Hull vibrations third-generation containership

MONOGRAPH PUBLISHED BY THE NETHERLANDS MARITIME INSTITUTE

Hull vibrations

third-generation

con

táinershi

S. Hylarides

M14

April 1977

2 0 MEl 1980

_{Lab. y. Scheepsbouwkunck}

ARCH LEF

Technische Hógescj

-Hull vibrations

third-generatión

con tainershi

Calculations compared with measúrements

CONTENTS

page

Summary 3

i

Introduction . 3

2 Particulars of ship and measurements 3

3 Calculations 4 3.1 Modelization 4 3.2 Stiffness matrix 4 3.3 Mass matrix 4 3.4 Damping matrix. 6 3.5 Excitation system 7 4 Results 8

4.1 Presentation of the results 8

4.2 Discussion of the results 8

5 Conclusions . 13

References 13

HULL VIBRATIONS THIRD-GENERATION CONTAINERSHIP

CALCULATIONS COM PARED WITH MEAS UREM ENTS by

DR. IR. S. HYLARIDES

Netherlands Ship Model Basin, Wageningen

Summary

In 1971/72, the propeller-generated vibrations on board a third-generation containership were calculated, using the finite element technique. No damping was accounted for in the calculations, and, therefore, a rough estimate of its effect on these results was made. The hull vibrations were measured on trials and a comparison with the calculations showed a satisfying correlation of thevibration

level predicted.

In order to study further the application of damping in hull vibration analyses, the calculations of forced response were repeated, with damping now being included.

In general, the results of the repeat calculations showed less agreement with the full-scale measurements than those of the original calculations On the whole the resulting vibration level was too low Comparison with other ships for which the same calculation technique was applied with more success showed that the rate of condensation of the finite element model was probably the cause Further investigation will be called for to check this supposition.

I Introduction

En an investigation programme into forced hull re-sponse calculations,, sponsored by the Netherlands Maritime Institute, a 10,000-ton cargo-liner [1] and

a 228,000-ton VLCC [2] were studied. In order to

broaden the experience and knowledge in this matter,

it was decidéd to also include in this series an analysis

of the forced hull response of a third-generation

con-tainership.

A complete hull girder vibration analysis of such a ship had been performed in 1971/72 and the stiffness

matrix was still available, whereas the remaining

com-puter input was partly present or could be easily

determined. Contrary to the first two ships, which were

excited by means of an out-of-balance rotary exciter,

the containership vibrations were generated by the

propellers. The magnitude of the propeller excitations was derived from model experiments. The undamped

level of the vibration response to these excitations was calculated. The effect of damping on these results was

estimated, which led to a satisfactory agreement with

the full-scale measurements [3].

Therefore, to study further the application of dam-ping in hull vibration analysis, the calculation of the

Fig. 1. Profile of the third-generation containership.

forced response was repeated with damping now being included.

2 Particulars of ship and measUrements

The ship investigated was a twin-screw turbine-driven containership, the overall dimensions of which are

given in Table I and Fig. I.

The propellers were 5-bladed, each absorbing

60,000 SHP at 135 RPM and a speed of around 33

knots. Their overall dimensions are also shown in Table I.

Table I. Particulars of ship and propellers.

Ship

length between perpendiculars

breadth moulded draft moùlded on F.P.

draft mouldedon AP.

displacement volume

Propellers

twin screw, outward turning diâmeter

number of blades pitch ratio P O.7/D expanded blade area ratio

274.32 m 32.156m 9.754m 32' 9.754m 42757 m3 7 rn 5 1.154 0.873 3

On trials, the ship operated at 9.144 m = 30' draft,

for which condition the calculations were performed. During these trials, the hull vibration measurements were performed by the Germanischer Lloyd. A

num-ber of the results could be used for correlation purposes

(vide Figs. 10-23). The vibrations were measured and

registrated, by means of inductive displacement trans-ducer, on a 14-channel graphical recorder. Fig. 2 gives an example of such a recording.

