Determination of non-linear drift force quadratic transfer function and synthesis of drift force time history

CHNAS.HIP SCIENTIFIC RESEARCH CENTER

Determination of Nonlinear Drift Force Quadratic Transfer Function

ard Synthesis of Drift Force Time HIstory

.ao .:Huanqiu Gu Maoxian.g

December 1986 CSSRC Rèport

English version-8ói12

(Presented at the Marintec Offshore. Conference, Shanghai, October 22-26, 1983)

P. O BOX 116, WUXI, JIANGSU

Determination of Nonlinear Drift Force Quadratic rransfer Function and Synthesis of Drift Force Time Historf

Digital oss-bispectral analysis (CBS) tediniques are us to terminethe q

riti

transf

f*tii (QTF) of a nx,or3 tanker, whi rT311 the ri1inear system be the high frxy

sea ve inpit and the 1c freqcy drift for axtput acting ai the tarilcar

2rP for

terminii the QF and theace applying this QW directly to athitrary sea ve iupit

(ij

the azxtlxir' s methed) for synthesizing drift force time histories are rsr'b

Estit

rilts are inpared th riintal ckervations with fair agreenait.. It is s' t

ti OES athed of analysis

has wide pri

applitice in analysingt

tank tests and fall soale p trials.

L.

rxxrrIcE

hit ied in rendan seas have hee observed to rionce large-amplie i

1ims

at

or nabiral frepeacies of the vessel-scoring system. Since the of sixth iicticns are well belay, t1e of individual waves and since y are the u1t of heat phnrTr.ria frnmi by wave airs of neighxing freuescies, this I*1rYTllrn is

fruently ten1 the lo-frequery (or differen-frcy) drift o11-4c This is of great imortan to variais ncored ocean structie 's syst having

irhr*ly

l-frequency respnses sudi as S.ingle int Moorings (SRA), (ilTrpiiarrt Platfores, Tision L Platfos or Tethered Bcyant Platfores (TIP or mP), Floating Production StuL

Offloading Systems (FPSO) and SemisuEirersi hi e Drill Rigs. It- is i .r, of inçortai

acmting for the involuntary speed 1rs of ship in waves.. In receit decades, a*i niuis

rns Jave beer sti over law-frequency nenlinear effects in ship and ri

hdredynamics and neny stedies, both theoretical and experimental,.have ' TT

While drift fuiC ismn1y a dc cuzIxment in regular waves, in irregular waves, it exhibits a slowly varying or oscillating riatore in addition to the dc cnçonent.. W1 there is any reasonable degree of energy transfer at or near the natoral frequencies of the noored system, large-amplitude os.iflations of the latter will oaii, saeetines with devastating result. Early stodies (i), [2) have aboyai that the wavedrift force acting

ai

a floating

structie is prcortional to the square of wave height,ith that the drift force is

a rcoliriear effect, to which rl i rl l analysis teotmique annct beapplied pinkater (3), 5), _[63, (7) , Pirikater and Oortmerssen (4) iindeonny

tiretical

and experimental studies By the not1 of thstrf±ed singularities ori -D and 3-D surfaces of a floating body, they obtained lady notions, i

,i,prnc rcs'

prxe gradients and wetted sace of the lady, thence by s'.Lrrf i ty-dI1 and

tbrongh t

ntainii

procbx±s of t ist. order quantities, they were able to six order drift for (îrrimit) lath for regular &1 irregular waves.. 1'r

results e ai.si cxmparal with experixrental

drvations.. Faltinsen et al (8)

, (14)

ai 1aigitrF1 nal and sway drift fursof floatix ies and develqed nds

for calailating the 2-D sway dritt force.. Tick [19) wes the fi to derive a for

.ea1r,lM-irg the u-bi-Spectzun (CBS) of a n1irar outot fran a I ii ±nt. TI i'1 1 [93, [io) , [u) following Tiric, deve1oed aid anolied the analysis to pI-iIcin of

