Some acoustical properties of ships with respect to noise control Part 2

STUDIECENTRUM T.N.O. VOOR SCHEEPSBOUW EN NAVIGATIE

Netherlands' Research CentreT.N.O. for Shipbuilding and Navigation

SHIPBUILDING DEPARTMENT MEKELWEG 2, DELFT

SQME ACOUSTICAL PROPERTIES

OF SHIPS WITH RESPECT

TO NOISE CONTROL

(Acoustische eigenschappen van schepen in verband met geluidbeperking)

PARTII

by

Ir. j. H JANSSEN

Technical Physics Department T.N.O. & T.H. - Deif t

Issued by the Counci' This report is not co be published unless verbatim and unabridged

CONTENTS OF PART I (Reoit no. 44 S)

pagç

Summary 5

Chapter 1: Introductión 5

§ i Some general remarks 5

§ 2 Aim of the report 6

§ 3 Contents of the report 6

Chapter 2: Measurement ôf sound 7

5 i Transducers 7

§ 2 Calibration 9

§ 3 Electronic aids io

4 Plotting sound measurements 10

Chapter 3 : Acoustical quality of ships 12

§ I Recent trends in noise criteria 12

5 2 Additional information on criteria 14

§ 3 Some examples of cabin noises in iix motorships 19

Chapter 9:. Some cnclusions 21

Chapter 10: 'Some calculated noise spectra compared

with measurements - 24

References 25.

CONTENTS OF PART II

(Report no. 45'S)

Summary ...'...

Chapter 4: Propeller nOise 5

5 1 Structure-borne noise due to propellers ₅

5 2 Transmission through the hull 6

§ 3 Transmission along the propeller shaft 7

Chapter 5: Engine room ñoise 9

5 1 'Air-borne and structure-borne noise near diesel engines . 9

5 2 Air-borne 'and structure-borne noise near reduction gears 11

-5 3 The distribution of air-borne noise in the engine room . 12

§ 4 Structure-borne noise in engine room boundaries 16

Chapthr 6: Transmission- expériments 19

5 1 Transmission in vertical direction ₁₉ 5 2 Transmission in horizontal direction 23

§ 3 Damping 23

Chapter 7: Sound pressure excited plate vibratións . 24

§ i

The coincidence model , , ' 24

5 Z Experimental facts 25

5 3 A simple model of a finite plate ...., 26

5 4 Experiments on a thodel casing

...29

Chapter 8: Radiation of souñd by vibrating plates . . ' 30

§ I Pressure, intensity and power of radiated sound 30

-5 2 Plates excited by point- or by line-forces .' 31

§ 3 Constant force or constant velocity excitation;

experiments 31

§ 4 Plates excited by area-forces 32

§ S Experiments in cabins 331

§ 6 Air-borne sound insulation 35

WITH RESPECT TO NOISE CONTROL

PART II

by

Ir. J. H. JANSSEN

CHAPTER 4. PROPELLER NOISE

I. Structure-borne noise due to propellers As is well known and illustrated moreover in figure 3.08, 3.11 and 4.03, the rotating propeller is a powerful noise source. The mechanism of the

noise production by a propeller is very complicated, unfortunately. Perhaps even as- much as five mecha-nisms must be distinguished in this respect. Obvious-ly, static and dynamic.unbalanceof the propeller ànd shaft cause low-frequency noise. Moreover, hydro-dynamic unbalance is responsible for part of the

low-frequency noise. I-f these three types of unbalañce

were nod pesent a rotating propeller would still

gen-erate sound either by the turbulence it causes orby

the rotating pressure difference at the blades. Apart

from this, cavitation may be the most important noise source associated with -a propeller. Even rather low-frequency noise may Originate -from

this- mechanism of sudden airbubble formation and

collapse. Especially the implosion phase, if occur-ring in the imthediate. neighbourhood -of a metal

surface, causes the well-known erosion or "pitting". Sununary

The aim of this report on the acoustical properties of ships is to present data for the assessment of the relative importance of noise sources, noise paths and noise reduction measures in ships as far as human comfort is concerned. It is therefore a more practical parallel to a preceding report "Acoustal principles in ship design".