In the Skagerrak, the measurements were performed

in the range from 65 up to 132 RPM (= 5.4 up to 11.0

Hz, which covered the blade frequency range). Weather conditions were:

swel no ne

sea glassy-rippled wind force l-2 Beaufort

3 Calculations 3.1 Modelization

In order to represent the complex and spatial charac-teristics of the hull mathematically, use was made of

the finite element technique.

First, there was the problem of choosing a restricted number of nodal points, in order to keep computer

time down, but without essential loss of the main hull dynamics. A distribution of nodal points as indicated in Fig. 3 was thought to meet this requirement. 3.2 Stjffness matrix

In the determination of the stiffness matrix of this

finite element model, a much more detailed model of

the structure was used, in order to achieve an adequate

representation of the specific construction. By means of condensation, the number of nodal points was

re-duced to those of the final model. In this way the characteristics of the eliminated nodal points were implicitly maintained. Fig. 4 gives an example of such

a basic finite element breakdown. In comparing the

densities of nodal points in Fig. 3 and 4, it follows that

the condensation technique was applied rather rigor-ously.

Special attention was paid to the representation of the stiffness of important local structures, such as the foundation of the main and intermediate strut, for a

correct introduction of the propeller shaft bearing forces into the hull. For the axial shaft vibrations, the thrustblock support is decisive, so that a very detailed

breakdown of the engine room double bottom was

made. Similar remarks h6ld for the boiler support.

Both shaftings with propellers were modelled in

detail in the finite element model, so that the hydro-dynamic propeller shaft forces were correctly trans-mitted to the hull structure via the bearings.

4

3.3 Mass matrix

The masses of the various parts of the ship were con-centrated in the final nodal points shown in Fig. 3. In

this respect, it must be noted that, due to the open hull

construction and the vertical cargo distribution, the

torsional hull vibrations were thought important. Therefore, an accurate representation of the torsional

moments of inertia over the various cross-sections was aimed at.

From Fig. 3, it follows that, per bulkhead, 5 nodal

points remained in the final model. The masses of

various parts of hull and cargo were shifted to these bulkheads, care being taken to ensure that their longi-tudinal centres of gravity did not change. Per

bulk-head, the mass was distributed over the 5 nodal points

in such a way that the following values are correct: - the centre of gravity, in height aswell as in breadth,

- the linear and torsional moments of inertia,

- the centrifugal moments of inertia.

Similar considerations hold for the superstructure. Constructional parts of large weight (e.g., rudder, shafting, propulsion plant) have been maintained in the model (vide Fig. 3).

This mass distribution led to a diagonal mass ma-trix.

SHAFT RPM PORT 1328 RPM SHAFT RPM STAD 1324 RPM

* PHASE REVERSAL DUE TO REVERSE POLARITY

-I

- ---

I I I

_.-A_

₌

Fig. 3. Modelization of hull structure and shafting and reduction to the nodal points indicated.

The added mass of water is considered by adding

the relevant values to the masses in the bottom nodal points, accounting for the direction. No values for the

added masses for torsional or longitudinal vibrations

were provided. The added masses depend on the num-ber of nodes in the overall vibration pattern. As shown

by Fig. 5, this dependency becomes smaller for the higher noded modes. In the calculation of the added

masses for the vertical vibration, a 10-noded mode was

assumed and for the horizontal vibration an 8-rioded mode, because in the frequency range around 11 Hz (blade frequency at service speed) the overall hull vi-bration pattern was thought to show about 10 and 8

nodes respectively.

Fig. 6 shows the mass distributions over the length

of the ship.

3.4 Damping matrix

In the frequency range around service RPM of the

ship, the damping is thought to be mainly caused by the complex ship deformation patterns itself [4, 5, 6]. The damping mechanism is still unknown and, there-fore, it is assumed to be proportional to the velocity

and to have a distribution similar as the stiffness

0.2 O., 6 £ CON 2Tt L CYLINDER FLAY STRIP AS V MP TOTICAL BEHAVIOUR as 'O tb X NUMBER OF NODES X IO 10 20

Fig. 5. Effect of vibration pattern on added mass for vertical

vibration.

matrix. In matrix equation the equations of motions

then become:

M+KK+K =f

in which

M is the mass matrix, K isthe stiffness matrix,

Ô isthe displacement vector, and

f

isthe excitation vector.