_____ of hipc in ixrngular waves,aid deb-r the qnadrati fq- fir

WIT) of rejstan by rodel tank experiments. Kim & [12) , P (73

floesen (203 , rs, dai, Niskad and. Fisher (18) bave applied the OES t:nrique to

lyscn of quadratic tranFr sicti%x of drift forceson roared cff-J1

Kim and Breslin (12) also used the quadratic transfer fuaction to resynttize the ft

fzc,

rer, witbout v1 -i

Hrn by experiirnt.. ri

7i [io) , Di) in a 4a-i 1

report, ssfu1ly 5hi the drift fu.cC time history of a ucorixq ship using QF derived fran OES. estinated drift £uxs. inpared xisrkah1y weil with that oined

by experinit. It bas been pwìed that the OES retlad of analysing drift fs is. a

FaTh1 and pranising technique.. The drawback is that the CBS notbod, as yet, is zH1 i a

long and tedious prolIre, ri.iring long s1ing.it-i-jrd, aid large cjfrr tinE. In

Sua Be-Qi is developing a inetbod of drift fu calcelating (to

be p*1i) 9+mi lar

to that of Pinkater 's, bot with imprtrt in

metl of

uprting the sxi order

tHa1

The present paper sests a dira± nEtbod of irift fCr

syni fran

experi.rreri.tally obtained arF, which ved a great deal of xinith time.. er, cring to

other ]imith_tiais, lt*jpn of h-1 Lrift- furr. as well as t of the QF is

act high, aid i1i

e irved u..

2- LU'-kINEAR DRIPf FOE

A L:35 nzl of a storage -a1*1- is tastof in ' Skec!ping Basin (6thn x 46n X ) of

(2uria Ship Scientific Researdi Center for the p.xrpse of validating

fi hi

ty of obtaining the ÇII'F of drift force fron el experiment.

The principe]. jmlr of the

I&E I

Lth of

terline 4.30n Beam B 0.686m

Pld

Draft T 0.29]rn

r1nt Weigt*

W 816.33kg Blc,dc efficient 0.937

Midship Section Coeffici On 0.995

Pritic (bofficient

Cp 0.942

Tham Stera

-With the exception of the eritrai at bcri, the tanker ncdel in general àppre a

rectangular barge. The idel is tasthe in heai ves and restrainei by an arrangeant

sn in Fig I.

types of wave tests were ndz.ted: zu.1ar and irregul r. Fbr the

irregular ease, t. spectra of the s shape bat slightly different rr1jttaie e u (sec Fig 4).

In Fig I, the carriage is f ix on the overhanging rails

The ¡iodai is nttei to the

wire-piLley - spring and force gange systn via a i±inbus-shaped frame. The latter i ci.is the ship nodel to pitdi and heave freely, thus placing no restraint to first order

¡iotions of the ship in the longitndinal plane. The length of the piano wire was rather

Lông, so that the vertic&1 penent of wire tension acting on the rrodel becrI's negligxbi

stell when criuparei wth changes in amdei dispiarit per triit heave. Frn to heave

and pitch is absolutely ressaxy for the neasurnt of seud order drift for, since

it LS lcx,wn that major onntributions to driftfors arise fron the products of .- first order quantities, such as first order notions, relative wave elevation and changes in watt1 surface. Fr tests in irregular waves, particular attention has been paid to the selection -of a proper spring censtant. .Pinkster rployed a spring which yilcic a free osciLlation freguency for the systeti which is less than the oit-off fiqnncy Of first order wave

spec and greater than the tper limit of the l-freqtency (szri order) drift force

spectrum. The sane selection principle was adoptnd in the experiment. This is to minimize

the interference of syston rse with the nemit of s

order force. The spring

nstants selected are:

BIE II

Regular Wave Test Irregular Wane Tt

Force e range 2kg 10kg

Spring censtant of the spring

arid wire 0. 05kg/Ci 4kg/an

-Weight 0.5 kg 1kg

A pertii of the reonrd in regular wave is s1s in Fig 2.

