NEDERLANDS SCHEEPSSTUDIECENTRUM TNO
NETHERLANDS SHIP RESEARCH CENTRE TNO
SHIPBUILDING DEPARTMENT LEEGHWATERSTRAAT 5, DELFT
*
SOME PROBLEMS RELATED TO THE USE OF
SCALE MODELS IN EXPERIMENTS ON SHIP ACOUSTICS
by
IR. J. W. VERHEIJ
Voor nieuw te bouwen schepen wordt steeds vaker een rede!ijke mate van geluid- en trillingcomfort vereist. 0m deze te kunnen bereiken moet veelal in het ontwerpstadium worden aangegeven welke lawaaihestrijdingsmaatregelen genomen dienen te worden. Deze maatregelen heïnvloeden n!. doorgaans het ontwerp.
Bij het afwegen van het relatieve belang van de verschillende geluidpaden en het effect van isolatiemaatregelen in deze paden, wordt met vrucht gebruik gemaakt van Iaboratoriumonderzoek op modelschaal. Een belangrijk voordeel ten opzichte van me-tingen aan boord van schepen is, dat de experimenten plaats vinden onder goed onder controle te houden omstandigheden. Verder zijn de kosten van het schaalmodel zelf en het experiment ermee. zeer laag in verhouding tot die welke gemaakt worden wanneer een schip voor metingen uit dienst genomen moet worden.
Bu het vervaardigen van schaalmodellen dienen alle lineaire
afmetingen met de schaalfactor verkleind te worden, dits ook die van de lasverbindingen. Lasverbindingen op schaal naboot-sen zou de modt.11en echter aanmerke!ijk duurder maken dan wanneergebruik zou mogen worden gemaakt van een eenvoudige druppel-lastechniek.
Daarom is nagegaan of afwi.ikingen van de gelijkvormigheid van de lasverbindingen, de schaalmodellen in akoestisch opzicht minder betrouwbaar maken. In de onderzochte modelconstructies bleken de geluidoverdracht-eigenschappen weinig afhankelijk te zijn van de aard van de verbindingen die werden toegepast.
Het akoestisch gedrag van de modellen was ook redelijk goed gelijkend op dat van overeenkomstig gebouwde prototypen.
RET NEDERLANDS SC}{EEPSSTUDIECENTRUM TNO
Rather high standards of comfort with regard to noise and vibra-tion are more and more required aboard new built ships. To meet these requirements, noise reduction measures must he taken at an early stage, because these measures normally influence the design.
For a quantitative estimate of the relative importance of dif-ferent sound paths and of the effect of isolation measures, lab-oratory experiments are performed with success on model scale. Important advantages of these laboratory experiments are the well controlled experimental conditions and the relative low costs in comparison with experiments aboard a ship, which has to be taken out of service for this purpose.
When constructing scale models, all linear dimensions must be reduced by the scale factor, thus also the welded joints. How-ever, modelling welded joints accurately would increase the costs of the models considerably in comparison with the application of a simple stack welding technique.
Therefore it has been investigated whether deviation from the similarity of welded joints results in a decrease of the reliability with respect to the acoustical properties of the models.
For the model structures which have been investigated, the sound transmission properties did not appear to be very depen-dent on the type of the applied joints.
The acoustical properties of these models were also reasonable similar to those of similar built prototypes.
CONTENTS
page
Summary 5
I Introduction 5
2 Scale models of mechano-acoustical systems 6
3 Investigations on model joints 6
4 Sound transmission in nominal identical structures 12
5 The use of an imperfect scale model 1 3
6 Conclusions and evaluation 15
References 16
I
IntroductionIn various branches of engineering physical scale
models are a well known means for solving practical
problems [1. 2]. Also in acoustics the usefuilness of
scale models which are dynamically similar to full scale structures (prototypes) has been recognized [3, 4]. A
number of applications have been published in literature.
Scale models for ship acoustic investigations are especially promising. In many types of ship, sources
of intense noise are often located near living quarters intended for long stay. This problem together with the
good transfer path for structureborne sound in the
steel structure of the hull, presents a challenge to the acoustician, always bearing in mind the necessity for structural strength, seaworthyness, economy and effective isolation. Moreover it is costly to retain a
ship for acoustical laboratory type investigations away from normal operational trade.
Because of the complexity of the sound transmission
paths only a minor group of problems can be treated
by the aid of mathematical or of electrical analogons. Physical scale model experiments are therefore indis-pensable. They offer three major advantages:
no interference with ship or yards operations - clean experimental conditions (no interfering sound
sources as on board)
- low costs of step by step modifications in the steel
model.
Usually a relatively small section of a ship will suffice
for a meaningful experiment [5, 6, 7]. For ship
acoustics, scale model experiments are useful
I. in research
- to find major trends with respect to the trans-mission of sound via different paths, a.o. for
setting up mathematical models
- to select the most promising full scale experiments
SOME PROBLEMS RELATED TO THE USE OF
SCALE MODELS IN EXPERIMENTS ON SHIP ACOUSTICS
by
Ir. J. W. VERHEIJ
Suinnìari
Scale models are often an useful tool in the research on noise reduction measures on board ships. There are, however, difficult practical problems in correctly scaling welded joints between plates and beams of the structures. Investigations have been performed in the influence of different jointing methods on the sound transmission properties of a series of model structures. Further a com-parison has been made between the sound transmission properties of these models and those of two similar full scale structures.
2. in consulting work
- to compare alternative arrangements or struc-t u res.
This report gives the results of some investigations into
the practice of scale modelling, especially into the
physical accuracy required of such models for
applica-tion in ship acoustics. lt concerns the unavoidable deviations from the model rules with respect to the
welded joints.
In chapter 2 a sufficient set of rules for making
proper scale models are mentioned and some related practical difficulties are discussed.
In chapter 3 investigations are reported on the trans-mission of structureborne sound and the sound radia-tion of steel scale models of a deck. These models have
been constructed using different methods of jointing
the deck plate and the stiffeners. Furthermore a com-parison is made between the sound transmission
prop-erties of the models and those of similar full scale
structures.
In chapter 4 special attention is given to the dissimi-larity of structures which has been made with normal accuracy from the same drawing (nominally identical structures).
In course of the experiments described in chapter 3, it appeared that the sound transmission properties of structures which had been made from the same draw-ing gave greater differences acoustically than could be explained by measuring inaccuracy. Therefore investi-gations on some potential origins of these differences
have been performed.
Finally, in chapter 5 a full scale and a model experi-ment on the sound transmission via rubber mountings
mounted on a steel deck are reported. The object in
view was to investigate whether the differences in sound
transmission via the two mountings and the steel
structure were similar for full scale and model scale in spite of the fact that the model deck structure had not the right model properties for sound transmission.