The proportionality factor K has been investigated be-fore [1, 2], showing to be about 0.001.

Another way to present damping is by introducing per modal response a dashpot-like damper (compa-rable with single mass-spring-systems provided by a dashpot damper), the value of which is a part of the

critical damping. Critical damping is that magnitude of damping for which no magnification due to dynamical effects occurs. This approach requires the normal mode analysis.

lt has been shown [2] that this type of damping

and the

"stiffness damping" described above are equivalent in the normal mode analysis. The "stiffness

damping", however, can also be applied in the direct

E E C O O C E O 1.0 0.5 C O

MASS DISTRIBUTION 0E SHIP AND CARGO

/

-e-NOOE

2.NODE

3. NODE A. N ODE

10-NODE

ADDED MASS FOR VERTICAL VIBRATION 2. 3 AND 4.NODE ADDED MASS FOR ATUWARTSHIP VIBRATION

Fig. 7. Coarse finite element model of a cargo vessel [7].

solution of the set of equations, so that the calculation of a large number of eigenvalues and corresponding modes can be omitted. Therefore, the "stiffness dam-ping" was used in this investigation.

A damping proportional to the mass matrix could,

in principle, have been used too [5]. The results of this approach are shown to be less satisfactory in the higher

frequency range than the approximation by means of

the stiffness matrix [4, 6].

At the time of the original calculations (1971) of the propeller-generated vibrations ofthe vessel investigated,

the information of the damping referred to above was not available, so that an estimate of the effect of dam-ping was made, based on the results of the undamped system. This estimate was based on a result of a very first attempt to calculate the hull vibrations by means

of a three-dimensional, finite élement model [7].

In this first attempt (1969), a very rough finite ele-ment model of a cargo vessel was made tó investigate the applicability of the finite element technique. The breakdown is shown in Fig. 7. In these calculations,

no use of condensation was made, so that rather rough

elements resUlted, representing very broadly the stiff

ness aspects of a complete deck or side wall panel.

With this finite element model, it was possible to calculate accurately the lowest naturaJ frequencies of the vertical hull girder vibrations [7].

However, with this finite element model, the forced

response of the exciter foundation was also calculated around blade frequency at service RPM. Et followed

(Fig. 8) that the full-scale measured response was situated at the mean level of the calculated, undamped

response, using a logarithmic presentation of the re-sponse. From this result it was decided to estimate the effect of damping by taking the mean level of the un-damped response and by situating around this lével a certain band to account for the variations met in the

full-scale results.

3.5 Excitation system

In this investigatión, concerning a turbine-driven ship, the main excitation consists of the propeller-generated

hydrodynamic forces and moments. The amplitudes

and phases of the various components of this excitation

system were determined by means of model tests. The

results

for the starboard propeller are shown in

Table IL

Table H. Propeller-generated hydrodynamic excitations.

o is the angle of shaft rotation, being zero for one blade in top position.

7 hull pressure-forces

longitudinal F = 1.0 sin (50-263°) tonf.

transverse F = 2.8 sin (50-263°) tonf. vertical F, = 3.2 sin (50_2600) tonf.

shaft forces and moments

longitudinal F = 5.0 sin (50 270) tonf. M5 = 6.0 sin (50 340)_tonfrn.

transverse F, = 5.0 sin (50 6°) tonf. M5 = 12.5sin (50 310) tonfm.

vertical F. 2.6 sin (50+169°) tonf.

The model tests for the hull pressure fluctuations were carried out in an atmospheric towing tank. At the time of these tests, the dominating effect that cavitation

can have on the pressure fluctuations was not known. However, from Fig. 8 it follows that cavitation only occurs on the propeller blades when these are in out-ward position far from the hull, so that the effect of cavitation may be assumed to be small and the results

of the model tests can be considered rather

representa-tive. This is confirmed by the overall agreement be-tween the results of the first calculations and the

full-scale results [3].