tper part of the

di-rrespends to a drift rui

recording, arid the lower part &irrespends to regular wa of

4m length and period of 1.6 snd. In the force record, osci 11 f-ic,nc of apprcimahely

30 sec. - period are observed which grn. fly attanuates to a constant n, drift force coefficient C (w) = F/tPß plotted as a fmction of wave are sFown in Fig 3., where F - Drift Force, P - Density df Water, g

due to Gravity, SA - Wave Amplitude, B - B. There are sa

degree ofetter in

Fig 3. As a matter of fact, the duration of eath test stould be properly sele toe long a diticn may include the interfer effect of reflected waves fran the heath eid.

Sin'1 rly, the wave height ueastesent is anti cn1, since drift force varies with the square

of wave height A typicel of recordings and spectrum analyses in irregular wave- test

is sIn in Fig 5., where (a) - Wave Record, (b) - Wave Force Acting on r4idel Ship

(This is iiostly drift force probably pelintaf by sane rrn1 of-fit er wave fbr,

i nt _{the itajor perti.on of the latter ìs released by nodal ship' s. loagithidire]. notions),}

(c) - Diete Fower Spectrum of Wave, (d) - Discrete :Sw of Wave Force..

Three peaks are observed in 5(d), the high freguency peak corresgonds th--th of first o.

wave spectun, the - intennediate - freguy peak correspends to the

-r1

of the

'Vessel-restraint systan and the low frequency

k rrcviis to

ohe1owcy ±t

-The MEN value of -5.66 x 1O

ski in

Fig 5(d) is the zean drift för, aid the speczn

analysis of drift force is xnàde taking the MFN as zero line. Jidging fran Fig 5(d), the

plarmid segregation of frequency TTifl5 for wave, systn resnse aid drift for

respectiiely s to bear cut very U. It is hard to sea this fran the ti hisy of Fig 5(b)., siixe

it is

the. superpsitiori of three speca of different freg cy

3. DTIC NSF FUN1

' sthdy of inprt aid tprt rl'inhip vereii

a thre invt

____ detes badc several de' Weinr in 1958 the Vb1'Ìr ço].yrrl!nJll as

apprciizate ftnictina1 ses

rtatien 0f rrnlr remi hi1ea a

inpxt e.g. heb a wave elevation input x(t)

aid the irìi.

wa (t)

iored object The Volrra 1yneni in .s .se nay be wri as (»te the

l"1

of mt

trm, -

-4+- ,

e nit+

in ail fnI 1ewig

frwi):

q()

7

+J3,)x (-

)dL, + f3c

X

9

---- -

.-.----.---

-- - -

4j...

J7 (j - -.

) x (t -) - - - -X-L)t .«L

(')

there t1e order Kerne]. fticin, asss tohe tiixe

invariant, syx*r11s

soth, aheolutely integrable aid transfpmnable in multiple dimansfnriai e.

Volterra irnel of zero order, a onnetant representhng resasta f a ing vessel and zero for a ncored vessel

first

order VOlt.-r

gcrrl,

ey-'

to fiist order iilse. trânsfer r*ir in a. 1ixar systEn, - the iuLji-1 *mning

represents the linear wave for dezritid by

f'tø.

sed arder V hr-r1 Kernel,

whidi is the quadratic transfer fnictii to he disoessed in this per ' integral ntain.irig t) represents the seid order -wave £u, generally of interest in its low

frequency nent only, which is the drift for, denoted by f'et) _if, aid have Fbutier transforos

-G,')

Jy,()e"Lt

'_{1d,o,dtJt ,k3.}

G1,L4a):f[

-in whidi

is

the first order tsàesfer funeti of ]ixear syster, Gzû.',,4s the qy4ratic

rxsfer fimcti.on. Higher order t.z mfr fx.Uictione ê n 1er±..,cl, the WiI

pDlyzr3flial is trurted at the serond order.