6
2 Scale models of mechano-acoustical systems The dynamical properties of a full scale
mechano-acoustical system may be learned from model experi-ments if the following "model rules" are met, ref. [3, 8,9]:
- the model should be geometrically similar to the full scale system with all linear dimensions reduced by a factor n
- the frequency is scaled up with a factor n
- the model should consist of the same elastic solids
and fluids as the original at corresponding positions. 1f the model rules as mentioned above have been met, the phase velocities of elastic waves of all types (dis-persive or not) are invariant for the geometrical scale. This means that wavelengths of all wave types are reduced by the geometric scale factor, if the frequency in the model experiments is scaled up by this factor. Lord Rayleigh stated this as follows, ref. [3]:
"Conceive two geometrically similar bodies, whose mechanical constitution at corresponding points is the same, to execute similar movements in such a manner that the corresponding changes occupy times which are proportional to the linear dimensions - in the ratio, say of 1 :n. Then if the one movement be possible as a consequence of the elastic forces, the other will be also. For the masses to be moved are as I :,i, the accelera-tions as I :n l, and therefore the necessary forces are as 1: n2: and, since the strains are the same, this is in fact the ratio of the elastic forces due to them when referred to corresponding areas. If the elastic forces are competent to produce the supposed motion in the first case, they are also competent to produce the supposed motion in the second case."
Since the same method of comparison applies both to elastic solids and to elastic fluids, an extension may be made to mechano-acoustical systems.
Alas, it is confusing that recent publications ref.
[10, II] are stating that bending wave patterns in
structures are not properly scaled with the above mentioned rules, due to dispersion. However, Rayleigh in 1877 and Schoch and Féher ref. [8] gave the physical arguments why this statement is incorrect and also "straightforward" calculations with the known for-mulae of bending wave speeds in plates or beams will prove this immediately.
If the wavelengths are scaled down at the same rate as the linear dimensions, the model can vibrate geo-metrically similar to the original system. From the publication of Rayleigh [3], who stated this law, it can be seen that when equal pressures and stresses act on the corresponding areas in model and original, equal velocities are found at corresponding positions and
moments. Thus if the excitation is scaled correctly the model vibrates geometrically similar to the prototype. As a consequence the ratio of vibration amplitudes for two positions of the system are equal for model and prototype. This holds also for the ratio of pressure and velocity.
Similarity relations for other impedance and transfer functions can be easily derived from this.
The similarity law as pointed out here is valid as long as effects due to gravity and flow may be neglected.
For dissipational forces the model is only correctly scaled by the above mentioned rules, if the dissipation
may be characterized with a loss factor which is
independent of frequency [8, 9].In practice the modelling rules are never completely met in the case of shiplike structures. For instance the precise modelling of closed tanks, lining, bulkheads and cables is very expensive if not completely im-possible due to physical restrictions. So it will be necessary to make a more or less intuitive decision of what simplifications are allowed without spoiling the desired dynamical properties of the model. One of the points of continuous concern is a correct modelling of the welding of steel plates and stiffeners together. When the scale factor is more than say two, it is a great practical problem to make welding joints that are geometrically similar to the full scale ones. Build-ing a model at scale 1: 10, continuous weldBuild-ing is very difficult, especially when plates of different thicknesses are involved. But also for intermittent welding the model joints are rather different from correctly scaled ones.
Therefore some investigations have been performed on the acoustical properties of model structures with different types of joints.
These experiments date from 1970. In recent years much progress has been made in the thin plate welding methods, especially for welding under inert gas protec-tion. At the moment rather accurate modelling of typical shipboard welding is possible. However, these techniques demand a very specialised craftsman who is normally not available in an acoustical laboratory because there is no continuous work in this field, Thus it is still relevant to investigate to what extent de'ia-tions due to simpler techniques are acceptable.
3 Investigations on model joints
Measurements have been performed on two nominal identical full scale deck structures and on eight model deck structures with various types ofjoints. The trans-mission of structureborne sound has been investigated and also the radiation of sound into a reverberation room.
Fig. I Full scale deck structure (1966). Only thc c\citer at the centre of the horizontal beam has been used. On the full scale structure "1972" only this centre exciter has been fitted on the beam.
floor
B
Fig. 2. Model scale deck structure. The miniature accelero-meters and the electromagnetic exciter can be seen.
1900
3300
fixing points of shaker
o
o positions of
accelerometers.---o
view from below
3300
150
600
section A-B dimensions in cm
dimensions in mm Fig. 3. Position of the deck between two of the insulation rooms Fig. 4. Dimension of the full scale deck structures.
of the Laboratory of Applied Physics of the Techno-logical University at Delft.
8
In section 3.1 the measurement arrangements and the structures are discussed.
In section 3.2 a description is given of the various model joints.
In section 3.3 and 3.4 respectively, the experiments on structureborne sound transmission and on sound radiation are reported.
3.1 Measurement arrangements
The deck structure which has been used for the experi-ments. consisted of a flat steel plate which was stiflened by beams in one direction.
Perpendicular to the deck plate a beam structure was fitted on which the excitation was exerted. This can be seen in figure I and 4 for a full scale deck and in figure 2 for a model deck.
The two full scale structures have been made by shipyard personnel with normal accuracy from the same drawing, but with a period of six years in between. They were fitted successively in an opening of a con-crete floor between two reverberation rooms with a volume of 105 m3 each (fig. 3). The thickness of the deck plate and the dimensions of the beams are repre-sentative of those applied in superstructures.
The full scale decks were supported at the edges by wooden laths. Gaps between the deck and the laths and between laths and concrete floor were filled up with a butyl filler.
The scale model structures were geometrically nearly similar to the full scale decks, all linear dimensions reduced with a factor 10. Also the upper reverberation room with concrete boundaries and the concrete floor with opening were modelled.
However beside the jointing methods several other deviations from the correct model rules for the mea-surement arrangement and the model decks were as follows:
- the bulb profile stiffeners as used in the full scale structure were modelled by bended flat strips (see cross sections fig. 5)
- in the models there was no welding seam between
the deck halves as in the full scale decks
Holland profile100x8 24 10
100_I
10 B full scale 0.75model scale dimensions in mm
Fig. 5. Cross sections of full scale and model scale stiffeners.
- for practical reasons the model room stood upside down, therefore the model decks rested on the "bottom"-side of the floor-opening. A thin layer of clay was used to close some gaps between floor and model decks. For one model the influence of a support by wooden laths has been investigated.
3.2 Different types of joints
In the two full scale structures the stiffeners were welded to the deck by staggered intermittent welding (fig. 6).
For the model structures soldering, tack-welding and a combination of tack-welding and glueing has been used, viz.:
three identical models with staggered intermittent soldering (fig. 6)
two models with tack-welds on one side of the beams at distances of 8 cm in between
- one
ofthese models modified by adding glue (Hot-tinger X-60 compound) on both sides of the beams in the edges formed by deck and beams and the other by doubling the number of tack-welds- two identical models with tack-welds at distances of 4 cm
one of these models modified by doubling the num-beroftack-welds. 100. a j 200 4 I 8 =0.75 16 b C d20, 40 orSO 0.75 thmensions in mm
Fig. 6. Different joint configurations
staggered intermittent welding (prototype) staggered intermittent soldering (model) tack welding (model).