A further complication was that the ship is propelled by 2 screws, which can operate in or out of phase. This

was studied by considered various phase differences

viz.: 00, 900, 1800 and 270°, in which 00 refers to the

case that both proppellers have one blade in top, 90° when the starboard propeller has one blade in top and the port propeller has a blade at (90/360) x 72° (both propellers are 5-bladed) before the top position, etc. From this, in general, 4 response curves result, indi-cating the beat phenomena.

8 Li

z2

102 8 6 4 2 4 Results

4.1 Presentation of the results

In Figs. 10-23, the calculated and measured responses

of several items of the ship structure are shown. Per

response are shown:

- the estimated effect of damping as a band around the

mean response of the undamped system, indicated

by the shaded region;

- the calculated response of the damped system, in

which the damping matrix is assumed to be propor-tional to the velocity, being distributed, similarly to

the stiffness matrix with proportionality factor

0.001;

- the measured full-scale response.

4.2 Discussion of tue results

In the calculated results, the effect of phase difference between the propellers is indicated. This effect,

how-ever, does not show up in the full-scale measurements.

Since this was not the aim of the full-scale

measure-VIBRATION CARGO VESSEL x LEVEL OF x CALCULATED. UNDAMPED o MEASURED

/

_o A

I

I

BANDWDTH DAMPED VIBRATIONOF

/

CALCULATED, DAMPED /1/ 65 70 75 80 85 FREQUENCY Hz

Fig. 8. Full-scale hull response compared with undamped, calculated response to indicate the effect of damping.

101 8

6

Fig. 9. Cavitaton pattern starboard propeller [31.

iü----t'----

MEASURED QL.

---

----

---..i...

10.2 10.4 10.6 10.8 FREQUENCY Hz

Fig. 11. Athwartship response of

rudder skeg. (I) z O o-V) w 104 106 108 110 FREQUENCY Hz io 10-lO EASURED

----I'll"

IUI!!IÌ

EXPECTED VIBRATION LEVEL

UNDAMPED RESPONSE O°PHASE 0 900 DIFFEREN + 180°BETWEEN X --- 270°) PROPELLERS 10.2 10.4 10.6 10.8 110 FREQUENCY Hz

Fig. 10. Athwartship response of top

of rudder stock.

10.2 10.4 10.6 10.8

FREQUENCY Hz

11.0

Fig. 12. Vertical response of top of Fig. 13. Longitudinal response of top

thrustblock foundation. of thrustblock foundation.

9 O X EXPECTED UNDAMPED VIBRATION RESPONSE -.-.-.- 90°(DIFFERENCE LEVEL 0°\PHASE PROPELLERS +_______..l8O0(BETWEEN

---- 270°)

0°PHASE O°» PHASE 0 -'--- 9O°DIFFERENCE 90°(DIFFERENCE + 1800(BETWEEN + 180°(BETWEEN X ---- 270°/PROPELLERS X ----S- 2700f PROPELLERS l0

!ARi

Gt

"IP'

EXPECTED VIBRATION LEVEL EXPECTED VIBRATION LEVEL UNDAMPED RESPONSE UNDAMPED RESPONSE

w V) z O Q-V) w ios 110 10.2

w I,, z o a-w io-5 lo 10.2 10.4 10.6 10.8 FREQUENCY Hz

Fig. 17. Vertical response of main boiler foundation.

106

110 10.2 10.4 10.6 10.8

FREQUENCY Hz

Fig. 18. Athwartship response of aft

end of deck 5 in aft deckhouse,

starboard side. io-5 W u, z O 106

EXPECTED VIBRATION LEVEL UNDAMPED RESPONSE O° PHASE 1 - 90°(DIFFERENCE + 180°(BETWEEN X 270°)PROPELLERS 10.2 10.4 106 10.8 110 FREQUENCY Hz

Fig. 16. Longitudinal response of

main boiler foundation.

---MEASURED G.L

---...