E1ze11 (9 ., [1o) , (1i xede a systiC study over the aplicaticni of

rind ui

Voitarra yr1 and cross-bisrtral analysis to represent i resistaie of in waves. In order to v1 ite the ity of sudi a methed of aialysis, he started f tjme-hmtories of input and outixt obtained by gees into analysis in freqxcy ,ir,iii4, aid- su$eqxit1Y resynth.ze- had into a ti3xe-xEi11

(u

, i' h)) nay be

ittas

C. ,..z)/Sca(--er0z)

j (q)

= ¿ü, -Wi ..Q..-2. C.i, #La-

-there S*Xxy ( Jit p-ai) is the.iiju!Ji"- of the trr.-.-.he.jtC :y {_i.. ,.P-z.) aid

s,cwf

-(s)

in whi.di

c..z(ct_r_jct-WJj ()

bar represents :tl-av- - Seer2 , ..D) is firii q-17fl4 lly, n

ubeoript Xi -s_-of iit X.W - It- :isly FWI

/

(m)

ike-ac (3) is theb1e-sidth vesp'

,iy be [U) :

js

.fGyscgc

C)

= f',(yJS

)3)& &)

or, by

kii.1y. the

tud t

.the,one bas

= J

(ca3.4S)2S, ()Si)4

In the ave f,...Th

is the

ft for, a do.

Syy (a.) ary t')

are r-pive1y the

ve fLi -(t)

fözor t) respectively. Eq. (9) is a triifi

pri; Ier,

. L..t iC!n is

paid to the ser te

on the . ich I-ri'y rires±s the 'low frepEuy or

freqtcy

n'nnt, as the firt. tenn iUy rer'

to in

fiy

4n

After obtaining Sy (w), should oil storage tankr he ncor

a .i by a i

and the i

iiir

tE(w) ] or y

fd,

.

the ....se

of the

le systn

(be it tion

or fuLtr

)

y bethtaid by

the usual li n systen relationship

2. Ct)

S,.(w)

I'"

in whiob the suipt z dtes systn's low rncy nttion re'n

or ystt's 1i

freqtcy strtiira3. for

repense.

For such a systan, the QTF G2 may be directly to H fferent

spa Soc (c.')

using eq. (10) and (II), and to find out for each case new low frequency drift spectxa

Syy (u') and systen respense Spectra Szz (C.)) witIut ftmther relian to ecper±n*. However, if after finding Syy (w), the nrxring-vessel systEn is nenlinear, t onuld

tot usially apply directly eq. in the frequency &rin A transformation of G2( w,, wi)

into its rrespendthg quadratic impuse transfer fiction g, (,

, t2) is xry in

order to use eq. (1) directly to yntbesize" a realization ôf yd) (t) fran a eartain ve

roi i ticn x. (t) onurespanding to a given have sctnzn Sxx (w). This . (t), in turn,

is sitituted into the ruìLineat differential equation verning the systEn' s notion, and

the tire-history of the systen' s output is calculated. Referenor (ii) , used a discrete expression of eq. (3)

2

(íii.t)

jK

(2

iiere

& (t) -

Dirac Ftniction; j k, - ags, t.*frth tale on integer 'vii'c

ftn

- to n;

t - sélected

mpi ing interval. Sinn larly, the diete expressicm for the

erordér

ift foi

is

(')

(n)

(Ii)

,iting oss is very tedious and long. In this paper a -- anthod thith

brought about rble saving in rzpiting time is propeed.

ver, in ei uithed,

it is ary to apply a digital low pass filtering.

Applying a digital low pass filter to QrF G., (LJ, , C), will filter out the rsiinai high f reqray onpanents arid yield a rather authentic low frequency Ç2rF. Thus

(i

in .thich H( W: + Wt) is the filtering factor expressed as a fuscticth of -n-2 = '. + 'z

i.e.G,(,u) inFiglO, 1lisweightedbyanst1tfactorHa.longalioeof.ft.t.

The filter ftniction is expressed as

S(4ri.z) ..

-

_{'___.}

wliich : a zero *ase-shift filter (15), inr

H is a real ñnxti..