3.3 Experiments
In designing the experiments the question must be answered what is a good criterion by which to judge the utility of a jointing method on model scale. As scale models are used to learn about sound trans-mission and radiation properties of full scale struc-tures, it is the similarity with respect to these properties between full scale and model structures that has been chosen as the criterion.
3.3.1
Transmission of structureborne sound
In the experiments the structureborne sound trans-mission has been characterized by the ratio of the mean square value of the acceleration at the excitation
position and that on the deck plate averaged over five accelerometer positions (fig. 4).
The measurement results are presented as level
differences following formula (1)
AL = La(exc)La(deck) = 101og (1)
<adeck>
where <.. > denotes time averaging and <..>
denotes time and spatial averaging. Because the ratio of the accelerations has no physical dimension, it should be similar for the full scale and model scale structures, in cases where the model rules have been met correctly (see chapter 2).
In the interpretation of the results of the scale model experiments two questions are to be answered. Firstly, what differences occur in sound transmission in the models due to the different jointing methods investi-gated and secondly what are the deviations from the sound transmission measured on full scale. Before an-swering the first question it should be known what differences might be caused by inherent measurement inaccuracy and by the unavoidable spread of trans-mission properties between model structures that have been made from the same drawing with the same joint-ing method. Structures of this kind will be called "nominally identical structures". To investigate these problems, repeatability experiments have been per-formed and several nominally identical structures have
been built.
In comparing the model experiments with the full scale experiments a priori disturbance of similarity due to experimental conditions was to be avoided as far as possible. This dissimilarity could be caused by the coupling of an incorrectly scaled exciter to the structure or by the use of incorrectly scaled accelero-meters and boundary support of the decks, but also by an inaccurate definition of the excitation spectra as will be explained later. In the full scale experiments an electrodynamical shaker was attached to the horizontal beam (fig. I) via rubber mountings. The mass of that part of tue exciter that was coupled to the structure
was l4OI0
kg. A contact resonance might be
expected near 2100 Hz.Opposite to the exciter an accelerometer with a mass of 3O iO kg was fitted. So in the model (scale 1:10) the mass coupled to the horizontal excitation beam
should not exceed (l70l0)l0
kg. because the ratio of mass of corresponding parts in full scale andmodel scale is iO.
By using the smallest accelerometer available in the laboratory with a mass of 250106 kg and an electro-magnetic exciter which did not load the structure, this condition was not violated seriously. lt was
experi-mentally checked, however, that coupling of an other exciter with a mass of only a few grams, changed the
vibration pattern of the excited model beam consid-erably. For the acceleration measurements on the
model deck plate accelerometers with a mass of
250 10_6 kg (type: Wilcoxon 90) were also used. Special measures were taken to avoid cross talk prob-lems using these electrically unshielded accelerometers. For the measurements on the first full scale structure (1966) only accelerometers with a mass of 30 l0- kg have been used, thus much less than l0 x the mass of the model accelerometers, because originally these experiments were performed withinthe scope of
another contract. However, on the second full scale structure (1972) the acceleration measurements have been performed firstly with the 30 l0 kg accelero-meter fitted to the structure in the usual way but secondly by adding an extra mass of 220 l0 kg between deck and accelerometer, thus giving a good model (scale 10:1) of the Wilcoxon accelerometers. As can be seen from figure 7h, the acceleration levels measured with added mass are considerably lower for octave bands with centre frequencies 2, 4 and 8 kHz (full scale). This influence on the vibration level of the added mass can be expected if a simple calculation on an infinite plate model is made. For this reason and also due to the difficulty of sufficiently strong electro-magnetic excitation of the models for frequencies higher than 16 kHz, the upper limit of the frequency range in the model experiments was the 1/3-octave hand with centre frequency of 16 kHz, corresponding with 1.6 kHz on full scale. The lower limit was the 1/3-octave band with centre frequency of 500 Hz (model frequency). The structureborne sound trans-mission has been measured only for two models also in the 250 Hz band. In all measurements the exciters were fed with pink noise filtered in 1/3-octave bands. Most results have been converted to I/I-octave band levels because for many transmission problems investi-gated on model scale such a resolution is thought to be sufficient. This data reduction makes the graphs easier to interpret without changing the general conclusions to be drawn.The method of conversion has been discussed in appendix A.
Results
The results for the structureborne sound transmission in the different decks are given in figure 7. From figures 7a and 7h it is seen that there are rather big differences for nominally identical model decks both in the case of soldering and tack-welding. Visual inspection of the nominally identical decks did not reveal serious struc-tural differences. lt was thoroughly checked that the
íL t lo o dB 30 20 dB 30 20
f,:
10 loa. Three nominally identical model decks.
-e 1[L 31.5 tack welded d 40 orts * - * - d 20 mm
10
- o--lo I I I 31.5 63 125 250 500 1k 10 fmoaa 2k Hzd. Different number of joints for the same model deck.
- ....- mean value full scale structures
g. Spread of sound transmission for eight
models (results for 31.5 Hz band are measured for two models only).
ÌLL L. L dB 30 20 10 Its t : 10 1 I I I I 31.5 63 125 250 500 1k 2k Hz 10 "'model dB 30 20
t:
b. Two nominally identical model decks. c. Different number of joints for the same model deck.
10
31.5
---tack welded: d 80mm - -- - - tack welded and glued
-o-i
63 125 250 500 1k 2kHz 10 0 fmod.l j(30 gram accelerometers) 1972 (250 gram accelerometers)h. Two nominal similar full scale decks; influence of accelerometer mass.
¡ L I: dB 30 20 10 o 10 31.5 63
Fig. 7. Structureborne sound transmission: AL = La(exc)L(deck).
dB 31) -20 ¶ I: I I I ) _10l I I I I I I 10 63 128 250 500 1k 2k Hz 31.5 63 125 250 500 1k 2k 4k 8k Hz 31.5 10 fmode 10 r e f - - wooden laths
thin layer of clay
I I
125 250 500 1k
10 ro 'model
2k Hz
e. Different jointing methods on the same f. Different boundary support for the
model deck. same model deck.
i. Spread of sound transmission for two full scale decks and mean value for eight models (31.5 Hz band two models only). dS 30 dB 30- dB30 tack welded d =80mm tin soldered
a = 20 roms (see fig. 6)
tack welded 40 mm (see fig. 6) 40*4 d4Omm 20 20 20 I I I 63 125 250 500 1k 2h H io (mead 10 I I I I 31.5 63 125 250 500 1k 3k Hz 10 31.5 63 125 250 500 1k 2k Hz C 10 'frodei
differences have not been caused by poor repeatability of the measurements. By repeating some measurements after the model deck had been removed from the floor and had been installed again, it appeared that only differences up to 3 dB could be traced to this origin. However, on average these differences were lower than 2 dB. Considering the spread between the nominally identical structures it must be concluded from the results in the figures 7a. . .7e that the different jointing methods and the variation of the number of tack-welds does not give models with essential different sound transmission properties.
