Towing tank experiments on ship girder loadings in oblique waves, a model presentation of selected results, Presented at the 4th National Congress of Theoretical and Applied Mechanics, Varna, Bulgaria, 1981

ÌEC:HNISCHE HOGESCHOOL DELFT

AFDEUNG DER SCHEEPSBOUW- EN SCHEEPVAARTKUNDE

DELFT UNIVERSITY OF TECHNOLOGY

Department of Shipbuilding and Shipping Ship Structures Laboratory

Report

NO.íHSSL

239a

by.

R. Wereldsma

Paper to be presented at the Fourth National Congress

of

Theoretical and Applied Mechanics, September 1981, Varna, Bulgaria.

TOWING TANK EXPERIMENTS ON SHIP GIRDER LOADINGS IN OBLIQUE WAVES

A MODAL PRESENTATION OF SELECTE.b RESULTS

-1-TOWING TANK EXPERIMENTS ON SHIP GIRDER LOADINGS IN OBLIQUE' WAVES,

AMODAL PRESENTATION OF SELECTED RESULTS

R. Wereldsma

Summary

Free model, tests on a segmented model with 12 segments and a rigid backbone

have been carried out in a towing tank in order to determine the global girder loading in oblique and head waves. The results have been analysed accordinthe normal mode method into generalized forces in vertical direc-tion, each dealing with a particular mode of vibration. Also static values due to the forward-speed-generated-wave-system have been evaluated.

The effect of the waveheight and wave direction on the vertical bending is illustrated. The design of the model and the requirements in connection with dynamic measurements are discussed. The results of the measurements are

given for model scale.

Introduction

For a rational analysis of the elastic behaviour of the ships' girder it is necessary to gain knowledge about the distributed loadings sensed by thé

ship structure during operational conditions. In particular when mass-elastic

structural dynamics becomes' important (springing) _{or when a spectral analysis}

for long term predictions needs to 'be performed, the usual regular tésts

sensing the midship bending moment, being the result of these distributed

loadings, will not be applicable, andil not

serve the puè

'-2-rM i fl I M. dn

Ml i'

Tc ndl un M I a

Ic

dd du iM

M

dn

M

ri

jal

d]Laj

L°

rc

c

-1. iii nfl nd1

k-,

LCdn Cid]

[J

Sd

o1

1F)

i I I I ni I '.+ Sdd] tdi j,FdJ

The n-coordinate.s are the rigid body motions of 'the mechanical system and the d-coordin'ates of the deflection 'and elastic deformation of the girder.

Since this paper is devoted' to structural deformation and' loadings, the

at-tention will be foäussed on the lower é'tis'of (3)'.

For a proper analysis o.f the ship girder deflection, it is necessary to have

the 'hull. free moving in the waves,. In order to measure the right hand si',de of the equa'tion, being the total éxcitation of the' girder, it is, necessary "to

avöid the mass elastic disturbances and ä, represented by the left 'hand'

a' special segmented módel having 2 segments hooked to a rigid backbone..

in this paper resúÏts of experiments in oblique waves under 2...50 and 450

with varioUs wavelengths are presented for the most importnt girder loading,

joe. the vertical bending..

4

Earlier experiments with headwaves have been reported in /1/

1'. 'Fundamentals' of the measuring technique

The general description of linear statics and dynamics of a meçhanical

strUc-ture can be formulated as /2/: ,

+ 'Ici {*} + is:I{x}, =

F} ' ,

(1)

For the case the structtire is floating in water the hydrodynamic effects have

to be taken into account.

Th'e equation has to be completed as follows /3/, /4/:

i'MI{} +

ic!'[*'} + i,Si '{'x:} '=

{'F} - iMi{} - ,iCi{*}

-

isi{x} ' (2)

L___'mechanical system'::--1

Lhydrodynamic effectsi

wave

excitation

When motions '(n) and deflections--(d are dea'it..with separate l'y we 'obtain .by'

partitioning': .