4

Cr7)

-A

the other hare, the nas& ,the for ' (t) iist a1 be filter th _______

high frequicy 'rise'. In order th 1çaxe the r1 e,al drift . fjt jj the

n1

(f ilter) result, the

filter fctinn in tire 3rini n.zmist nfw!fl stri±1y its terrt in the fricy an H (n-z), i.e.

= j fH(.O-2)e'S-L.z (IL)

filtered .drjft Y(t) is dted by a s_ript F,

'bl

*i

jF(t) =Jy

CtI)k(t.) d.t1, , suth a inii _ir"1° resse is e

by FT t4i

116) t17J

A itere

wi&iit

ani faster nthod f in p1 of e1. (12) (13) is

-dii. Starting fr G1 (Ji , ,j,

Pier

tzar.,rrn ? (..D.) of the r1: çrd

drift for y (t) s ObtaiÌ Th by y cbir an inverse Fourier t1'Th..frrn,

s order far y (t) itself is obtained. 1be

iil-pii y

(t) is i1i*M

inst the neas a filtered value of .y» (t). ,,

the .1 uiJs&

d.ft

be pred

in a

sli3*ly d ffr.'gli

sion fran e. (1)

(t-t.)

x &-t2)tid±.

1 )

.:Jj()ffxC() e

L

.LJ5F

cw)e

It is fih1e to

synthesize y (t) by sçutingthe rn1}e integral of eg. (17),

it

still is a lengthy p)re further simplifythe 1 nil $-inn, ai ueting that

= .J1 + , . (17) ny rewritten as

12t)

(r )ffx c)I

(A2 -i)

-).'

a

JLñJx ("')X(--

'1

G,'»

-") dJe't-z (í)

In the above uatinn, the integral within the square bradei is t1 than the irier

iafn of y (t), i.e.

y(a)

(17)

Eq. (19) is a siiile integral. KnG2 ,

its v1" acily teken 1in _of oenstant aria the onesçcix3ing próducts with iii I t,rrn.. X( LJ,), X( IL1. -C..',

frirm, t.hçir carry±ng out the integratiim. Sin G.. tekeson grrFPrit 1re Only in

a 11 region of the pliii (Fig 64,çear '. axis . = 0, i

jriifl

(19) are easily l'ur Then by an iiiv FEr,

flt) is

ln,I . (12).

of synthesis

is

ait 180 tns and 3 ti by !)'J-fl's o..4hr 1L1 by

«i (17) t1y.

Fig 6 is a- at4'dC viof G2( ¼, i1j ,. ing the

-vari.c

tie of G2. G is. j..rL Of G2 . area is

Of it

r 1w-fr uacy dr]Ít

t1C1tirTli

4. r.is

The evaltion Q is br 3 l-rw'JJuw as2shown_in Fig 7. in ibimth

l,

02

are used te oross-biseaSXXy -and

ip-1 -s'ely.

is

d te

']i]at

. QiP G2.

In order to feed srfficit du.int of kfrequency into ailysi.s

[7) ,

th]y 1000 iivi1

re .rerd., ourredieg to ab

180 cycles\

of low frcy oncillati.

9 divi into 20 secti, ei of 100 sec.

duration and eà.ob section .ns analysed .seri ly using oross-bispectral Rn4ng wi

tb) Ì1 to obtain the eighted vrages. 'fle C0l t a total of 13 irs YIvr*r

tire

on U JET-1N (20 Sion),

l,

nry an i'lus

of Socy.

Fig 8 is an i4rie

of -dn1us

I Sy I

.

02 is in jnnip

qj 1.i. to .0l,., bit si

it is f

:the

. self-tai

ft-iare

eilrt-irin

Of in the p f.,r.., by Eq. (7) Fig 9 is

an itrîc s

of .

