + 𝑀𝑎𝑑𝑑 (∞)]{𝑥̈ } + ∫0 [𝑅(𝑡 − 𝜏)]{𝑥̇ (𝜏)}𝑑𝜏 + [𝐾𝐵 ]{𝑥} = {𝑓𝑤𝑎𝑣𝑒 } +{𝑓𝑑𝑟𝑎𝑔 } + {𝑓𝑉𝐼𝑀 }(1)[𝑀]{𝑢̈ } + [𝐶]{𝑢̇ } + [𝐾]{𝑢} = {𝑓𝑀𝑜𝑟𝑖𝑠𝑜𝑛 } + {𝑓𝑉𝐼𝑉 }(2)
In (1), [MB] is mass matrix of TLP body and [KB] is restoring force
coefficient matrix. {x} is a vector of TLP motion,. [Madd()], [R(t)] and{fwave} are added mass matrix, retardation function matrix and wave
force vector, respectively, and they were calculated by HOBEM(Choiet al, 2001; Hong et al, 2005) and convolution(Cummins, 1962). fdrag isa drag force by current and it is calculated byanalysis

INTRODUCTION
VIM or VIV by current is a main design load in in deep draft platform
such as spar, TLP or slender bodies such as risers, tendons. And, manystudies were done by many researchers(Gopalkrishnan 1993, Bourguet
2011, Jain 2012, Chen et al. 2015) about vortex induced responses.
VIM or VIV induces lateral motion perpendicular to current direction.
So, it induces sway and roll of floating body and lateral vibrations oftendons. In some situation, lock-in happens if VIM frequency isidentical to sway frequency. In that case, lock-in of heave, pitch, yaw
as well as sway, roll may occur due to coupled effect if the floatingbody is strongly connected with tendons. And, it may affect fatigue
damage of tendons.
The objective of this study is to compare TLP motions and fatigue livesof tendons with or without including TLP VIM or tendon VIV in

1𝑓𝑑𝑟𝑎𝑔 = 𝐶𝐷 𝜌(𝑉 − 𝑥̇ )2 𝐷𝛥𝑠2(3)where CD is drag force coefficient,  is water density, V is a current
speed, D is a diameter of TLP and s is a characteristic length. fVIM is
VIM forces of TLP. It is
1𝑓𝑉𝐼𝑀 = 𝐶𝐿 𝜌𝑉 2 𝐷𝛥𝑠 sin 2𝜋𝑓𝑡
22562(4)