' '

dJ

Jn

'(3)

of the mass effects model due to ship motio distortion wave sensed by loading displacement of the

pick ups Istructure,

(strain gauges.) i

wet surface

t

pressure effects (waves and moving surface)1

The requirements for the structure of the model can be listed as follows: Model to be tested needs to be free movable in approximated rigid body

modes.

Lowest structural natural frequency high in comparison with the highest

frequency .of interest (frequency of wave encounter).

The hydrodynamic effects (waves and motion interaction) are fundamentally sensed as pressures on the hull surface.

Mass effects due to motion acceleration have to be considered as an

important structural load contribution.

5. The stiff model needs to be so flexible on some places that a measurement

(e.g.. with strain gauges) can take place (compromise).

The right haud side of equation (4) equals the sum of, in the first place,

the hydrodynamic loading due to waves, in cbmbination with hydrodynamic

load-ings due to ship motions and in the second place the inertia forcés due to the motion acceleration. This sum equals the very girder loading we are look-ing for. This total loadlook-ing equals the distortion sensed by displacement or force pick ups /5/ as given by the left hand side of equation (4).

Additional requirements for the model design can be listed as follows: Backbone constructed of light weight material and of high bending and torsional stiffness, to avoid parasitic mass effects of the backbone. Segments constructed in such a way that the internal stiffness is suf-ficiently high and the mass is in accordance with that of the correspond-terms other than the stiffness correspond-terms. This condition can be obtained by making the structure so stiff that the lowest natural frequency of the

struc-ture moving in water is high as compared to the highest frequency of excita-tion. This is a requirement for the structure of the model on which thé measurement takes place. The fulfilment of this requirement enables us to reduce equation (3) tò the following form:

Isddl{d} = {Fd} - IMdI{iL} - IMd l{ri} _lcd l - ISdI{n} (4)

- tI

Fig.1 Typita( force transducer recoidugs of the fransient vibration

of the model

Rigid Backbone Force Transducer _{© Segment}

20//JI

7-10 _16-10

ing location of the ship.

c. The flexures measuring the forces exerted by the segments on the backbone need to be sufficiently stiff so that all the natural frequencies are sufficiently high, still haing flexibility to allow a measurement.

As an example of the dynamic performance of the model in Fig. 1 a recording

is reproduced of a vertical force signal of one of the segments together with a transient response of an impulsive disturbance.

From this recording a lowest natural frequency of 20 Hz can be deduced, which is a factor 10 above the maximum frequency of interest, being appr. 2 Hz.

2. The shi' model, the measuring irograimne and the data rocessi

The ship model

The bodyplan of the ship is shown in Fig. 2. It is a tanker with bulbous bow ng

The model has been built to a scale of 1:66.66 and has been tested in fully loaded condition.

The programme of measurements

The experimental programme can be seen as an extension of the experiments

reported in /1/, where the saine model has been tested in headwaves with the

attention focussed on very short wavelength for the investigation of spring-ing phenomena. In this case however, attention has been focussed on the

effect of oblique waves on the ships' girder loading,. For the reason of wave

obliqueness the tests have been carried out in the NSMB seakeeping laboratory of 215,000 TDW. The particulars of the ship

Table I. Particulars of the ship

are given in the following table,:

Length between P.P. 3F0.0 in Bredth moulded 46.9 m Depth moulded 24.5 m Block coefficient - 0.84 Prismatic coefficient 0.85 L.C.B. in percentage of L. 3.13 Deadweight 215,000.0 tons Horse power 28,000.0 HP r.p.m. 80 r.p.m.

-

6.-of the Maritime Research Institute in the Netherlands (MARIN).

in table II a review is, given of the test conditions of the mödei.

