* l/d > 5 and H/D = 1 Mass term of Morison dominates

Transcription

1 1 3.6 LOADS Source and conequence of non-lineariie Sinuoidal wave and ylinder rucure: η =H/ in z λ H d x * l/d > 5 and H/D = 1 Ma erm of Morion dominae * linear wave eory: D fz;x= =.5 π c m D H/ gk co kd+z/co kd co Kinemaic defined o ill waer level Toal load obained by inegraing o ill waer urface * Toal load F = d f z ; dz = F co Force frequency = wave frequency mean force =

2 For irregular ea: - Can be wrien a a um of inuoidal. - Linear wave eory linear load and linear mecanical yem. Te load and reone roerie can be caracerized by e ranfer funcion: H ηf = F / H ηx = x / If aumion above ufficienly accurae relflec load and reone e roblem can be olved in e frequency domain i.e.: ; ; X XX S S ηη η = = σ d S XX X ; = > max 1 ex X x x X P σ Variance: Sor erm diribuion Long erm diribuion: = + + T H X X d d f x x F 1 ex 1 1 max σ ν ν

3 3 Wa are e aroximaion? * Inegraion i carried ou o ill waer level mean weed urface for floaer. * Boundary condiion are fulfilled a e ill waer urface. * Vicou force are negleced. If all ee erm are accouned for o ome order e oal load will coni of e following erm: F = F mean +F LF + F WF + F HF Mean force Slowly varying force frequency j i Wave frequency force frequency j Hig frequency force frequency j + i T > 3 5 >T > 4 T < 4 Tyically: FLF and FHF an order of magniude maller an FWF Tee load rocee will rimarily be of concern if ey i ligly damed eigenmode

4 4 Dynamic amlificaion Load: F = F co eady ae moion: u = u co θ were: u = Q k λ 1/ Saic reone Dynamic amlificaion DAF For = DAF = 1/λ λ =.1 DAF= 5 λ=.1 DAF = 5 Fixed laform: F WF generally mo imoran F HF may be imoran if i i a naural eriod. Floaing laform: F mean F LF F WF generally mo imoran F HF can be imoran for TLP ringing and i wiing.

5 5 Load on a drag dominaed ile fz =.5ρ c D Du u Kinemaic above mean free urface i a callenge. 1. One can elec a regular Soke 5 order wave.. If a inuoidal wave i ued Weeler recing I mo common. Will undereimae eed for ee wave. Le u ado a inuoidal wave and look a fz well below e ill waer urface. in in in

6 6 A Fourier exanion of in in will ow: in in =.85in+.17in3 -.in5+.. Inerial erm: roorinal o co A drag i imoran inegraion a o be carried ou o e exac urface: F TOT _ DRAG η in in = K d D zin in dz.5co.85in For e inerial erm: F TOT _ INERTIAL.5co +.44in +.17in Remember a for lender rucure load will In addiion o e wave frequency alo aear a mulile of e wave frequency:

7 7 Deign of drag dominaed rucure jacke and jack-u U o m in e Nor Sea T n = 1 4 U o 1m in e Nor Sea T n = -6 Pinned or fixed imoran for naural eriod. If T n < ca laform beave quaiaially and a deign wave aroac i convenien for obaining deign load. If T n > more deailed analyi may ave o be done in order o roerly ae e dynamic beaviour.

8 8 Deign wave aroac: a A roer 1 - load i obained by exoing e rucure o a regular wave wi eig equal o e 1 - eig and a conervaive aociaed wave eriod ofen mo unfavourable of 9% band. b A Soke 5 order i mo ofen adoed a e regular wave model. c A conervaive way of accouning for curren i o uilize a 1-1 curren rofile. d Effec of dynamic can be aroximaed by eimaing e DAF given by: DAF = λ 1/ Examle: T=15 T n =1.5 λ=.15 DAF=1.3 e Quaiaic 1- load found a wor load a e Soke 5 wave i eed roug e rucure.

9 9 Time domain analyi If an accurae aemen of dynamic i o be obained e equaion of moion a o be olved in e ime domain. m x + cx + k x = q I i no eay o find a very recie way o erform uc an analyi. Mo exerience i gaered for rucure eenially beaving quaiaic. Norok N-3 give ome guidance. For e Kviebjørn jacke Tn = 5 in deign calculaion e following aroac wa followed: quaiaic load wa eimaed uing Soke 5 order wave and 1 - wave eig. A number of 3-our imulaion eed and acceleraion e equal o zero were erformed for e wor ea ae along e 1 - conour line for and.

10 1 3 Te 3-our maxima were idenified and a Gumbel diribuion wa fied o e daa. Te ercenile correonding o e exreme obained by e Soke 5 wa eimaed. A value of 95% wa found. 4 Te ame 3-our imulaion were reeaed bu now e rucure wa ermied o move i.e. a full dynamic analyi wa carried ou. 5 Te 3-our maxima were again eleced and a Gumbel model wa fied o e daa. From e fied model e dynamic exreme value a a ercenile of 95% wa eimaed. 6 Te dynamic amlificaion wa eimaed by: DAF = x_3rmax_dyn_.95/x_3rmax_qa_.95 7 Caraceriic deign load are calculaed uing e value obained by Soke 5 wave mulilied by dynamic amlicaion facor.