The instrùments used for the measurements by the Technisch Physische Dienst are described briefly. Also

some information on recent trends in noise criteria is given. Noise spectra, as measured in cabins of different ships,

are compared, stressing the importance of the distance between noise source (e.g. engine room or propellers)

and cabin.

Results of measurements on structure-borne sound (vibrations) and on air-borne sound due to propellers or engines are compared with results obtained during, excitation of parts of a ship's structure by means of a tapping

machine

With the aid of theoretical and experimental models the various possible noise paths are identified and investigated as to their respective contributions to noise in a cabin.

The conclusions about the origins of a cabin noise may be of some value for an "engineering estimate", as

is illustrated in the last chapter. A list of réferences is given.

For practical reasons the report is published in two parts; part I (chapters 1, 2, 3, 9 and 10) containing

introduction, information on instruments, criteria and a summary and illustration of results; part II (chapters

4, 5, 6, 7 and 8) containing the results-of measurements and some theoretical considerations.

Cavitation noise always accompanies cavitation al-though erosion may not be present. To the multiple

noise producing mechanisms of a rotating pro-pellor the "singing" must be added. However

in-teresting

a- thorough treatment of these

noise sources might be separately, in this report only a few vibration spectra of the hull plates near the

propellers _{as measured in several ships will be}

presented. Even the definition of "near the

pro-pellers" is

difficult. For one ship, built at "De

Scheide" Flushing as yard number 297, on board of which extensive acoustic- measurements were carried out, the measuring station for propeller noise _{is indicated in a cut-away-sketch of, -the}

stern in figure 4.01. In figure 4.02 the

corre-sponding spectrum is shown together with a range

for many other similar spectra, as measured on

board some twin-propeller ships. On -board of one

of the larger twin-propeller ships also airborne ñoise noise measurements were performed. In figure 4.03 -is shown the noise spectrum measured in an empty store space. just above the two propellers. Clearly,

the vibrating hull plates in the vicinity of the

6

I

\ _I; i o

Fig.4.01 Cut-away-drawing of the aftership of two sisterships as investigated at "De Scheld" (yard numbers296 & 297, 12,400/14,700 tons). Structúré-borne noise due to the propeller has been measured during .a builders' trial trip

(upper propeller blade tip just below waterlevel); the accelerometer was placed at various points ñear what is called "exc(iting) pos(ition) B"; the spectrum is given in figure 4.02. Also, propagation measurements were performed

afterwards; the structure-borne- noise- was, excited by means of a, rapping machiné (positions A and B).

60 50 40 aa 30 > w 20 w > IO o

32 63 125 250 5 iem 2 4em eem Hz

centre frequency cf - oct. bands

Fig. 4.02 Structure-borne noise (vibration) spectra as measured in t-he shell plating near the propellers of some

sea-going vessels.

In chapters 7 and 8 the excitation of plates by fluctuating pressures and the radiation of sound will be- treated more in theoretical detail. Results of measurements concerning the propagation of propeller-and-shaft excited acoustic vibrations of

the hull are given in the next paragraphs.

2. Transmission through the hull

The rotating propeller-and-shaft form a rather

complicated source -of structure-borne sound; each

part contributes to the total noise. So, for example, the bearings may squeal and rumble; at the same -time the propeller may be cavitating, thus con-tributing largely to the total noise level. It is nearly impossible to separate the various noise contributions while the propeller is running. Once the propeller proper, has excited the surrounding water the associated more or less random pressure

variations are propagated outwards. After-reaching

the hull they, in turn, excite the hull plates. The adjacent parts of the structure will vibrate under the action of fluctuating forces and moments. It must be admitted that substituting these forces and moments by one tapping machine, in order to simulate propeller noise excitation of the hull,

is fairly optimistic. For acoustical engineering pur-poses, however, it is necessary to have at least a roùgh idea about the propagation of these vibra-tions from the source to spaces of interest to noise

control. To gain information in this respect a

tapping machine, as is in common use for building

acoustics, has been placed in various positions. It

r

1

4Yo

-/

z// /

r

V-r

-n.

rw

-

v'i

II g e

lo g 8 7 6 SC z o e

t

- 3C 2C a -a4C 32 63 125 250. 5 1 20X1 4 8 Hz

centre freqoency of -fact. bands

Fig. 4.0-3 Air-borne noise spectrum, as measured in a store-room near the propellers of a large sea-going vessel (c.f. the upper two curves of figure 4.02). Considerable hearing damage risk exists -for people working in this

room; for comparison is shOwn the noise safety level limit

(N.S.L.), which is slightly lower than the ISO-noise

rating for hearing conservation (c.f. chapter 3).

will be clear that -the results of this paragraph can

serve only to indicate a general trend.