-- ,

,-!!!1UI

EXPECTED VIBRATION LEVEL UNDAMPED RESPONSE O° PHASE

Q ---

90°(DIFFERENCE + 180°('BETWEEN X 270°) PROPELLERS 110 10.2 10.4 10.6 10.8 FREQUENCY Hz

Fig. 19. Athwartship response of fore

end of deck 5 in aft deckhouse, starboard side. 110

ii'.

-u-,

...

-0 + X EXPECTED UNDAMPED VIBRATION RESPONSE O°-270°) 90° (DIFFERENCE PHASE 180°(BETWEEN LEVEL PROPELLERS VJW4WJJW4

IIIIHII

_"'lin

+ X EXPECTED UNDAMPED VIBRATION RESPONSE 0°PHASE 90°(DIFFERENCE --- 180°('BETWEEN LEVEL PROPELLERS

---

27O° MEASURED QL.

II

AJ2rWÌZ#JJ

IÀ6

X EXPECTED UNDAMPED VIBRATION RESPONSE 270°) O°PHASE 90°(DIFFERENCE 180°(BETWEEN LEVEL PROPELLERS +

-MEASURED .L.

---

---O X EXPECTED UNDAMPED VIBRATION RESPONSE 270° O°PHASE 90°(DIFFERENCE 180°(BETWEEN LEVEL PROPELLERS

+---

----10.2 10.4 10.6 10.8 110 FREQUENCY Hz

Fig. 14. Longitudinal response of

afterside of centre of turbine

group.

10.2 10.4 10.6 10.8 11.0

FREQUENCY Hz

Fig. 1 5. Vertical response of afterside of centre turbine group.

_____

-MEASURED QL.

illílíl

d#Jdddd

w U, z o û-10 10 106 z 2 u, Ui io-?

10-LU 'n z O, Q-'n LU 10' 10' 10.2 10.4 10.6 10.8 FREQUENCY Hz

.. u...

PA

w

EASURDGL.,d

Ä A

I'll'

liP!!!!

EXPECTED VIBRATION LEVEL

UNDAMPED RESPONSE

0°\PHASE 90°(DIFFERENCE

+--- 180°(BETWEEN X ---- 270°) PROPELLERS

Fig. 23. Athwartship response of fore

end of deck 3 in fore

deck-house, starboard side.

10-e 11.0 10.2 10.4 10.6 10.8 FREQUENCY Hz

Ïi

__

ASURED QL.

EXPECTED VIBRATION LEVEL

UNDAMPED RESPONSE - . 0°PHASE e --.-- o° (DIFFEREN + 180°(BETWEEN X --- 270°' POPELLS

A#AVMAYA

r r vr

---

M AS RED GL

UI".'

-!!Uuuuiî

EXPECTED VIBRATION LEVEL UNDAMPED RESPONSE e - 0°PHASE G) Y. 9O°DIFFERENCE + 1800(BETWEEN X --... 270°) PROPELLERS 110 10.2 10.4 10.6 10.8 110 FREQUENCY Hz

ments, attention was probably not paid to this effect, so that no conclusioñs can be made in this respect.

What is more essential, however, is-the fact that the full-scale results agree satisfactorily with the calculated

results with estimated effect of damping (shaded

re-gion), whereas generally speaking the results with the

calculated damping are considerably lö This difference between the calculated, damped response

and the measured full-scale response is generally larger

than those found for the cargo vessel [I] and VLCC

[2], suggesting a relation with the finite element model.

Therefore, the distribution of the nodal points over

the three ships is given in Fig. 24, indicating in some way the density of this distribution. Whereas thecargo vessel in transverse directidn generally has more nodal points over a smaller area, the density of nodal points for this ship is greater than that for the containership.

Furthermore, the density of the nodal points of the

VLCC is greater than for the container vessel.

The effect of condensation is that the coefficients of the stiffness matrix become smaller, whereas the terms in the mass matrix, which is diagonal, become larger.

The latter is self evident, the former is explained as

follows.

The base oit he terms of the stiffness matrix is the

system of forces which have to be applied at the

struc-1.1

â4d11ii

- --D G.L. EASU

.. u...