Therefore the transmission properties of eight different models have been characterized by the band of results as given in figure 7g.
To judge the utility of the different methods a com-parison was to be made with the full scale transmission measurements. But then the question arises what typical
dg 10 dB 10 o 10 - zu - 30 40 31.5 63 1966 1972 125 250 500 1k 10 /
/
//
c. Two nominally identical full scale decks.
2k 4k 8kHz
spread might be expected for nominally identical full scale structures. To get an indication, it was decided to repeat the first full scale experiment (1966) with a newly built structure (1972).
The results can be seen in figure 7h. lt appears that also in these full scale experiments, differences in sound transmission up to IO dB are found. Visual inspection of the two structures revealed that the distortion due to the welding process was certainly different at corresponding positions, but not more than in normal shipbuilding practice. Again it was checked that the main origin of the differences was not poor repeatability of the measurements. So the results indicate that when a number of full scale or model structures is made from the same drawing and with normal accuracy, the sound transmission is to be characterized by a rather broad band of possible values.
Certainly this spread will depend on the complexity
dB
10
o
10 o
Fig. 8. Radiation efficiency: 10 log s.
tack welded: d-4G mm
mean value for two full scale decks
- -- - - mean value for eight nmodels
d. Spread for eight models and mean
values for models and for full scale decks.
40 I
31.5 63 126 260 500 1k 2kHz
10 (ooze
a. Three nominally identical model struc-tures.
I I I
31.5 63 125 250 500 1k 2kHz
o frvzu
b. Two nominally identical model struc-tures. tin soldered: d = 20 mn, o -lo o t dB o 10 t 4° 40 I 31.5 63 125 250 500 1k -- 10 I 3k Hz
12
of the structures and the transfer function chosen. In appendix B recent results of measurements on board four sister ships are discussed.
Comparing the model results with the full scale measurements a reasonable similarity is found except in the octave band with centre frequency 31.5 Hz: see figure 7i. One of the possible sources of error could be a dissimilarity of the power spectral densities of a5 for model and prototype due to differences in excita-tion, as has been pointed out in Appendix A. However, for an essentially different model exciter the same de-viation between model and prototype for the 31.5 Hz band has been found. Therefore probably other un-known causes for this deviation may be assumed. Perhaps an incorrectly scaled boundary support will have more influence at lower frequencies because of
the small number of resonant modes.
3.3.2
Sound radiation efficiency
When structureborne sound is generated in the deck, sound will be radiated into the surrounding air. The sound radiation may be characterized by the radiation efficiency of the decks.
This quantity gives the relation between the average value of the velocity of the deck and the radiated sound power. Because the deck forms a part of the floor of a reverberation room, the radiation efficiency can be obtained easily with the aid of a simple relationship between the average particle velocity of the deck and the average sound pressure in the reverberation room. Using velocity levels and sound pressure levels this relation is:
l0logs=LL+10log(A/4S)
(3) where s = radiation efficiency A = total absorption (m2) = 0.167V/T V = volume (m3)T = reverberation time of the room (s) S = surface of the deck (m2)
L = sound pressure level (dB re 2 iO N/rn2) L = velocity level (dB re 5 10_8 m/s)
In the reverberation room the sound pressure and the reverberation time has been averaged over three microphone positions. The positions in the full scale experiment "1966" were not exactly known. So in the model experiments the geometrical similarity of the receiver positions is disturbed.
But as long as the sound field is sufficiently diffuse, different sets of microphone positions will give nearly the same average sound pressure level. The deck velocity has been averaged over the five accelerometer positions shown in figure 4.
The measurement results
are shown in
figure 8. Again there is some spread between the radiation efficiency of nominal similar structures on model scale as well as on full scale. The differences however seem somewhat smaller than for the structureborne sound transmission.On the basis of comparing the radiation efficiencies of the model structures with those of the prototypes, the different jointing methods were equivalent to that in the prototype. In figure 8d it is shown that the mean values of eight model structures deviate little from the mean value of the prototypes. Only for the 125 Hz a more serious mean deviation of five decibels occurs. Also the spread of the results of the eight model struc-tures ¡s given in this figure.
4 Sound transmission in nominally identical structures
In chapter 3 it was reported that considerable dif-ferences in transmission of structureb3rne sound has been found for structures which were made with normal accuracy from the same drawing. Poor repeatab-ility of the experiments has been excluded. A possible reason could be the different deformation of the struc-tures due to the welding process. Two experiments have been performed to investigate the importance of this effect.
In the first experiment a model deck structure con-structed by using tack-welds (d = 80mm), was deformed by supplying heat into the deck plate with aid of a flame. This has to be done in three stages, successively increasing the deformation. Each time the structure-borne sound transmission, as defined in chapter 3, was measured and compared with that in the original situation. For the measurements, unlike the descrip-tion in chapter 3, a small electro-dynamical shaker and accelerometers with a mass of 2 l0 kg were used. This was allowed because in this case no comparison with a full scale measured transmission function was aimed at. The shaker was fed with pink noise filtered in octave bands (250-2000 Hz). In figure 9 the change
dB 20 stage A - stage B stage C o 10 31.5 63 125 250 500 1k 2k 4kHz
-Fig. 9. Change of structureborne sound transmission LLB = L(exc) La(deck) by heat deformation of a model deck. In the stages A, B and C the deformation has been in-creased, successively.
of sound transmission by heating is given. In stage A and B the deformations were representative for the distortion observed on the full scale structures but bigger than for the eight model structures of chapter 3. in stage C, the deck stiffeners came free from the deck at many positions between the tack-welds. This exag-gerate deformations were not representative for any structure investigated until now. However, it can be seen that the sound transmission had not been in-fluenced seriously. But the results of stage B show that different distortion of the plate can give a partial explanation for the differences between nominally
identical decks.
In the second experiment the acceleration response of an unstiffened flat plate has been measured, before and after deformation of the plate. The dimensions of the plate were similar to that of the model deck plates described in chapter 3 and a similar boundary support has been used. Firstly the acceleration of the undistort-ed plate was measurundistort-ed at ten positions when the plate was excited by a small elcctro-dynamical exciter. After that the plate was deformed with the aid of a steel ball and a hammer. Small pits were beaten in the plate along six lines corresponding to the positions of the deck beams in the model decks (fig. lO). This was done in two stages. In stage A, the depth of the pits was nearly equal to the plate thickness (0.5 mm) and in stage B it
was increased to twice the plate thickness.