Table II. Review of measurements, of the experimental prograimne

Run number Wave heading a <'degrees) Wave height (P-P, cm) Wavelength Model speed (rn/sec) Encounter frequency ('Hz') shiplength 10 1.60 0.544 2 3 ,1,0 10 1.90 1.40 . . 0.498 0.591 4 225° ,' 1:0 1.20. . 0.95 0.64.6 '5 ' ' IO. .40 1.147 6 5 .80 ' H 0.830 7 . 5 1.00 . '0.723 8 .

io

:,, .60 0.9.90 9 . 1 80° FO :, 1 .00 1. 35 0.. 874 10 Ii, 180° , 10 ,' 10 .55 ' .60 ' . 1.272' 0.507 12 ' ' 1:0 .40 ', ' 0.552 13 .. 5 '.80' ' 0.467 14 45° 5 1.00 0.95 ,' 0.437 IS ' 10 1.20 0.411 16 ' ' 1:0 1.40 ' 0.386 17 '18 10 10' 1.60 1.90 ' 0.371 0.347 19 ' -

.-.

O 1.35 -20 45° 10 .80 0.9,5 0.468 21 , 22, 23 4:5° 225° 225° 10 10' 10 1.00 1.00 '

!°

Ò.95 ' 0.435 0.725 0.829

c. Data processinz and reduction

Discretisation in time and s.ace coordinates

7

For the processing of the measured data a single discrete frequency approach is made. So., the time variable part of the loading can be represented by rotating vectors. The amplitude represented by the length of the vector, the frequency by the speed of rotation and the phase lag by different angular positions of the vectors. An example is given in Fig. 3.

Besides the time dependent part due to the waves also s.tatic loadings of the

hull girder can be distinguished. This static,loading will be caused a.o. by

the wave system generated by the forward speed. This effect makes the model to trim and gives an extra girder loading in vertical direction. t can be

distinguished from the wave loading by the fact that it is a time invariant

phenomenon, only depend:ing on the forward speed and the lines of the ship.

Transformation to natural coordinates

in order to obtain a better insight in the 'arious effects of the loading on

the girder defiectións and nominal sectional integrated stresses (bending moment, shear force, torsional moment) the regular single axial ship coor-dinate has been transformed to natural coorcoor-dinates/4/. For that purpose it

is necessary to know the shape of the various modal eflections in which the

ship may vibrate (eigenfunctions).

Since this was not veli possible to ànalyse for the real ship, it has been assumed that for this long tanker a regular uniform beam analysis may result

in sufficiently accurate apprdximations of the vibration shapes of the ship.

The required number of modes depends on the characteristic wavelength of the loading in comparison with the characteristic wavelength of the modal de-flection (distance between the nodes). The solvability is assumed to be suf-ficient when the 'characteristic mode wavelength' equals the 'characteristic load wavelength'. Since the shortest wavelengths are appr. shiplength, i.e.

the characteristic load length appr. ¿ of the sliiplength, the 3rd elastic

mode (4-noded mode) having a characteristic length of _¿ of the shiplength

may serve the purpose of solvability.

Therefore, the actions on the 2 discretized sections along the hull girder are transformed to similar actions on the 5 natural coordinates, i.e. two motions and three eigenfunctions. Since the model is free to move the rigid

body coordinates are not of much interest (the forces belonging to these coordinates are transferred into ship motions) and only the first 3 elastiá modes will be taken into consideration.

Wi

Wo

I 111111 I

III

Normal modal dei lectivos coordinates.

-8-StatIc load due to weight and buepancy distr,butions. (estimated)

Static load due to fward speed wave. (N) Vertical loading decomposed in generalized harmonic torces. [N/an wandmght]

\

\

.\

\

-.

\

I

\

I

.1

I I I I Ç

N

N

N

N

N

\

\

9

The conversion of the load pattern as sensed by the 12 segments to the new generalised forces is done through a weighted integral procedure.

1'

f

. (x).q(x)..q.i(u) dx

over the shiplength

where: q(x) is distributed load

ii (X) is the natural coordinate under consideration

I' is the. generalised force

x is the axial girder coordinate.

The shapes of the applied natural coordinates are given in table III.

The lay-out of the. girder loading in generalised forces is shown in Fig.. 4.

