semi-displacement vessel lecture 2

8/3/2019 Semi-Displacement Vessel Lecture 2

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Vertical shear forceVertical shear force in the deck

2 2

3 3

2 2

2

5 3 5

2

3

3 33

35 33 35

33

2 2

4 4

3

4

5

3

2

5

2

4

0.5( ( ) ( )

( )

( ) )

e

A B

B

B

i t

d ddt dt

d d d

dt dt d

d dy yd

V M A

A B B

C C

t dt

dy

dt

e

y

X

t

= + + + +

+ + +

+ + +

3 3 sin( scos( sin ) n )( )i0.5e e

BB

i t i t k X e e yF i ky

=

Vertical shear force in the deck

2 2

4 4

2 23 33

3

4

3 33

3

4

0.5(

)

e

A B

B

i t

B

d dy y

dt dt

dy

V M

y

A

B C

X

dt

e

= + +

+

3 30.5 sin( sin )e ei t i t

B X e F e i ky

=

Vertical Shear Force

Zero in head/following seaZero for long/short wavesSensitive to rollMass distribution

Pitch Connecting Moment

Zero in head/following wavesZero for short/long wavesRoll motions

Vertical Bending (split) Moment

Sensitive to heave/pitchMass distribution


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Vertical Bending Moment

Theory

Experiments

Beam seaFn=0.49

Pitch Connecting Moment

Experiments

Theory

=45Fn=0.49

Vertical Shear Force

Experiments

Theory

Beam seaFn=0.49

Error sources in theoretical model

Transverse wave systems

Hull interaction

Interaction steady/unsteady flow

Non-linear effects

Error sources in the model tests Time window

Heading control

Non-constant wave conditions

Short-term statistics

Given significant wave height and

mean wave period

Assume longcrested sea

2

2

0 0 0

0

( ) ( )s H d

=


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Short term split moments

90

135

105

75

120

150

145

180

Nonlinear effects

Long term predictions

Operational areas

Scatter diagram

Operational limits

Probability of exceedence Q

2

1 1

8.7

( ) exp( 0.5( / ) )

110

M N

jk jk

j i

Q R R p

QN

= =

=

= =

Design values of pitch connectingmoment

132 000 kNm

2 120 000 kNm

3 961 kNm

156 890 kNm

60 m

120 m

DNVNumericalcalculation

Vessellength

Design values of split moment

36 200 kNm

579 000 kNm

1 918 kNm

53 989 kNm

60 m

120 m

DNVNumericalcalculation

Vessellength

Local and global slamming effects


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Slamming drop tests outside DNV Wedge impact

Wetdeck Slamming

=

Stiffened wetdeck

Stena Discovery (1997)

126,60 x 40,00 x 4,80 m ; 40 Knots

Hydroelastic slamming tests Drop tests of horizontal plates

Correctly scaled elastic properties of steeland aluminium

Calm water and varying wave conditionsand impact positons


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Measurement unit

Experimental and theoreticalpressures

Pressure (bar)

P3 theory

P1 theory

P3 experiments

P1 experiments

Time (s)

Pressure distribution due to elasticvibrations


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Local slamming effect

Slamming must be considered in thecontext of structural reponse

Local hydroelasticity should be consideredwhen angle between free surface and hullsurface is less than 5 degrees

Very high slamming pressures areunimportant, i.e. they cannot be used asstatic loading

Global wetdeck slammingstudies by Chunhua Ge

Heave and pitch of each rigid body

Connected by equivalent beam

Global slamming effect.Two-node longitudinal bending

Vertical shear force at

front cut

time (s)

( )VSF NNum.3modes

Exp.

Slamming force (inertia force

included)

time (s)

3( )F N

Num.3modes

Exp.

Experimental Error

Sources Importance

Wave amplitude along track Yes

Seiching (sloshing) in the tank No

Wave measurement Yes

Roll, yaw and sway Yes

Sinkage No

Trim Yes

Mass distribution Yes/No

Wetdeck geometry Yes

Speed No


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Relative ExperimentalErrors

for Case 2

VSF 1 VBM 1 VSF 2 VBM 2

Rel. Error 0.18 0.29 0.26 0.17

Global force response at two cuts

Trim is most important

No random errors included

Theoretical Error Sources

Incident wave nonlinearities No

Hull interaction Yes

Nonlinear side hull forces ???

3D slamming No

Details in slamming loads No

Transverse bending No

Transient phase No

Importance

Global slamming effects

Wagner method is unnecessary

Cannot be used during water exit

Both water entry and exit are important

Kutta condition matters

Effect of gravity for long duration impact

Slamming

Must be analysed from a structuralreaction point of view

Differences in time scales outrule physicalphenomena

Further developments must focus on direct

incorporation of slamming analysis inglobal wave-induced motion analysis

Springing and Whipping (Morris)Exaggerated two-node vibration


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Slender body theory and globalvertical ship vibrations

3 33

HD w w f U a U

t x t x

= + +

Vertical hydrodynamic force per unit length:

( )2 2

23333 33 332

2 2

32 2

2

exc

daw w w wm a a U U U a

t x t dx t x x

wgbw EI f

x x

+ + + +

+ + =

Beam equation:

Note:Transom stern effects give important hydrodynamicdamping at high speed

Natural period for two-node verticalvibrations

Green water on deck Green water on deck

Plunging type water on deck

(WOD)Hammer-Fist Type WOD


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Hammer-Fist Type WOD Hammer-Fist Type WOD




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Hammer-Fist Type WOD Hammer fist and karate

Green water front velocity u as afunction of distance x from the bow

u

gh

/x h

h=waterheight above

the deck inthe bow

Impact pressure on verticalstructure on the deck

Wedge approximationof green water front:

semi-displacement vessel lecture 2

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