The differences in plate response (averaged over the ten accelerometer positions) for constant held current through the exciter, is shown in figure 11. As can be seen differences are hardly beyond the measurement accuracy.
Fig. IO. Flat steel plate (thickness: 0.5 mm) deformed by beating small pits.
dB (octese barrds)
20
stago A (depth of pits; 0.6 rorro)
L1 stage B (depth: 1 rorro)
'o-Fig. Il. Change of average acceleration response of a flat plate for constant held exciter current and successive deforma-tion of the plate by beating pits.
= bending wavelength in plate).
The re3ults of these two experiments indicate that the differences in the deformation of the deck plates may not give a sufficient explanation of the differences found for the sound transmission properties of nominal-ly identical structures.
5 The use of an imperfect scale model
5. I Investigations on alternative structural design The sound transmission properties of a model structure
which is used for laboratory investigations may be rather different from those of the prototype ship which is modelled.
For very carefully scaled structures it has been reveal-ed already in chapter 3 that one of the origins of these
differences is the unavoidable statistical spread for nominally identical structures. So each particular structure ort full scale as well as on model scale, must be considered as one possible realisation of arr ensemble of structures with statistically varying properties, which could be built from the same drawings. The relation between the mean transmission properties of the ensembles of full scale and model structures should be related by the theoretically derived scale factors. The statistical variation of sound transmission prop-erties of complex shiplike systems is one of the reasons why it does not make much sense to study the discrete frequency response of one particular ship with the aid of a scale model. Even the measurements on board a sistership will fail to give accurate answers in this case. In practice other reasons should be added. Because due to physical and economical limitations the model rules are violated in several ways. Only a part of a ship will be modelled and in that part only the for the sound transmission most important structural com-ponents.
Therefore the problems which should be investigated on model scale are:
- what are the general trends in the transmission of o-1 m er I L 31.5 63 125 250 500 1k 2k 4kHz (model
14
sound in a particular class of ships (see ref. [6].
p. 107)
- what is the relative importance of different noise reduction measures.
In the next section a simple experiment illustrates the latter application. The difference in vibration isolation for two different mountings has been predicted accur-ately from a model scale experiment, whereas the main structure, a model deck, had transmission properties considerably different from the prototype for several frequency bands.
5.2 Sound transmission via different resilient mountings
A full scale deck structure (1972) and one of the model decks from the experiments of chapter 3, have been used for sound transmission experiments with rubber mountings.
Two resilient mountings have been cut in a block shape out of different rubbers:
mounting A: 45°Sh; 7x12x6 cm mounting B: 55°Sh; 7x12x8 cm
From the same rubber samples model mountings have been cut (scale 1: 10). Both on full scale and model scale the sound transmission via the mountings and the deck
dB (1/3-octave bands)
30 scale model (spot welded: d 40 mm)
-- - full scale deck 1972
20 / ' -lo -20 31 5 63 125 250 500 1k io n 2k Hz
Fig. 12. Structureborne sound transmission from excitation
point to a position at tile centreof the deck.
vo
resilient mountingA
steelseating..
____
K)2A V1Bstructure has been determined. The differences for the two mountings on full scale and those on model sa1e are compared. From the experiments of chapter 3 it was already known that the structureborne sound transmission from the beam structure to the deck plate was considerable different for prototype and this particular model deck for several frequency bands. This is illustated by figure 12, where a point to point transfer function has been given both for the prototype and the model. The excitation position was on the vertical beam structure (the same position as described in chapter 3) and the response position was on the deck plate. In the experiment with the resilient mount-ings, the mountings have been fitted on top of a very simply shaped foundation (see figure 13 and 14). In the model the difference =LL.JBLvA has been determined for the velocity response on the beam structure, when both mountings successively were excited by the sam.e vertical velocity u0 (see figure 14). The same has been performed for the sound pressure response at a certain position in the model reverbera-tion room below the deck (ALa =Lp,BLp,A). The measurements have been performed with pink noise, filtered in 1/3-octave bands.
For the full scale mountings only the difference in sound pressure response at a position in the full scale reverberant room has been measured.
The reverberant room was not geometrically similar
deck-Fig. 13. Model deck and model mounting.
o
2E3Fig. 14. Sound transmission measurements via two resilient mountings LXL=L flLVlA and .\L0 ---L,,tß---LP2A. 10
t
vo
dB ship on model scale will be sufficient for the study of
the effect of resilient mounting systems on accommoda-tion noise. And in this reduced ship not all details in the main structure and accommodation need to be scaled, because not the accurate prediction of transfer functions is aimed at, but the change of accommoda-tion noise due to an alternative mounting system (including realistic modifications of seating structures).
6 Conclusions and evaluation
Different methods for the jointing of beam stiffeners and plates of shiphike deck structures on model scale do not influence the sound transmission properties seriously. The methods investigated are soldering, tack-welding and a combination of tack-welding and glueing and also the number of tack-welds has been varied. However, the differences of transmission prop-erties between the models are primarily caused by the unavoidable statistical spreading in the sound trans-mission properties for nominally identical deck struc-tures. The different distortion of the model decks was suspected to be an important source for this statistical spread, hut experimental investigations performed on this subject did not support this opinion convincingly. Sound transmission measurements on two full scale structures, geometrically similar to the models, indicate that the spread found on model scale will be typical of full scale structures too. Comparison with the spread for sound transmission in four sisterships suggests that for more complex structures and more complex excita-tion the spread could be somewhat smaller. Further the analysis bandwidth may play an important role. The average transmission properties (octave band results) of a number of scale models are rather similar to the average of two full scale structures for the frequency range 63-1000 Hz. Only for the 31.5 Hz band did considerable deviations occur. Further investigations are needed to get an explanation for this deviation. So the jointing methods used on model scale seem to be acceptable in the frequency range mentioned.
Deviation of transmission properties in comparison with prototypes does not make scale models worthless. Often the influence of a sound reduction measure can be estimated from a scale model experiment.
For shiphike models in general it will be sufficient to build only a small part of the ship on model scale and to use for this part only the most important structural components. Only the structure that is to be modified and its connections to the main structures should then be modelled very accurately to obtain an accurate estimation of the noise reduction. This point has been illustrated with an experiment on the difference in sound transmission via two rLlbber mountings.
30
moornieg
- AI.,, model
- AL, model moonlirig t. L -. - AL,, full ucale mounting
20
10
0315 63 125 250 500 1k 2kHz
Fig. 15. Difference in sound transmission via two resilient mountings.
to that on model scale. Only the volumes meet the model rules.
In Appendix C some interesting details on the model experiments with the resilient mountings are described. They concern the reciprocity method which is used for the measurement of the sound transmission and further the method by which the problem of meeting simul-taneously the contradictory model rules for gravitation-al forces and inertigravitation-al and elastic forces has been solved.
The results of the measurements are given in
figure 15.