Table III. Applied normalized natural coordinates

Normalized mode

section

number

displacement

2-noded 3-noded 4-noded

+0.4708 0.3952 +0.3205 2 +0.2486 0.0295 . -0.1573 3 +0.0380 -02566 -0.3887 4 . -0.1433 -0.3863 -0.2641 5 -0.2749 -0.3.333 +0.0861 6 -0.3450 -0.1298 +0.3798 .7 -0.3450 +0.1298 +0.3798 8 -0.2749 +0.3333 +0.0861 9 -0. 1433 +0.3863 . -0.2641 10 +0.0380 +0.2566 -0.3887 11 +0.2486 -0.0295 -0.1573 12 +0.4708 -0.3952 +0.3205

Zarro forward speed. Moving load dintribution. frequency equal to encounter frequent5. Pattern dependent on wane length and hull lines. 'o 30 20 10 -30

!VaVß

w

z DettI tank G ItSMO tank

Stili water condition; Forward speed l.35m/sec.

o Heading angle of waves oc225 G Heading angle of waves z n 45

Forward speed O.OSm/sec.

- ---

---

-A. C.

Io

-z 20 -30 40 30

Wareheigt*p-p IOcm; Wavelength raMo O/L 1.0 -40 _{+Warveliert p-p IOni;Waveiength rat.oX/LQ55}

o Still water condition.

Forward speed 1.35mfsec. Head waves non t80

-20

---30

xx Forward speed i. I5mflec. (From))))

. Forward speed 0.ÇSin/sec.

o.--o Forward speed Q68m/sec. tFro.(lfl Fig.5 _{Static load distribution due to forward speed wave system for various conditions.}

2 I 141516 1 1° I 110 111 ft2 a

t

50 -1000

-

_{w w} E 1000 z Shpcoordnate X

Fig.3 Five types of overall loadings on the hull girder of _{a ship(in shipcoordinates.)}

50 z -50 50

-ra

aii\

_"w

(stimalid olalic Still waler

loading (loaded). Pitch and liaran, land other motiinnsj f reel1 adjusted. Static girder load-mg due lo wave

y5tti geineraled by the forward speed. Pitch.tseav, and other rigid body motions hilly adjusted. Vertical loading due to wanes. arcludinig the effect of motions. Hon'uontal loading due to oblique wares, including the effect of motions. Torsional loading dun to oblique waves, including the effect niolioni. Non pero forward

speed, wan, pattern dependent on shiplines O

and speed

3. Results of measurements

a. Presentation of the results of the vertical load distribution in

'shi2 coordinates'

Static values

From table uwe select run number 19, being a test without waves and a

for-ward speed of 1.35 rn/sec.. This test has especially been carried out for

comparison purposes with the experiments in /1/, where a similar test has

been carried out at the Deif t University tank.

In Fig.. 5a the result of the NSMB-test is compared with the Deif t University

test. The comparison can be estimated as satisfactory.

Run numbers 9 and 10 of table Ii enable us to study the effect of headwaves

on the static forward speed wave loading.. The results are collected in Fig. 5b together with those..of run 19. It may be.concluded that the loading of the

'ship wave' is independent of the headwaves encountered.

For the tests with oblique waves the nonsymmetrical condition of the model and the artificial type of support (spring support) under the carriage give rise to disturbances of static and dynamic nature. Therefore the mean value has been taken from the recordings of run No. 1 through 8, 22, 23 (225°

waves) and separately from run No. 11 through 18., 20 and 21 (450 waves). These tests have been carried out with a forward speed of .95 rn/sec.

The results of both seriesof tests are given in Fig.. 5c.

Finally the curve of Fig. Sc, being the static girder loading, 1under oblique

wave conditions, for a forward speed of .95 rn/sec has been compared with similar curves however with different speeds as has been reported in /1/. The result of this comparison is shown in Fig. Sd.