First of all, the tapping machine was placed as close as possible to the sterntube. By fixing accel-erometers to the hull plating the vibration level

could be measured. Figures 4.04 and 4.05 show the

results for propagation in the horizontal direction, i.e. normal to the frames; figures 4.06 and 4.08

along the frames 11

and 25. Afterwards, the

tapping machine was placed in the steering-gear

compartment; figure 4.10 shows the results of pro-pagation measurements in the horizontal direction.

§ 3. Transmission along the propeller shaft

In the precedirig section measurements were

re-ported on the propagation of structure-borne

- sound through the hull. As propagation along the

massive shaft might be very important, the tapping

machine was placed on a shaft bearing and the

o

a, o

20

30

32 63 125- 250 500 1 2 4 Hz

- _{-- centre frequency of . oct. bands}

Fig. 4.04 Propagation of structure-borne noise. Exciter

position A (figure 4.01 ).; the level differences between the

successive measuring pOints (indicated in figure 4.01 by

rings; identified by frame numbers) and point il are

plotted for the propagation in the shell close to the

propeller shaft. For frequencies between 50 and 300 Hz the unbalance exciter had to be used; between 150 and 9000 Hz the tapping machine (c.f. figure 2.05). There is no good agreement between the two sets of curves for low resp. high frequencies; for the latter the attenuation is roughly 1 dB/frame. Ship: "296".

- 10 -20 -30

L

w

A' p,

'-

.'.e. '

1Iii

63 125 250 500 1 2(220 4000 8000 Hz

- centre frequency of oct. bands

Fig. 4.05 Same as figure 4.04, except measuring points (indicated by squares in figure 4.01). Ship: "296".

32 63 125 250 l 2D 4 8

I-- centre frequency of- t. bands

Fig. 4.06 Structure-borne noise levels in frame 11 relative to the point i level (see figures 4.01 and 4.07). Ship:

"296". Again the low frequency range does-not agree with

the higher frequency range (c.f. figure 4.04). NS.L -/ »1 '¼-- --

.-

><:s-'

t..

'---'

I I

4,

, i.-;'< 6

/

-' I J '-10 e 0 a, o C V -a 10 V- -20 3032 *10 e

.10

Fig. 4.07 Sketch of measuring

points on frame 1.1 (see figure

4.06). Ship: "296".

Exciter positionA (figure 4.01).

Fig. 4.08 Structure-borne noise levels in frame 25 relative

to the point i level (see figures 4.01 and 4.09). Ship: "296".

Fig. 4.09 Sketch of measuring

pints on frame 25 (see figure 4.08). Ship: "296". The

infer-ence from figures 4.06 and 4.08

is that the structure-borne noise

levels are more or less uniform in .a frameif only one or two decks are present. Ship: "296". Exciter positiOn A (figure 4.O1).

centre frequency of - oct. bands

Fig. 4.10 Propagation of structure-borne ñoise. Exciter position B; the level difference between the successive

measuring points (indicated in figure 4.01 by crosses;

identified by frame numbers) and point 1 are plotted for

propagation in the shell at the height of the tapping

machine The attenuation is now roughly 0.6 dB/frame (c.f,. figure 4.04). Ship: "296".

32 53 125 250 500 - 2 4

8 Hz

- - -centre frequency of oct. bands

Fig. 4.11 Propagation of structure-borne noise. Exciting position: shaft bearing 5 (tapping machine on "top" of

bearing); the level differences between the successive

measuring points on the bearings (see figure 4.01) and pòint S are plotted. The inference is that propagation is approximately symmetrical with respect to the exciting point and that the high frequency range is attenuated by s much as 7 dB/bearing is contrast to the lw frequency range. The level difference (13 dB) between bearing 5 and bearing 6 (or 4) depends mainly on the measuring

position at 5, of course; actually it was situated close

to the keel. .10 - _si-o 10

2oW%,

it-32 63 125 250 500 1000 2 4000 6 Hz

vibration levels in other bearings were measured (see

figure 4.01). The results are given in figure 4.11.