From the model experiments it appears that the dif-ference in response for the two mountìngs is indepen-dent of the transmission path chosen, because AL0 = AL
within the measurement accuracy.
One may expect that this will be the case not only for the two positions chosen, but also for other re-sponse positions on the structure and in the reverbera-tion room and also that the same will be valid for the full scale structure. From the full scale experiments it is seen that AL is nearly equal to the model results for the corresponding frequency bands.
With this case study it is illustrated that for a correct prediction of the effect of an alternative structure with the aid of a scale model, it is not always necessary to require that the sound transmission properties for the whole system are scaled correctly. For this particular case, when the model mountings are modelled accu-rately, thus having the proper stiffness and when further the impedance ratios at the point of attachment are scaled correctly the most important conditions for obtaining a good prediction have been fulfilled.
In general for predicting the effect of resilient mount-ing systems with the aid of a scale model, the mountmount-ings and the structures below and on top of the mountings should be scaled accurately, giving the proper imped-ance ratios. However in general only a relatively small part of the ship will influence the impedance at the mounting positions and mostly the transmission path of interest for machinery noise is that in the verti-cal direction. Therefore a relatively short "slice" of a
16
For a test of the dynamical similarity of full scale structures and model structures, correct modelling of the excitation, both in space and time, is a priori equally important as the modelling of the structure.
References
I. LANGHAAR. H. L.. Dimensional analysis and theory of models, Wiley and Sons, New York, 1965.
BAKER, W. E., P. S. WESTINE and F. T. DODGE, Similarity method in engineering dynamics: Theory and practice of scale modelling. Hayden Book Comp., Inc., New Jersey,
1973.
LORD RAYLEIGH. The theory of sound, Vol. 2, Dover Publica-tions. New York, 1945, 429.
KOSTEN. C. W., Note on similarity tests of sound isolation, Report of the 1948 Summer Symposium of the Acoustic Group, Phys. Soc. London (1949), 87.
JANSSEN, J. H., Model experiments on sound transmission from engine room to accommodation in motorships, NSS-report No. 87 S.
Ten Wolde. T., Reciprocity experiments on the transmission of sound in ships. Thesis, Technical University Delft, 1973.
VAN T0L, F. H., A model study of damping layers applied in ship structures. Proceedings of 5th ICA. Liège, (1965), paper F63 (see also NSS report No. 133 S, 1970).
SCHOCH, A. and K. FÉHER. The mechanism of sound trans-mission through single leaf partitions, investigations using small scale models. Acustica 2 (1952), l89.
TEN WOLDE. T.. Model rules for the sound radiation by ship hulls, Ministerie van Defensie (Marine), Hoofdafdeling Materieel, Bureau Scheepsbouw, Torenstraat 172, 's-Gra-venhage, Netherlands. 1968. available on request.
PLASS, K. G., Schlierenoptische Untersuchungen der Schall-abstrahlung von Blechen und periodischen Strukturen an Modellen, Acustica 23 (1970). 265. See however also erra-tum, Acustica 24(1971), 178.
TEUBNER, V., Wasserschallabstrahlung von Platten mit und ohne Versteifungen. Acustica 31(1974), 203.
STEENHOEK, H. F. and T. TEN WOLDE, On the validity and application of the reciprocity principle in acoustics, 1970. Available at the same address as ref. 19].
TEN WOLDE, T.. J. W. VERHEIJ and H. F. STEENHOEK, Reci-procity method for the measurement of mechano-acoustical
transfer functions, Journal of Sound and Vibration 42
(1975), 49.
BERANEK. L. L. et al., Noise and Vibration Control, McGraw Hill Book Company, 1971, 105, 127.
APPENDIX A
Transfer functions for 1/3 and 1/I-octave band.
I Influence of power spectral density
In a linear system the transfer functions defined by the 1/3 or I/I-octave band level differences at two dif-ferent response positions may vary considerably depending on the power spectral density distribution
ofthe excitation within the filter bandwidth. Therefore a transfer function for a given bandwidth will only be well defined
if
the power spectral density (see e.g. ref.[14]) ofthe input signal is given.
For doing a perfect model experiment (see chapter 2) the stress distribution in prototype and model should be similar not only at the corresponding positions but also at the corresponding moments (linear dimensions and time scale reduced by the same scale factor).
This implies similar spectral densities for the corre-sponding 1/3-octave or 1/1-octave bands in prototype and model experiments.
However for the experiments described in chapter 3, different types of exciters have been used for the full scale and the mode] scale experiments. Owing to this. it is possible that the stress distribution in the model was dissimilar to that in the prototype and that the spectral density ofthe output signals of the accelero-meters near the exciters was different for the corres-ponding 1/3-octave bands. This may have caused dif-ferences between model and prototype transfer functions.
2 Calculation of 1/1-octave band differences
A second problem is the conversion from 1/3-octave
band results to I/i-octave band transfer functions. As stated above, the power spectral densities within the corresponding octave bands should be similar for model and prototype. For a perfect model this should be valid both for a position near the exciter and at response positions elsewhere. But where the aim of the experiments is to check this perfectness, this condi-tion should be fulfilled primarily for the acceleracondi-tion response at the source. Because due to the 1/3-octave analysis the frequency information within this band-width is lost and the only thing that can be done before calculating the octave band differences, is to make the 1/3-octave band spectra similar for prototype and model experiments.
In our calculation flat 1/3-octave band spectra have been used.
For the calculation of L(exc)L;(deck), the 1/3-octave band spectrum of L(exc) has been made flat and for the calculation of the radiation efficiency 10 log s = LL(deck)+ 10 log (A/4S), the spectrum
of L1,(deck).
The following formula's have been used: - for ALa = La(exc)La(deck):
13
AL(oct) = 5 lO log IO_L(i)/iO} dB (Al) - for IO logs:
10 logs (oct)= 110 log l0b0(0}} 5 dB (A2)
As an illustration of the influence of the shape of the
Table I. Example of conversion to 1/I-octave bands for different excitation spectra (L,, dB re IO m/s)
1/3-octave band I / 1-octave band
50Hz 63 lIz 80Hz 63Hz
measured spectrum prototype (1972)
L,, (exc) 110 lOI 121 121
L (deck) 100 103 102 106
IO -2 19 15
flat spectrum La (exc) 100 loo loO 105
L; (deck) 90 102 81 102
IO
2
19 3500 Hz 630 Hz 800 Hz 630 Hz
measured spectrum model
L,1 (exc) 79 82 84 87
L; (deck) 75 82 74 83
4 o 10 4
fiat spectrum La (exc) 80 80 80 85
L; (deck) 76 80 70 82
18
1/3-octave band spectra on the octave band level dif-ferences and by that on the difdif-ferences between model and prototype, results are presented in table I for a
full scale and a corresponding model scale measure-ment. From this example it is seen that for fiat excita-tion spectra the transfer funcexcita-tions in model and proto-type are equal. For the actually measured spectra the transfer functions (1/1-octave bands) differ Il dB!