It can be concluded that the curve with the intermediate speed of .95 rn/sec

fits well with the curves obtained for other speeds, i.e. 0.68 and 1.35 m/sec.

ynarnic values

The results of run numbers I through 5, &, 22 and 23 are given in Fig. 6 fo.r

the vertical load. This figure gives an illustration of the numerical results as listed in table IV.

The results of run numbers 11, 15 through 18, 20 and 21 are collected in table V. Finally the results of run No. 9 and W are given in table VI.

From run No. 7 and 22 and 6 and 23 of table II it can be concluded that

Table IV. Amplitude A in (N) of the vertical load variation per section and relative phase beteen the sections for various wavelength ratios. leading angle 225°, forward speed 0.95m/sec.

w = encounter frequency in radians/sec; = phase angle in radians.

Vertical load per section A cos(wt - ) in N/section

X/L 1.9 1.6 1.4 1.0 0. :0.6 0.4 Section w 3.13 3.42 3.71 4.06 4.5 5.21 6.22 8.03 Nô. A A A A A A A A 12 9.8 0 12.5 0 2Ò.O Ó 35.0 0 57.7 0 80.3 0 62.3 0 26.5 0 11 2:1.7 o.59 25.1 0.67 34.4 0.84 47..1 0.85 53.9 0.88 55.1 0.79 41.4 0.73 25.,9 1.07 10 13 3 0 80 15 2 0 92 21 8 1 16 30 4 1 27 38 8 1 57 42 2 1 83 27 9 1 96 22 4 2 16 9 2 5 2 45 3 14 2 51 5 3 2 48 10 0 2 44 21 1 2 45 86 9 2 56 35 3 2 70 26 3 2 94 8 8.1 3.63 9.0 3.73 11.9 3.86 16.0 3.76 19.4 3.36 36.1 2.96 42.6 3.11 29.3 3.64 7 10 6 3 83 11 2 3 93 15 5 4 09 20 3 4 09 20 3 3 86 31 7 3 26 42 6 3 43 29 9 4 28 6 9.4 3.81 10.4 3.98 14.8 4.21 19.1 4.25 18.5 4.11 26.6 3.48 40.4 3.76 32.3 5.00 5 4.5 3.51 4.9 -3.88 7.7 4.22 10.7 4.28 10.5 4.3Ó 17.1 3.71 30.0 4.23 Z9.8 5.78 4 4.3 1.39 4.8 1 64 4.8 2.12 4.9 2.52 4.2 3.32 10.6 3.96 24.9 5.10 29.2 0.43 3 11.8 1.37 12.5 1.59 i5..3 1.85 17.6 2.05 11.5 2.44 4.9 4.35 30.0 5.96 31.3 1.44 2 14.9 1.45 15.9 1.68 20.2 1.90 24.5 2.07 17.9 2.34 3.4 1,72 25.1 0.43 23.3 2.50 1 3.2 0.23 4.5 0.04 7.7 0.35 11 Ò.50 17.Ó

ó.52

5.7 0.48 22.3 1.25 9.2 3.81

Table V. Amplitude A in (N) of the vertical load variation per section and relative phase between the sections for various wavelength ratios. Heading angle 450, forward speed 0.95 rn/sec.

w = encounter frequency in radians/sec.; = phase ngle in radians.

Vertical load per section: A cos(wt- ) in N/section.