SO3 perfo the anpitatien

*

So

Sooc (n,1

The real, imaginary aod nodulus of ti1frk _{quadratic fcfi- function G C 0., Oj)}

slcai in Figs 10, 11, 12 resptive1y _{ferring to} (7) CUl , the d n*rn- aoc

will b too 1, ath G2 freakishly large va1' _{whea the ve spectrua}

approaches the higher and 1 _{ont-off frqueacies. In this paper, vl's of G.,( Cas, "i)}

re deletai, .theaever the _{(L.i) c11i-rd in lonlatirg Saoc (bn.,, .n..) faIls bel} 8% of its peak value. _{nuis the blank area in}the G, ( ¿.s, .}z.) diagr

reat regks

where either G2 = O or it is pirpesely 1c4-cR _{a&.t- of freak values.}

5.

DIUIa

5.1 Fig 1.3, _{ares the quadratic amfer fuac of maan drift £u G, C 'mi ,-o) cttair}

fron irregular waves and the cffitiit C( o)

_(nvert

_tothe sa _{_______}

as G.,) of Fig 3. _{It is observed that the agrmit was zx,t too good. As T1ze11 (10)} peinted out, the scatter of added resistance _{ff ici n1- -in the case of shipe iing} in regular waves is also rather large; the 90% _{fidan beunds on the estinates of G,}

-o) in his

imiilation stedy, is in neigItour1d of O 8 to 1.33. i this i ,

the differonoes betweon the estixrtes fran regular and

irregular wave eerimts did it

appear to be so significant statistically. In the presont case, owing to peirity of regular and irregular tests nducted, analyses of a preliminary natvre ry.i1d only be wiio.

In regular wave tests, the characteristics of puetinatic wave getieratars nay have brijkt

abut a slight deorease in the aacy of the

_{generated waves in the longer wave periods,}

thus producing a lowering of drift onefficiont in these _frequencies.

In irregular wave tests, saitli.ngs of input and output data have nct been pretreated,

hence sar _{spurious "noise" signals may have been}

_{in the estites of G}

(w ,-) which affected the iragnitnde and"fr. . ts peak value. The faca that

for t.'' 3.8 rad/sec., the CE'S netbd yi1ds values _{of e lower than that of regular} wave tests, might be explained by insufficient -

-.. of first order wave fi

acting on the m-r1p1 during regular wave tests. _{However, the .ft £c. iinatth}

by eq. (8) for irregular waves usix this G, C _{.i ,-.') estimated either - regular}

irregular wave test did not differ sudi and'agreed quite _{wall with the maasurod} drift force (Table 3)- This is mainly due to the fact that frequencies of large

discrepancy in estirated G2 C

_{t.i ,o) did not incie with wave frw}

_{of im.nn}

r for the particular wave

_trin.

TE 3

Irregular

_Strun

ve Irregular ve Test CS Prediction Regular ive Test Pri

(maan)

(f-invr)

I 0.32kg _{0.31kg 0.34kg}

II 0.34kg 0.37kg 0.37kg

5.2

Fig. 14, 15 sz the tire rrrn.in r'n1ts

,ofsynth.i ed and maasiired drift forces.

synthesis was nducted by using the filtered QIT G, ( w ,J) obtained fx _{tests in wave}

I and applying eq. (19) to obtain the tire histories of drift torces _{mirespending to} certain specific tine histories of wave I

_{II respectively. Pn these figures it is}

seen that the agreeait of estimated

_{iiid )o freqcy drift farce ceciUations is,}

in general, reasonable. Especially alnahl. is _{fact that syr±hsis of ].cw freqncy}

drift force tijie history of wave II be carriM out OIT G, C £J , U1.) which is

eseiTnatal fr maasur of --- .

, t

aii1it _{ofestinated drift foz}

oscillations are in general than

_{t neas, and the oiUations iwi i}

_and

sax,ther, aitbugh the frecies and

e in

1 9Ynt.