It is well-known that iow frequency noise or

vibrations. (at infrasonic frequencies) originating from a rotating propeller-and-shaft may be per-ceptible all over the ship, whereas the higher

fre-quencies are more or less confined to the hull parts

near the soûrce. For the ship in question this

statement is confirmed. The general behaviour in

other types of ships will not differ very much

from this. Comparison of the results given in

chapter 6 shows however that large differences in

details may occur.

CHAPTER 5. ENGINE ROOMNOISE

§ 1. Air-borne and strùcture-borne noise near

diesel engines

In general the most important sources of noise in a ship will be found in the engine room.

De-TABLE 5 I.

pending on the type of propulsion machinery the main sources inside the engine room will be either diesel engines or reduction gears. These will be

treated in this and the next paragraph.

In various countries an enormous amount of data about the acoustic output of diesel engines

has been collected.

Mostly the spectrum of the air-borne noise as measured in octave bands at a distance of i to 3 m from a marine diesel engine shows a marked top;

the level "top Lu" is given by

5.01

top L 30 log (n/u0) + 12 log (Nmaz/No) - 6 dB

where

n

= the actual number of revolutions per

minute;

= i revolution per minute;

Nniax = the rated maximum power in SHP;

N0 = I shaft horse power (SHP).

ship engine crank-shaft n (RPM)

power

N (SHP)

spectrum top level L (cf. equation .O1) meas (dB) comp (dB) I main 114 5500 101 101 H G ,, 118 118 6600 8000 107 105 102 103 297 119 7600 107 103 J A ,, 122 145 4400 12500 115 101 101 108 B 215 4000 110 107 B aux. I 245 1500 110 104

C,D

main 250 6250 113 112 A aux. 280 1500 102 104 F G ,, 375 375 390 300 101 99 102 101 H J ,, 375 375 240 2Ó0 96 100 99 99 E

C,D

,, 428 480. 325 220 100 98 103 103 M N ,, 600 600 480 480 103 106 107 109

o

main 750 1650 113 119

V (pumping station) 180 IÖOO 98 98

lo

This relation is, slightly changed, taken from a

book by Slawin [31].

In addition to the data Slawin presents, table S.J gives a summary of measurements carried out by the T.P.D. [2]. Some corresponding spectra are

shown in figure 5.02. From this, figure 5.01 can be

derived. It is thus possible to calculate the air-borne noise spectrum due to diesel engines with a fair degree of accuracy, provided the rated

mum shaft power N,nq (in horse power), the maxi-mum number of revolutions per minute ,,laXand the actual n are given. This relation (5.01) and figure

5.01, of course, are derived from measurements on

actual diesel engines.

No noise reduction was attempted; only present-day diesel noise is taken into account. As soon as

reduction measures would have been applied, more

refined computation procedures should be used in

o E 10 1 3032 o E 10 S

if

-3

î--

200 loo 63 125 250 500

l

2 4000 8 Hz

-

centre frequency af oct. bands

Fig. 5.01 The (air-borne) sound pressure level near a

normal diesel engine is determined approximately by three

data, viz.: 1. the actual number of revolutions per minute (n); 2. the rated maximum value of n (n,nax); 3. the rated maximum power Nma, SHP). With the aid of this figure and with relation 5.01 the level and the octave spectrum curve may be estimated. The experimental dita for this

figure are drawn mainly from [2]. For example: for

n = n,,1, 200 revs/rain and Nrna,. = 1000 SHP the peak is located at 100 Hz, 100 dB.

centre frequency ai oct. bands

Fig. 5.02 Some experimental spectra, supporting figure

5.01, drawn from [2].

t

1

z.

Fig. 5.03 Vibration measurement on the

bed plate of a diesel generator. The

battery-operated spectrum indicator (c.f.

figure Z.02) is extended with a 1/3 octave

band filter for frequencies below 100 Hz. The position of the accelerometer can be

seen.

order to predict accurately the resulting noise

levels.

Besides the air-borne sound due to diesel engines

also the structure-borne sound ("vibrations") is important. In this paragraph some velocity levels for several engines as measured on the bed plate

are given (see also figure 5.03).