X/L =

1.9 1.6 1.4, 1.2

Lo

0.8 0.6 0.4 Section w = 2.1 2.33 2.4 2..59 2.74 2.94 3.19 3.47 No. A A

A

A A A A c A 12 16.0 0 17.8 0 28.2 Ó 39.9 0 49.6 Ó 63.2 0 57.0 0 16.8 0 11 14.0 0.48 15.0 0.47 21.9 0.42 30.1 b.34 35.7 0.31 43.9 0.12 43.9 6.13 17.6 4.43 10 5.6 1.41 5.7 1.61 6.4 1.81 5.4 1.93 3.4 1.87 5.5 4.30 19.1 4.74 32.0 3.56 9 6.3 2.67 9.1 2.73 15.1 2.90 22.2 3.07 24.4 3.26 35.2 3.36 38.6 3.58 36.3 2.77 8 10.2 3.28 11.7 3.19 19.0 3.15 28.7 3.14 36.4 3.21 50.4 3.13 54.4 3.11 36.3 1.87 7 12.4 3.44 12.7 3.39 19.1 3.30 27.4 3.16 37.5 3.12 50.0 2.93 56.7 2.73 38.1 0.92 6 11.6 3.39 13.4 3.36 19.4 3.32 26.9 3.18 33.5 3.08 41.5 2.75 51.1 2.36 42.2 0.09 5 .7.4 3.68 7.5 3.63 11.2 3.50 13.8 3.29 19.6 2.96 23.7 2.51 36.1 1.89 43.1 5.66 4 3.0 4.76 3.6 5.07 3.7 5.02 4.4 5.11 0.7 0..26 5.9 0.78 20.9 0.88 36.3 4.95 3 8.3 0.07 9.0 6.17 13.4 6.17 17.6 6.06 23.1 6.08 29.3 5.96 33.3 5.87 26.6 3.82 2 14.1 0.22 14.4 0.19 20.7 Ô.11 27.2 6.26 34.2 6.10 40.3 5.86 41.7 5.37 25.6 2.40 1 6.1 0.72 _.6 0.86 8.6 0.56 11.5 0.36 16.1 0.02 19.7 6.02 _{19.6 5.29 14.4} 1.88

- 1:4

range considered and the results can be presented as forces per unit of

wave-height./5/.

For a mOre realistic condition of random waves jE is preferred, before reduc-tion to secreduc-tional girder moments, to present the results in natural coor-dinates, so: that for each natural coordinate the wavelength dependency.can

be illustrated' as shown in F1g. 4 per example.

Table Vio Amplitudé A in (N) of the vertical load variation per

sectioñ and relative phase between the ections for various wavelengh ratios. Heading angle 180e, forward s,peed 1.35

rn/sec.

w = the encounter frequency in radians/sec; = the phase

angle in radians.

b:. Presentation of the results in 'natural coordinates'

According the outline gven in par. 2c the measured load distribution has been reduced to generalized forces belonging to the chosen system of natural

coordinates.

Vertical load per section:

A cos(wt - ) ifl N/section

H AIL = :1.00: 0.55 Section-= 8.00 No. A ct

A

1:2 4:5.9 0 14.2 0 i I 32.5 0.97 19:6 1.29 10 25.8 2. 15 15.8 2.44 9 H. 26.0 2.84 18.8 3.51 8 H 28.0 3.20 2i..2 4.16 7 24.2 3.57 17.1 4.91 -. 6 19.6 3.916 16.5 5;.85 5 13.2 4.4:5 15.9 0.38 4 8.6 5,. 41 13.7 1 .33 3 10.5 0.06 14.3 2.32 2 _H

78

0.70

8.3

3.31 10.8 1. 10 3.7 5.00

Static values

The 'forward-speed-wave' of the model, strongly dependent on the forward

speed /1/ of the model has been decomposed in generalized force distributions. For the two conditions AIL = 1.0 and 0.55 (run number 9 and 10), the results

are shown in table VII.

Table VII. Generalized forces for vertical bending for the

2-, 3- and 4-noded elastic:deflections expressed in Newtons,, forward speed 1.35 rn/sec.

L5

-For the static loading due to the forward-speed-wave only a fractional in-fluence of the incoming waves may be expected.

It can be concluded that the bow and stern wave system of the ship at forward speed generates a significant contribution to the vertical bending of the

hull., strongly dependent on the forward speed of. the model /1/ and more or

less independent of the waves and direction of waves in which the ship is sailing. It can also be concluded that only the 2-noded and 3-noded

deflec-tory modes are strongly effected by this loading and as a consequence the

midship. bending moment and the bend-i-ng-.moment at -1/-4

and--3/4--poi-nts-.of--the----hull. In table VIII the mean value of the generalized forces for vertical bending are given when oblique waves are present.