=

1!!UIÌi

8 EXPECTED UNDAMPED VIBRATION RESPONSE 0°PHASE 90°IDIFFERENCE LEVEL. PROPELLERS

-.---+ 180°(BETWEEN X --- 270°f

Fig. 20. Longitudinal response of aft Fig. 21. Athwartship response of aft Fig. 22. Longitudinal response of fore

end of deck 3 in fore deck- side deck 3 in fore deckhouse, _{end of deck 3 in fore} deck-house, starboard side. starboard side. house, starboard side.

10.2 10.4 10.6 10.8 1.10 FREQUENCY Hz 10 z O Q. 'n 1°_G

I

'n z

= = = = =

I = = =

= =

=I - r

.. e

s Ò S f0 s s S O S 5 O2 MODAL POINTS 162 NOOAL POVNTS L.: 288m TRANSVERSE SECTION

ture, in order to keep each nodal point in its place,

wheñ one point is moved one unit of length in one of the coordinaté directions. The force needed to móve

this point gives the diagonal term of the stiffness matrix. Hence, each point is shifted in each ol the coordinate directions, thus leading to as many systems

of forces as the number of degrees of freedom. These systems of foràes fOrm the columns of the stiffness matrix. Due to Maxwell's relatiOn a- syìîunetric

ma-trix results.

Condensation is given by selecting those points at

which no -external forces or inertia forces apply. Allow the displacements of these nod4l points to be collected

in the displacement vector the remaining in

Partitión .the force -vectorf añd stiffness m4trk K accordingly, so that we have:

12

TRAMSVERSE SECTOW

170 NODAL. POINTS

314 n,

Fig. 24. -DistributiOn of nodal points in final model of the-ship

s- -s

e s s s

._

.

.

.

.

.

.

[K11 _{K121 r:'} LK21

K22] L2

-then

= K22'K2

so that [K1 1-K12K22

K11 =11

So the ternis of this condensed .stiffiess matrix are the

forces to move one nodal point one unit of length and

keeping the others in their places. Since less points are

now kept in their place, the force to move a point oJe unit of length is certainly smaller than originally. But

the forces to prevent the other points from moving will generally become smaller too.

s s e

-]

Hence, the stiffness terms become smaller due to condensation and the mass terms larger, which effect is uñknown-, but, considering the three ships

investi-gated, it may result in lower response levels. A partic-ular effect is that the masses in the various nodal

points start to begin an own life, independent of the

original structure.

Still, the question is still open as to why the- un-damped system, in which a rough estimate of the damped response was made, has led to very satis-faetory results.

Whilst ,=0.00i, the equivalent value of the rate of critical damping around 10.5 Hzß = = 3.4%[2];

hence, it can be concludèd that a rather low value of damping has been used, so that this is not the reason for a too low response.

in general it can be stated that.the condensation has

to be done in such a rate that the expected deformation

pattern will be approximated in a representative way.

In the determinatiön of theadded mass, it was assumed

-that the expected vertical hull girder vibration mode

would have about IO nodes. For the chosen final nodal poiht distribution (Fig. 3), such a vibration pattern

would lead to about two transverse frames with nodal points between each pair of successive nodes. In the

first instance, such a distribution cannot be considered as being too coarse.

Therefòre, the first explanation seems to be the most

likely one: the condensation has been continued too far, so that too weak terms in the stiffness matrix re-sulted. In fact, the breakdown of the structure used in order to derive the stiffness matrix was done in such greater detail than the breakdown used for the

deri-vation of the mass matrix that a certain incOmpatibility

becomes apparent. Implicitly the stiffness matrix

re-presents the hull to a müch greater degree than the diagonal mass matrix. -It is possible that a mass distri-bution, condensed in a similar way to the stiffness matrix [8] (so that a full mass matrix results, the terms

of which are smaller than those of the diagonal nass matrix as was used) could lead to a better result.

5 Conclusions

From the original (1971) calculation of the forced hull response, an estimate was made of the effect of damping

on the calculated ündamped response. Measurements

on the ship showed satisfactory agreement.