_{= for these}

nay be: (1) ithe frequency interval A usedr for lti1M-4ng G, might: be toe large. Actually only vali along 4 lines of oenstant -.oxear _{.a =0 amis was esed- in} estimation. In duing the tire &rnain synth.t , H ny fl

_{r.{atp veli}

_{of_G2}

obtained by interx,1atjon, a source of l ,1i,Hiw

that might have_

finer details of G2 oomrrjng in tb _{4hh.rIírti of..at= O axis.}

(2) Tbe analysis of G arid the tian &iir1 synthesis e ptLJLM1 on b different xter (the Lomar on JL'T-l6 arid the latter on tJS-l3O), having diffèzit /b with different standard sets of t' s. This ast have loiiered the amacy of resyntkis.

.( 3) C%ing to thee long duration of wa generation in the eakeiing tank,

wa'q (usually r1 i "setting

-

tinrrth

the waves"), its

parasitic long free waves and snirious waves of reflection might have C r,tid. This brings

athbiguity in the asstznnd

sian distribtion of wave elevation and statity of the

wave spectrum. FurthaL '. will have to treat this in greater detail, and to find a faster

and better metFd of obtaining G2 C ,

5.3 The tid of analysis for f4nd4ng the

of wr1ir low fry outp.zt frcin a

linear high friency stôchastic irirt is a methed of great practical value For example, r '& U.0) hás peinted out that if

1ve aleration is used as an inpit. thsteaó of

wave élevation arid the obser fuLl thrust as an outpit, ti applying the

OES atd, one nay ge

a direct relationship ben full scale trials

and tank test or

tretical results

The prest 4hii

t.r,nléi snggest that propeller designs sld be

optimized with nsideraticsi to the totsi low frequmcy resistan and e variations

in the ast frequmitly enunt

sea sft

of a ship. This uld help save rqy

required for driving the ship. This arid other respects of ship operati.eris arid o

structore perfonience involving unni -unr experirta]. hydrodynamics in stochastic ways

are areas ere the OES analysis and the operator

ald act the oballaie.

6. EEDcFNr

This nrk was carried out inder the spen.rship o the Cnina Exnic C?IyTtritt. Lt

amstiti±es a part of the project 'R & D rf SPM systan as a floating prcidiiction, stare

and off i r jng inalt which is aduinistered thina State Shipkuildïng Corp. fl

ork is nducted with the assistance of the staff of the Seakeepirig Deparbamit and

Cputing Center of China Ship Scientific Research Center.

OES

i.

F. A. Hsu & K. A. Blenkarn: "Analysis of Peak Mooring Forces

b Sl

V1 Drift

l].ation iii ndan Seas", Ol 1159, 1970.

G. F. M. Rearry & A. J. Hrmu, "The Slow Drift ciflabres. of A____ in Inn Seas", (YI'C 1500, 1971.

J A. pster "low

'requency

PhnNna .Associated with Vi n'1at Sea",

SPE 4837, 1974.

4 J A. Pirikster & G. Van Corssen "Oinputation of the FLVSt arid Swid ader Wave

on kodi Oscillating in Regular Waves" SIid Tfl1

fl4!t1

on

Nurirm1 ship Hydrodyrics 1977.

-J. A. Pirikster: "I Frequency Se- Order Wave Forces on Vl- ?±ed at Sea", 11th

_______ on Naval Hydrodynamics, 1976.

J A. Pirikster "low Fruency Seid Order Wave

ting br

an FiHrtg StrI]cblres",

Thesis, E. Voenam Eñ. Zonen B.V. Wageningaii.

J. A.- P±nkster: "Mesan and tow Frequency ive Drift

rt xieering Vol. 6, 1979.

0. M. Faltinseri, O. Kzaerland, N. T.itpis & H. Waldethang ' ydrodyixaziic na1ysi of

at Si ngi Point tkxxring Systens" 3S '79.

J. F. Ti cti i. "Application of Cross-Bispectral Analysis of Ship ii - in Wave", PD-749l02, 1972.

J. F. Ti ci i

"The Apju1ication of the Funcbal PolynrtTTuiti nrie1 to ship

Resista probleñ", 11th Sympasitn on Naval Hydrodynamics, 1976.