Table VIII. Mean values of the generalized forces for the vertical

load distribution, decomposed for the 2-, 3- and

4-noded deflections in (N) for wave conditions having

45° and 225° heading and a forward speed of 0.95 rn/sec.

AIL vertical bending 2n 3n

4n.

1.0 +40.5 -42.5 -6.5 0.55 +38.4 -42.1 -3.9 vertical bending 2n 3n 4n 45° 225° +15.7 +18.8 -22.7 -24.2 -0.75 -0.12

.1 25 75L L 0 .251, -so E o'--25 -50 7550 -25 -50 -75 1 50 25 0 -50 -75 75 50 25 o -25 -50 -75 z, o -25 2 4 s B 11 -J

-

¡6

-SLW

\\ }TAYW

I I 2 3 Section - -7

Fig6 Results of tests for oblique waves(225°). Vertical load distribution as a function

of. wavelength X/L. Forward speed O95m/sec. .

Waveheight 0.1 m peak to peak valúe.. Values given for model scale.

I J, 10 11 12 k 1 1.9 16 1.2 to 0.6

17

-Dynamic values

The time dependent part of the load distributions as illustrated in Fig. 6 has been decomposed in generalized forces for the various modal deflections. The resulting generalized forces are again time dependent, and as a conse-quence of the frequency discretisation, harmonically variable with wave en-counter frequency. The amplitudes of the generalized forces for vertical bending are collected in Fig. 7, presented as a function of AIL for the two oblique wave conditions 225° and 450rn It can be coñciuded that apart from the

frequency of encounter the generalized forces for the 1wo wave conditions are of the same order of magnitude, so that geometrical conditions may play a more important role than the angle of heading of the waves.

4. Conclusions and evaluation

The development of fast electronic instrumentation has opened the possibility to design towing tank experiments to measure the global time- and space-dependent load distribution of a ship structute generated by waves. These distributed loadings are the very information for a rational strength, de-flection and vibration analysis of the ship structure

The static loading due to the wave system generated by the forward speed (bow and stern wave) contributes substantially to the 2-noded and 3-noded deflec-tory mode and are of the same order of magnitude as the incoming wave gener-ated time dependent loadings.

This static loading is strongly dependent on the forward speed and loads the girder only in a symmetric way, i.e. only vertical bending is the resült of

this loading, that as far as the accuracy allows to conclude, is less effect-ed by the incoming waves and their directionof heading. (For the) case

hydro-elastic resonance phenomena are not present, it can also be concluded that speed reduction, a measure to be taken by the master under severe conditions

tO lower the ship girder loading,, reduces this static loading substantially,

this apart from the incoming wave load reduction.

The dynamic loading due to the waves, broken dom into generalized forces, shows the well known wave length dependency.

The forward speed dependency for the 2-noded vertical bending load is shown in Fig. 8a where from /1/ three different forward speed values have been ob-tained and compared with the measurements reported in this paper. By

trans-20 . 10 VI 28.- -2-ti FORCE 24 l6 1 . li..

8-t'

_î o t i t i i 0.4 0.6 08 tO 1.2

Wavelength ratio kIL E 28 a. 26 9f 20 16 C . 12 '8 .. 4' i 'o

î

. 50 E 40 30 2.00 '&,.n FORCE 068 0.95 t35

Forward 'speed lm/seci-....

D.

Forward speed sensitivity of the ?-noded -generalized force for vertical (tending, due

to waves. 1.9 i. -i t i 0.4 06 0.9 1.0

Ii

1.6 1.6 1.9 Wavelength -ratip k/L 24 9f 20 12 'b 6 04 06 08 1.0 1.2 1.4 1.6 1.9

Wavelength- ratio k/I.

a -a Waoehe.ght p_p v5cm

u Wavetteight p-p ioroa} head waves v 45 3-n FOREt

Waeeheighf p-p' Scm i

Wavetteight p,p.n 10cm-JHead' waves oc22S1

Fig.7 Amplitudes of generalized, forces for the ' H

vertical bending due to waves with heading 225° and 45°

O' Interpolated' value -20- ,"

t, -

-30Z '

el

-Fig8'B- Sensitivity-for the wave heading angle óf the 2-noded generalized (croe fo, vertical bending, due lo wanes.

