Nonlinear ship responses in head waves

Nonlmear Ship Responses in Head Waves

L.J.M. Adegeest

Report No. 984-P June 29, 1993

The Eight Int. Workshop on Water

Waves and Floating Bodies, St. John's,

Newfoundland, 23 -26 May 1993, Canada

Dfllft Unhrerstty of Technotooy Ship HydrDmschanics Laboratory IViekelweg.2

2628 CD Dem The Netheriands Phone 015- 78 68 82

^ National Research Council Canada

Consell national de recherches Canada Institute for Institut de

Marine Dynamics dynamlque marine

THE EIGHTH

INTERNATIONAL WORKSHOP

ON WATER W A V E S

AND FLOATING BODIES

Preliminary A b s t r a c t s

St. John's, Newfound/and

23-26 May 7993

Nonlmear Ship Responses in Head Waves

Leon Adegeest"

June 29, 1993

Abstract

In this sttidy the a t t e n t i o n is addressed to the non-linear behaviour of vertical bendiiig moments in a ship i n moderate a n d severe seas. T h i s effect occurs as a very s t r o n g increase of the bending m o m e n t in sagging c o n d i t i o n and a slight decrease in hogr-ging c o n d i t i o n c o m p a r e d to linear predictions. As a result of this phenomenon the stress level in the deck p l a t i n g becomes: much higher t h a n predicted by l i n e a r methods.

A new set of experiments has been set up i n w h i c h the first three .'harmonic components.of the motions, bending moments and shear forces have been ana-lyzed. T h e experiments have been or w i l l be per-f o r m e d w i t h a s t a n d a r d Wigley h u l l per-f o r m as .well as w i t h a W i g l e y h u l l f o r m w i t h a d d i t i o n a l bow f i a r e . In this a;bstract sorne e x p e r i m e n t a l results have been compared wiith a large-amplitude s t r i p theory-based, s i m u l a t i o n m o d e l .

It is shown t h a t although the motions can be cal-culated w i t h a linear approach u n t i l quite severe situations, this c e r t a i n l y does not hold for the i n -ternal loads, even for a linear hull f o r r p such as a W i g l e y is.

T h e m a g n i t u d e of the nonlinear components i n the bending m o m e n t s is strongly related t o the arn-plitude of the relative m o t i o n at the bow: T h i s irn-plies t h a t even i n very l o w a m p l i t u d e waves, a con-siderable c o n t r i b u t i o n f r o m higher harmonics is ex-perienced i f the e x c i t a t i o n frequency is close a r o i i n d the peak in the r e l a t i v e m o t i o n transfer f u n c t i o n .

A d d i t i o n a l bow flare appea;rs to increase higher order components i n the bending moments espe-cially in the bow region dramatically,

'Sliip Hydromechanics Laboratory, Delft University of Tèclmólbgy

Figure I : Design ordinates of two Wigley variants (not on-.scale)

1 Experiments

A lack of published e x p e r i m e n t a l d a t a on the a m p l i -tude dependent nonlinearities of bending moments exists. Dalzell [1,2] studied this phenomenon al-ready i n 1964 but these e x p e r i m e n t a l results have j u s t been presented i n the f o r m of bending moments in sagging and hogging c o n d i t i o n , not p r o v i d i n g i n -f o r m a t i o n about the i n d i v i d u a l harmonic compo-nents. The goal of this new set of experiments was to o b t a i n a systematic series of d a t a on the a m p l i -tude dependency of vertical ship responses in head waves. The a t t e n t i o n was foctissed on the first three harmonics of the b e n d i n g moments ;and shear forces in the midship cross section and the cross section at a quarter length f r o m the bow as w e l l as of the heave and pitch m o t i o n and .the force i n l o n g i t u d i n a l di^ rection. T w o h l i l l f o r m s have been tested', i.e. a standard! Wigley h u l l f o r m w i t h m a i n characteris-tics L = 2.5 m, L / T = 18 and L / B = 7. T h e second hull f o r m was a W i g l e y hull f o r m w i t h the same un-derwater geometry :biit w i t h a d d i t i o n a l bow flare, see figure 1. Table 1 shows the test program.