J. F. F17pii: "The App1ihi1ity of F%nti.ona.l Po1yn!yni.tl Input ()4..L !del to

Ship Besjstanoe in Wai'es", AD-A010860, 1975.

12 C H Kirn & J P Breslin "Predicb.on of Slow Drift Oscillation of a Ship in Heed Seas", BCS '76

-13. 16th 1TLt: ort of the Ocean

inceti, CTTuI4.

14 0 M Falb.ruseri "Drift For and Slowly Varying on Ship

0ffre SLwt

jnjaves"._rian Marjj

Pesth t.b. 1. 1978.

W.D. Stanley:"Digital .sigal. processing"., Reston

Publishing Company. INC.., 1973.

J.S. Bendat and A.G. Pierso-l:Raado

data: Analysis

E. J. Prs,

D. i & R. W. MisJd ¿ F. J. Fi: of Drift Force Quadratic 'fransfer Futiis by Digital -bispectra]. Analysìs, CIC 4440, 1982.

L. T. Tick: _{The Estinatiou of}1rarcthr _{mctis of}

Qirtie Systa!E,

Vol. 3, N,. 4, 1961.

20 R. 8orresi: "cperi.xita]. Deteenination of the _adratic !Pri,cfv _Governing

Slowly Oscillating Pha in Irru1ar ves, C 3104, 1978.

Fig. I Arrangement of Model Restraint Under the Carriage

1..Ip

II

ii

çJ

2o 2.3 .3O .35 4.0

Fig. Curves of Mean Drift Force Coefficient

4g '4-

Fïg. 4 Wave Spectrtmi (I

-

ii---)

o

:

&

L Fig. 6.e55 e. 0565 pc 2.98,' P J(R- 715 P TD 26. 7. RES dôIÇ6

F; O.6261f1 6+tEA$ e-c.. 69 -ø3

ø.&35/s

P.'JfiR e:3e3

P.sT esss

RES.

øóf4Z 64

Scheme Showing Properties Of Complex _Ftction G2 (u

i 2)

In The aifrequency Plane

11

i

Fig. 5 Sample Record And Analysis of irregular Wave Test

CP.S os I I I

*t)

t

-

L!J

H

S

ji

U3Q) 6r4,cs

-J

Pr.t

&fft

r)

EaipÁcs

Fig. 7 Flow Diagr of Computation

12

C e 02

-

'±L

'1_42L.

4 _FPT

-{

(')

_f

r,

JA

WA

4F' E 3U0 -6 4S/0 q

Fig. .8 Isometric Sketch Of Modulus Of Wave, Wave, Resistance Cross- bispectrum Of Sea State 1. Froude number O

A

A 4 _I, d-03 13 ,o.. _- 4-os F4

Fig. 9 Isometric Sketch Of Modulus Of Wave, Wave (wave) Cross-b1sectrum Of Sea Statt 1, Froude Number O

.6.

.

2.0/ .04

£2,

14

Fig. 10 Reál Part 0f EstimatEd Quadratic Transfer Function G2

(j

Fig. 11 Imaginary Part Of Estimated Quadratic Transfer Function

Fig. 12 Modulùs Of Estimated Quad±a tic

Transfer Function G2

'y

CßS Q$t!a,.V,4

X by ?ii/as.

.rt

17

Fig. 13 Estimated Mean Drift Force

I.0 - _-- - -- o0++

«

I-o -20 Ky -'4 -2.0

Fig. 14 Time Domain Results, Synthesized And Observed, Wave I

-18

o bj 97IfII5CJ

t , Cad ulà twi'

4 - 000, ° _'2 4/ _-- -I.e S.S,....

24

e.. - o .+.i+,.. o_____'o - -

_.00o

-- 1., _{*444t.p4.t44tt+} 41++44++ 41 SeC 000O -2.o o ¿y cipenment .+ /cu/aî/o»

:

- 7.0

Fig. 15 Time Domain RèÈults, Synthesized And Observed, Wave II

19

lo