Fig 8 ' Two noded generatized force for vertical wave - bending

1

1) i Wane heading 180v O OLFT-lavk X NStIB'- tank 30- 20-io o -io-'

,_

/

\

'

Forward speed Q95m/sec.

. X (15MB-tank

O from Fig.'8A 360

'

i

/

Wave tieacting-.

19

-ferred to Fig. 8b to illustrate the effect of heading angle of the waves on

the 2-noded generalized force for vertical bending.

It can be concluded that a strong heading sensitivity exists, important for 2-dimensional wave spectra in which the ship may sail.

It may also be concluded that for the girder loading, apart from the frequency df encounter, the wave geometry, i.e. the wavelength relative to the ship-length is more relevant than the heading angle (225° or

450)

When

hydroelas-tic resonance phenomena are of importance also the encounter frequency needs

to be considered.

Finally it must be stated that the breakdown of the spatial coordinates in natural coordinates opens the possibility to analyze the ship girder loading in more detail, that insight in the dynamic behaviour is deepened and that the way is paved for a spectrum analysis in the linear range of

waveheight-to-load transformation.

In this respect the discretisation of the wave loading to a pure sine wave is not necessaryany longer and a more realistic description of the record-ings by means of a narrow band random signal analysis is preferred.

Acknowledgement

The Board of Deans of the Delft University of Technology is acknowledged for the recognition of this research and their supporting advice for the

neces-sary funds to carry out the experiments, at the NSMB. Also the kind

coopera-tion of staff and technicians of the SaiepingLaboratory of the NSMB needs to be mentioned. Finally the intensive cooperation of mr. J.F. de Waal, mr. W.B. Tinbergen, mr. H. Boersma, mr. J.H.M. van der Leeden, mr. C. de Krey and mrs. I.Y. Bolle, all being collaborators of the Ship Structures Laboratory of the Department of Shipbuilding and Shipping of the Delft University of Tech-nology, for the manufacture of the model, the information reduction of the measurements, the lay-out and typing work is gratefully acknowledged.

List of symbols

A = amplitude

Ici

= mechanical damping matrix

20

-D = draft of ship or model

d = elastic deflection {F} = force vector

h = waveheight (amplitude)

L ship length between PP

IMI = mechanical mass matrix

1Ml = hydrodynamic mass coefficient matrix

= length unit, (meter) n = rigid body displacement n = abbreviation for node

N = force unit (Newton)

q = distributed loading (N/ni)

I Si = mechanical stiffness matrix

ISI

hydrodynamic stiffness coefficient matrix

s time unit (seconds)

x = coordinate along, the ships axis

A = wavelength

generalized force

subscrípts:

n refers to rigid body motion

= refers. to elastïc body deflection.

List óf references

/ I / Wereldsma, R. and G. Moeyes:

'Wave and structural load experiments for elastic hips'.

11th Symposium on Naval Hydrodynamics,London, April 1976.

/2/ Húrty, W.C. and M.F.. Rubinstein:

'Dynamics of structures'. Prentice Hail, 1964.

/3/ Wereldsma, R:

'Normal mode approach for ship strength experiments, a proposal'.

Proceedings. of the symposium 'The Dynamics of Marine Vehicles and Structures in Waves', London, April 1974.

/4/ Bishop, R.E.D. and W.G. Price:

'Hydroelas!ticity of ships'

ç

21

-/5/ ereldsma, R.:

'Towing tank experiments on ship girder loadings in oblique waves,

a modal presentation'.

Report No. 239 Ship Structures Laboratory,, Delft University of

Technology, March 1981.

Author' s affiliation

The author is professor in Naval Architecture at the Department of