T h e relevance of t a k i n g i n t o account nonlinear ef-fects is clearly shown by l o o k i n g at the time-records resulting f r o m these experiments. Figure 2 shows

Experiment M o d e l P e r f o r m e d Wave force n i e a s ü r e m e n t s O r i g i n a l W i g l e y Yes

8 sections

Wave force measurements Wiigley w i t h bowflare Not yet 8 sections

Forced Vertical ' O r i g i n a l Wigley Yes oscillations 8 sections

Forced vertical Wigley w i t h bowflare Not yet oscillations 8 sections

Measurement of motions-, O r i g i n a l W i g l e y N o t yet bending moments and 3 sections

shear forces i n head waves Wave force measurements

Measurement of motions) W i g l e y w i t h bowflare Yes bending moments and 3 sections

shear forces in head waves

Table 1: Towirig tank test p r o g r a m

by p l o t t i n g the m a g n i t u d e of the the nonlinear Fourier components di vided ,by the magnitude of the first.harmonic fór a certain wave steepness. Figure. 3 shows these ratios for the bending moments at m i d -ship and at a quarter length f r o m the bow. Similar plots for the m o t i o n responses have been prepared -too, these plots:showed peaks in the cur ves up to,9%

for the p i t c h m o t i o n and only -5% in case of heave. From these consicierations i t has to be concluded that i t is not allowed to assume the nonlinearities in the bending moments t o be weak. The origin of this very strong nonlinear behaviour is the large a m p l i t u d e relative m ó t i o n .

2 Mathematical Model

fn, many ' f u l l y nonlinear' methods a weak nonlinear behaviour is assumed. A s was shown by the ex-perimental results, t h i s assumption is certainly not valid i n case of the b e n d i n g moment responses. T h e a i m of the m a t h e m a t i c a l m o d e l described below is to predict the nonlinear loads 'sufBcieritly accurate enough' i l l order ito'be able to make approximations of long t e r m d i s t r i b u t i o n functions or to use 'the model in probabilistic ship design.

The specific nonlinear phenomenon of interest, i.e. the nonlinear b e n d i n g moments, especially oc-curs i n slender vessels (experience) s a i l i n g i n head and bow waves. For those type o f vessels the exci-t a exci-t i o n forces are h i g h l y d o m i n a exci-t e d by exci-the pressure

H t t v a : Pitch ' - " - H a y t ' i n C.O.C.

0 "-5 I . . 1.6 2 I.S Tireo (si

: B i n d l K i U i D i i o i Orrfia BtBrftflf MêlstDi OrdIO ia.co.C.

Figure 2: Fragment of recorded signals f o r (a) mo-tions and wave and ( b ) vertical bending rnpments for the W i g l e y w i t h bow flare

a part of the recorded signals in regular waves at the peak frequency of the relative m o t i o n trans-fer function- at the bow i n a wave w i t h steepness H/X « 0.0-14. T h e waves arid' motions show a very regular sirie-hke response vyhile the bending moments are s t r o n g l y effected.by higher harmonic components.

T h e relative i m p o r t a n c e of the rionUnear compo-nents in the various recorded signals can be shown

lïAVEFORCE r3 rn=o;3 WAVEMOMENT F 5 Fn=0.3 , Z F / i l ( N / m ) ( T h o ü j a n d ü ) 1 • , .

4 \ - • •• - - •

A

Figure 3: Relative c o n t r i b u t i o n of nonlinear com-ponents for H/X = 0.02 in (a) heave, (bi) pitch, (c) midship, b e n d i n g m o m e n t and (di) b e n d i n g ' m o m e n t at a quarter length f r o m the bow

in t h e u n d i s t u r b e d waves or the so-called Froude-K r i i o f f pressure. T h e magnitude o f t h e pressure due to the d i f f r a c t e d wayes w i l l be much smaller t h a n the mag.nitude of the pressure in the Undisturbed waves, which is the result of the incident wave po-tentials in combina;tion with- the hydrostatic pres-sure. I n terms o f ' o r d e r s ' , the m a g n i t u d e of the first order Froude-Kriloflf pressure is a first order quan-t i quan-t y , while quan-the m a g n i quan-t u d e of quan-the firsquan-t order d i f f r a c quan-t e d and radiated wave pressure can be considered as a 'one-and-a-half order quantity, i m p l y i n g that i t is smaller i n m a g n i t u d e than the first order Froude-Kriloff-pressure b u t larger t h a n the second order Proude-KrilofF pressUre.

T h e easiest way to dea;l w i t h the m a i n c o n t r i b u -tion causing the nonlinear effects, i.e. the integral of the pressure i n the u n d i s t u r b e d waves oyer the instantaneous w e t t e d surface, is i n a time d o m a i n model.

T h e instantaneous wetted surface lis defined by" the b o d y i n its a c t u a l position in the u n d i s t u r b e d waves.