1f an analyser is available with FFT capacity, transfer functions are easily obtained with a big resolution in the frequency domain. Then with a generalized form of the formulae (Al) and (A2) broadband transfer functions for fiat input spectra may be easily calculated.
APPENDIX B
Sound transmission in nominally identical ships. Recently TPD has carried out noise measurements on board four nomïnally identical tugboats. The measure-ments have been performed during the sea trials under nominally identical conditions.
Two different shipyards have build two of the ships each, using identical sets of drawings. Octave band sound pressure levels measured in two cabins and in the hospital are presented to give an idea about the spread in sound transmission properties for such com-plex systems including that of the comcom-plex structure-borne sound sources. In all three spaces the rigidly mounted main engines are expected to be the domina-ting sound sources. The exhaust pipes and the auxiliaries have been resiliently mounted and airborne sound transmission from the engine room could not have generated the levels measured actually. In each space the sound pressure has been measured at one micro-phone position in the centre. The results are presented in table 2.
Although the number of results is too small to draw statistically justified conclusions, a typical uncertainty of about 4 dB for octave band pressure level predic-tions should be expected to be unavoidable due to the statistical variations of nominal identical sources and transmission properties.
Table 2. Maximum difference for L measured aboard four sister ships position
hospital cabin 38* cabin 73
main engines on tank top, frame 39-47 * for three ships only
From chapter 3 it is seen that the transmission prop-erties of nominally identical model structures give somewhat greater differences than the aboard measure-ments. This is rather disappointing because the model structures are so much simpler to build and experi-mental conditions in model work are better controlled. However in the light of the above results it does not seem to be necessary to demand much greater similarity in their construction.
APPENDIX C
The experiment with resilient mountings.
i
Reciprocity methodFor the measurements of the sound transmission via the rubber mountings A and B to a position on the
excitation beam" and one in the reverberation room respectively, a reciprocity method of measurement has been used. Instead of excitation on top of the two mountings with a known velocity v, the beam was firstly excited with a known force and the blocked forces ori top of the two mountings were measured. From the theory of reciprocity measurements [121, it is known that the ratio of the blocked forces in the vertical direction on top of the mountings A and B for constant held excitation at the beam position is equal to the ratio of the velocity responses at the beam position for constant held velocity excitation in vertical direction on top of the two mountings. The direction of the point force excitation on the beam in the reci-procity measurement is the same as that of the velocity response of the beam in the direct" experiment.
Secondly the reverberation room was excited by a small loudspeaker and again the blocked forces on top of the two mountings were measured.
From the theory of reciprocity measurements (see ref. [6] and [12]) it is known that the ratio of the blocked forces in the vertical direction on top of the mountings A and B is equal to the ratio of the sound pressures at the loudspeaker position, provided the volume velocity of the loudspeaker ("reciprocity"
LD dB(A)
deck frame nr. (oct) dB
31.5 63 boat-deck 55-60 7 4 boat-deck 70-75 3 5 main-deck 65-68 5 2 Hz 125 250 500 1k 2k o 2 1 4 4 5 5 3 5 3 4 5 3 2 4* 5* 4
experiment), and the vertical velocity on top of the mounting ("direct" experiment) respectively are kept the same for experiments A and B. The loudspeaker in the reciprocity experiment should be small in com-parison with the wavelength of sound in air and be built in, in a small box (monopole source).
The measurements of the blocked forces were per-formed with the method described in ref. [13]. On the top of the mounting a rigid block was fitted, which is excited by the mounting. The vertical acceleration of the centre of mass was measured and from Newton's law (P. Ma:), the force excerted on the block is calculated.
When the impedance of the mass jZf = /wMj is much greater than the driving point impedance for the vertical direction on the top of the mounting, the calculated force F is equal to the blocked force. For the measurements on the mountings A and B the same mass has been used. Thus the ratio of blocked forces is equal to the ratio of acceleration responses of the mass.
The reciprocity method has in this case the advan-tage of simpler excitation of the system and the mea-surement may be extended easily for other translational or rotational components on the top of the mounting (see ref. [13]).
Further it is rather easy to apply the correct static load both on ful! scale and model scale.
mass for measurement of blocked forces F soft mountings resilient mounting under investigation seating deck static preload
Fig. Cl. Sketch of model scale arrangement for the measure-ment of sound transmission via resilient mounting.
2 Correct static preload on model mountings
For the transmission measurements on full scale a blocking mass of about 170 kg has been used on top of the mountings. To get a scale model (scale I: 10),
which is dynamically correct following the rules of chapter 2, a model mass of 170 l0- kg has to be used on top of the model mountings. Due to the invariance of the gravitiational acceleration the static load of this model block causes static stresses and strains in the model mountings, which are ten times smaller than those in the full scale mountings. This may cause deviations from the geometrical similarity for model mountings and thus incorrect scaled sound trans-mission properties. To get correct static preload, on top of the model mass an additional mass has been mounted. This additional mass has been decoupled dynamically from the "blocking mass" with the aid of very soft mountings (see fig. Cl and C2). The total mass of the two blocks was about 1 .7 kg, thus hundred times smaller than the full scale mass. Because the cross section area of the model mountings is hundred times smaller than those of the full scale mountings the relative deformation of the full scale and model moun-tings will be equal.
Fig. C2. Experimental arrangement. The model k excited by a small electrodynamical exciter.
PUBLICATIONS OF THE NETHERLANDS SHIP RESEARCH CENTRE TNO LIST OF EARLIER PUBLICATIONS AVAILABLE ON REQUEST
PRICE PER COPY DFL. IO.- (POSTAGE NOT INCLUDED)
M = engineering department S = shipbuilding department C = corrosion and antifouling department
Reports
1 14 S The steering of a ship during the stopping manoeuvre. J. P. Hooft, 1969.
115 S Cylinder motions in beam waves. J. H. Vugts. 1968.
I 16 M Torsional-axial vibrations of a ship's propulsion system. Part I. Comparative investigation of calculated and measured torsional-axial vibrations in the shafting of a dry cargo motorship.
C. A. M. van der Linden. 1-1. H. 't Hart and E. R. Dolfin, 1968. 117 S A comparative study on four different passive roll damping
tanks. Part II. J. H. Vugts, 1969.
I I 8 M Stern gear arrangement and electric power generation in ships propelled by controllable pitch propellers. C. Kapsenberg. 1968. 119 M Marine diesel engine exhaust noise. Part IV. Transferdamping data of 40 modelvariants of a compound resonator silencer. J. Buiten, M. J. A. M. de Regt and W. P. Hanen, 1968. 120 C Durability tests with prefabrication primers in use for steel plates.
A. M. van Londen and W. Mulder. 1970.
121 S Proposal for the testing of weld metal from the viewpoint of brittle fracture initiation. W. P. van den Blink and J. J. W. Nib-bering. 1968.