The response obtained from calculatións in which

damping was directly accounted for, however, showed less agreement.

Comparing these latter results with those obtained

from similar investigations on a cargo ship-and a large

oil tanker (VLCC). indicates that a probable cause for

an increasing deviation between calculations and

measurements- may be sought in the rate of

conden-sation applied in the successive analyses.

Whereas the stiffness matrices are condensed to the final system in a mathematical way and the mass ma-trices -are obtained- by lumping the mass distribution directly in the final nodal points, it -may further be

expected too that -a more consistent mass condensation coùld lead to higher accuracies. -

--

-These two possible reasOns, however, require further investigation. - - -

-References

HYLARIDES, S.: Damped hull vibrations of a cargO vessel,

cal-culations and measurements. Netherlands Maritime Institùte, Monograph no. M 5, May 1976.

HYLARIDES, S. and R. VAN DE GRAAF: VLCC-deckhouse

vi-bration. Calculations compared with measurements. Nether-lands Maritime Institute, Monograph no. M 6, July 1976. B0YLST0N, J. W., D. J. DE KOFF and J. J. MUNTJEWERF: SL7 Containerships.. Design, Constructions and Operational

Experience. SNAME Transactions, Volume 82, 1974. HYLARIDES, S.: Damping in propeller-generated sliip vibra, tions. NSMB publication no. 468, 1974.

MCGOLDRICK, R. T.: - Comparison between theoretically and

experimentally determined natural frequencies and modes of vibratioñ of ships. DTMB Report no. 906, 1954.

-ROBINSON, D. C.: Damping characteristics of ships in vertical

flexure and considerations in hull damping investigations

DTMB Report no. 1876, 1964.

-7-. HYLARIDES, S.: Ship vibration analysis by finite elemelit-

tech-nique.. Part II: Vibration analysis. Netherlands-Ship ReseaÑh Centre TNQ. Report- no. 153 S, May 1971. - -8. MEYERS, P., W. TEN-CATE, L. J. WEVERS and J. H. VINK: Nu

merical- arid experimental vibratiOn analysis of a deckhouse. Netherlands Ship Reseárch Centre TNO., Report no. 184 S,

December 1973. -

-j-PUBLICATIONS OF THE NETHERLANDS MARITIME INSTITUTE

Monographs

M 1 Fleetsimulation with conventional ships and seagoing tug! barge combinations, Robert W. Bos, 1976.

M 2 Ship vibration analysis by fiiite element technique. Part

III: Damping in ship hull vibratiOns, S. Hylarides, 1976.

M 3 The impact of Comecon maritime policy on western

shipping, Jac. de Jong, 1976.

M 4 Influeñce of hüll inclination and hull-duct clearance on

performance, cavitation and hull excitation of a ducted propeller, Part I, W. van Gent and .7. van der Kooij, 1976. M 5 Damped hull vibrations of a cargo vessel, calculations and

measurements, S. Hylarides, 1976.

M 6 .VLCC deckhouse vibratiOn, Calculations compared with measurements, S. Hylarides and R. van de Graaf, 1976.

M 7 Fiñite element ship hull vibration analysis compared

with full scale measurements, T. H. Oei, 1976.

M 8 Investigations about noise abatement measures in way of ship's accommodation by means-of twO laboratory facili-ties, J. Bui ten and H. Aartsen, 1976.

M 9 The Rhine-Main-Danube conñection and its economical

implications for Europe, Jac. de Jong, 1976.

M 10 The optimum routeing of pipes in a ship's engine room, C. van der Tak and J. J. G. Koopmans, 1977.

M 11 Full-scale hull pressure measurements on thê afterbody

of the third-generation containership s.s. "Nedlloyd Delft",R. A. P. J. Schulze, 1977.

M 12 CavitatiOn phenomena and propeller-induced hull pressure fluctuations of a third-generation containership, A. Jönk and J. van der Kooij, 1977.

M 13 Hull vibratiOn measurements carried out on board the

third-generation contáinership s.s. "Nedlloyd Delft",

R. A. P. J. Schulze, 1977.