F i r s t order c o n t r i b u t i o n s f r o m the radiated and d i f f r a c t e d waves have been incorporated in the f o r m

Omega ( r a d / s ) _{Omega f r e i d / s ]}

n u t i u a H i / l l . M *• > i f i r r - U B M . / H . i n

Q nLrTl4<DM*/R<r»o ' C r ^ o i . s U

Figure 4: Wave forces and moments f r o m experi-rfients and simulations

of impulse-response f u n c t i o n s as was used before i n different time d o m a i n models [3,4,5]. T h e frequency domain results have been calculated w i t h a 3D panel p r o g r a m .

The Salyesen-Tuck-Faltinsen-forward speed for-m u l a t i o n s have been Used which has proven to be very valuable in ship n i o t i o n predictions.

3 Comparison with

Experi-ments

Results of wave force measurements and simulations in steep waves are shown in figure 4. I t can be seen t h a t the numerical-results hardly show any differ-ence f o r the W i g l e y w i t h and w i t h o u t f l a r e . I n these figures the response a m p l i t u d e has been de-fined as ( m a x i m u m - n u n i n i u m ' ) / w a v e height. T h e experiments have been p e r f o r m e d in the waves w i t h different steepnesses up t o the highest possible wave regarding t h e model's freeipoard,

M o t i o n responses f o r b o t h W i g l e y h u l l forms are shown i n figure 5. I t a p p e a r e d t h a t the motions are stronly linear i n the wave a m p l i t u d c i in the experi-ments as well as in the s i m u l a t i o n s .

A n example of a v e r t i c a l bending moment trans-f e r trans-f u n c t i o n is sho.wn i n trans-figure 6. F r o m the simula-tions a strong nonlinear behaviour is f o u n d for the i n t e r n a l loads, especially for the Wigley w i t h bow flare. A comparison between the nonlinear compo-nents of the midship b e n d i n g moments is shown i n figure 7.

HEAVE MOTION

Wiclrr. Fn ^ D.3

PITCH MOTION

I l | l i 7 . Fn 3:0.3 P I U : h / Z . U , [ d g t / m l

Figure 5: M o t i o n responses f r o m experiments and simulations

V e r t i c a l B e n d i n g M o m e n t o r d . 1 0

Tn = 0.3. BWIO<l)/Zet« ( H m / m l

Figure e; F i r s t order midship bending moment

V e r t i c a l B e n d l n e M o m a n l o r d . 1 0 V e r t i c a l B e n d i n g M o m c n l o r d . l o

Fn a 0.3 Fn s 0^3 BUIO(g)/ZeU-a [ N / m - Z ]

4 Conclusions

From the experiments i t appears t h a t the nonlin-earities in the bending m o m e n t responses can not considered to .be. weak. Therefor nonliriear methods have .to ;be used' i n order to calculate- the bending moments, especially when the relative motions are large compared to the draught of the vessel.

T h e only possible way to solve this, p r o b l e m nu-merically seems to be i n the time d o m a i n . I n this s t a d i u m a large a m p l i t u d e strip m e t h o d has been developed, only t a k i n g i n t o account the nonlinear F r o u d e - K r i l o f f force. T h i s approach resulted i n sat-isfactory first order m o t i o n and bending, moment predictions. A n underestimation of the higher har-monics is obtained in case of the internal loads. For t h a t reason the code w i l l be extended w i t h a large a m p l i t u d e c o n t r i b u t i o n f r o m the radiation arid d i f f r a c t i p n potentials. .

-References

[ I ] J . F . Daheü. An invesiigaiion of midship bending momenis experienced in extreme regnlar waves by a Mariner-type ship and'three variants. Technical Report. S.SC155, ;Ship S t r u c t u r e C o m m i t -tee, 1964.

[2] J-.F: Dalzell. An inves lig ation of midship bending moments experienced in extreme regular waves by models of a tanker and a destroyer: Techni-cal Report SSC-.1.56j .Ship..Struct ure C o m m i t t e e , 1964.

[-3] C C . Hsiung. Time domain analysis of ship mo-tions and sea loads in irregular head seas. Techn i c a l Report D R B A C R / 9 1 / 4 2 0 , CeTechntre f o r M a -rine Vessel Design and flesearch, Techn.lTniv. of Nova Scotia, Halifax, 1991.

[4] B . K . K i n g , and R , F . Beck. Seakeeping calcu-lations w i t h f o r w a r d speed using time-domain analysis. I n Proc. of Hih Symp. Naval Hydro-dynamics, pages 47-66, 1988'.

l[5] S.J:. Liapis. Time-domain .analysis of ship mo-tions, P h D thesis, U n i y . of M'ichigan, li986'. '

Figure 7: M e a n and double-frequency midship bending moment