122 M The corrosion behaviour of cunifer IO alloys in seawaterpiping-systems on board ship. Part T. W. J. J. Goetzee and F. J. Kievits,
1968.
123 M Marine refrigeration engineering. Part Iti. Proposal for a specifi-cation of a marine refrigerating unit and test procedures. J. A. Knobbout and R. W. J. Kouffeld. 1968.
124 S The design of U-tanks for roll damping of ships. J. D. van den Bunt, 1969.
125 S A proposal on noise criteria for sea-going ships. J. Buiten. 1969. 126S A proposal for standardized measurements and annoyance rating of simultaneous noise and vibration in ships. J. H. Janssen. 1969. 127 S The braking of large vessels II. H. E. Jaeger in collaboration with
M. Jourdain, 1969.
128 M Guide for the calculation of heating capacity and heating coils for double bottom fuel oil tanks in dry cargo ships. D. J. van der 1-leeden, 1969.
129 M Residual fuel treatment on board ship. Part III. A. de Mooy, P. J. Brandenburg and G. G. van der Meulen, 1969.
130 M Marine diesel engine exhaust noise. Part V. Investigation of a double resonatorsilencer. J. Buiten, 1969.
131 S Model and full scale motions of a twin-hull vessel. M. F. van Sluijs, 1969.
132 M Torsional-axial vibrations of a ship's propulsion system. Part II. W. van Gent and S. Hylarides, 1969.
133 S A model study on the noise reduction effect of damping layers aboard ships. F. H. van ToI, 1970.
134 M The corrosion behaviour of cunifer-lO alloys in seawaterpiping-systems on board ship. Part IL. P. J. Berg and R. G. de Lange.
1969.
135 S Boundary layer control on a ship's rudder. J. H. G. Verhagen,
1970.
136 S Observations on waves and ship's behaviour made on board of Dutch ships. M. F. van Sluijs and J. J. Stijnman, 1971. 137 M Torsional-axial vibrations of a ship's propulsion system. Part III.
C. A. M. an der Linden. 1969.
138 5 The manoeuvrability of ships at low speed. J. P. Hooft and M. W. C. Oosterveld, 1970.
139 S Prevention of noise and vibration annoyance aboard a sea-going passenger and carferry equipped with diesel engines. Part I. Line of thoughts and predictions. J. Buiten, J. H. Janssen.
H. F. Steenhoek and L. A. S. Hageman, 1971.
140 S Prevention of noise and vibration annoyance aboard a sea-going passenger and carferry equipped with diesel engines. Part 11. Measures applied and comparison of computed values with measurements. J. Buiten, 1971.
141 S Resistance and propulsion of a high-speed single-screw cargo liner design. J. J. Muntjcwerf, 1970.
142 S Optimal meteorological ship routeing. C. de Wit, 1970. 143 S Hull vibrations of the cargo-liner "Koudekerk". H. H. 't Hart,
1970.
144 S Critical consideration of present hull vibration analysis. S. Hyla-rides, 1970.
145 S Computation of the hydrodynamic coefficients of oscillating cylinders. B. de Jong, 1973.
146 M Marine refrigeration engineering. Part LV. A Comparative study on single and two stage compression. A. H. van der Tak. 1970. 147 M Fire detection in machinery spaces. P. J. Brandenburg, 1971. 148 S A reduced method tor the calculation of the shear stiffness of a
ship hull. W. van Horssen, 1971.
149 M Maritime transportation of containerized cargo. Part II. Experi-mental investigation concerning the carriage ofgreen coffee from Colombia to Europe in sealed containers. J. A. Knobbout, 1971. 150 S The hydrodynamic forces and ship motions in oblique waves.
J. H. Vugts. 1971.
151 M Maritime transportation of containerized cargo. Part 1. Theoretical and experimental evaluation ofthe condensation risk when transporting containers loaded with tins in cardboard boxes. J. A. Knobbout. 1971.
152 S Acoustical investigations of asphaltic floating floors applied on a steel deck. J. Buiten. 1971.
153 S Ship vibration analysis by finite element technique. Part II. Vibra-tion analysis. S. Hylarides, 1971.
154 S Canceled.
155 M Marine diesel engine exhaust noise. Part VI. Model experiments on the influence of the shape of funnel and superstructure on the radiated exhaust sound. J. Buiten and M. J. A. M. de Regt, 1971. 156 S The behaviour of a five-column floating drilling unit in waves.
J. P. Hooft, 1971.
157 S Computer programs for the design and analysis of general cargo ships. J. Holtrop. 1971.
158 S Prediction of ship manoeuvrability. G. van Leeuwcn and J. M. J. Journée. 1972.
159 S DASH computer program for Dynamic Analysis of Ship Hulls. S. Hylarides. 1971.
160 M Marine refrigeration engineering. Part VII. Predicting the con-trol properties of water valves in marine refrigerating installations A. H. van der Tak, 1971.
161 S Full-scale measurements of stresses in the bulkearrier m.v.
'Ossendrecht'. Ist Progress Report: General introduction and information. Verification of the gaussian law for stress-response to waves. F. X. P. Soejadi, 1971.
162 S Motions and mooring forces of twin-hulled ship configurations. M. F. van Sluijs, 1971.
163 S Performance and propeller load fluctuations of a ship in waves. M. F. van Sluijs. 1972.
164 S The efficiency of rope sheaves. F. L. Noordegraaf and C. Spaans,
1972.
165 S Stress-analysis of a plane bulkhead subjected to a lateral load. P. Meijers, 1972.
166 M Contrarotating propeller propulsion, Part I, Stern gear, line shaft system and engine room arrangement for driving contra-rotating propellers. A. de Vos, 1972.
167 M Contrarotating propeller propulsion. Part II. Theory of the dynamic behaviour of a line shaft system for driving contra-rotating propellers. A. W. van Beek, 1972.
168 S Calculations and experiments with regard to the stopping of a ship with diesel propulsion and fitted with a controllable pitch propeller. C. B. van de Voorde. 1974.
169 5 Analysis of the resistance increase in waves of a fast cargo ship. J. Gerritsma and W. Beukelman, 1972.
170 S Simulation of the steering- and manoeuvring characteristics of a second generation container ship. G. M. A. Brummer. C. B. van de Voorde, W. R. van Wijk and C. C. Glansdorp, 1972. 172 M Reliability analysis of piston rings of slow speed two-stroke
marine diesel engines from field data. P. J. Brandenburg, 1972. 173 5 Wave load measurements on a model of a large container ship.
Tan Seng Gie, 1972.
174 M Guide for the calculation of heating capacity and heating coils for deep tanks. D. J. van der Heeden and A. D. Koppenol, 1972. 175 S Some aspects of ship motions in irregular beam and following
waves. B. de Jong. 1973.