This data used in connection with the results of

§ 4 of this chapter

("structure-borne noise in engine room boundaries") and of chapter 6 § i

("Transmission in vertical direction") provides

sufficient information for the approximate cal-culation of vibration levels in engine room walls

and adjacent parts of the hull.

In figure 5.04 and 5.05 the available data is

sum-marized. Nearly all measuremens were carried out while the engine was running under full load.

Large, slow-speed engines seem to be quieter than small, respectively high speed engines. Moreover, higher velocity levels seem to be found for resi-liently mounted engines than for rigidly mounted ones; this is to be expected. No data was available on the influence of load or speed. In view of the

relation 5.01 a similar simple behaviour for the structure-borne sound due to diesel engines may

be expected.

'-i

o.

375

-

C 250 E,7l5 297,119 A, 145 "ma),. RPM 800

E o o

t

90 e. E C e 60 o. o w -o 30 N. 0

\

1 /rnIS 125 250 500 1 2000 4 8 Hz

centre frequency of or_-f oct bands

Fig. 5.06 Vibration spectra of diesel engine bed plates will

be found mostly in the shaded area of this velocity level -frequency plane. The velocity levels of points vibratiii with an effective acceleration equal to the acceleration due to gravity are on the line marked g; the line marked

I A corresponds to those points with an effective dis-placement equal to 10-10 m (c.f. chapter 2 § 4).

In figure 5.06 the velocity spectra region for vibrations of diesel engines seatings in the f-L

plane is shown.

2. Air-borne and structure-borne noise ñear

reduction gears

Although many measurements, on the air-borne as well as' on the structure-borne noise -due to marine reduction gears have been carried out the available data still (just as with diesel engines) seem to be insufficient for a better understanding

of the sound production as a function of the

relevant variables such as transmitted power, tooth

form, tooth irregularities and dimensions [32] etc. The noise spectra show a typical discrete fre--

-quencies character. In figure 5.07 some octave band spectra f air-borne noise due to main- propulsion gears on board large tankers are given; figure 5.08 presents spectra for four "identical"

turbo-genera-:iuià..

_I

_I

_I_

1:Itç.

I

uiiuir-.

40 30 -a. 6 cyl., 60 kW, 1500 revs/mm, 4 str b.. 12 cyl., 1100 HP, 900 revs/mm, 2 str c. 12 cyl., 500 HP, 600 revs/mm, 2 str d. 12 cyl., 1250 HP, 900 revs/thin, 4 str e. 4 cyl., 30 kW, 1200 revs/mm, 4 str

11111

IrddiI,IU

rrvvvv-.

I1f41AAI

70

1111

TillAi

iiuìii

p,

32 63 125 250 500 1 2000 43 8 Hz

-- centre frequency of + oct bands

Fig. 5.05 Vibration, spectra at be.d plate of five other diesel engines (c.f. figure 5.04):

12 cyl. V, 1001-IP, 1150 revs/min,.rubber mounts

6 cyl., 525 HP, 475 revs/mm, rigidly mounted

6 dyl., 225 HP, 750 revs/mm, rigidly mounted

6 cyL, 180 kW,. 620 revs/mm, rigidly mounted

6 cyl., 7050 HP, 115 revs/mm, rigidly mounted

32 63 125 250 500 1 2 4 8 z

centre frequency of oct. bands

Fig. 5.04 Structure-borne sound (vibration velocity)

spectra for five diesel engines as measured on the bed plate (c.f. figure 5.03; source side of the rubber). All

engines were resiliently mounted (rubber);

-110 100 110 50 60 w E C 40 o e

t

C w o w o, 20

t:

12

tors the air-borne noise of 'vhich was largely

deter-mined by the gears used.

In figure 5.09 five typial vibration spectra are shown; they were measurel on the fóundation of

each reduction gear. In general the spectra of

reduction gears differ from diesel engine spectra mainly in. character, not in level, as far as

air-borne noise is concerned; vibration levels measured

on the respective foundations, however, show that

reduction gears are considerably quieter in the low frequency range.

32 63 125 250 500 t 2

40 8

Hz

- centre frequency df.1oct bands

Fig. 5.07 Reduction gears aré well known sources of

air-borne nóise in turbine propelled ships. In the engine rooms of some large tankers thèse spectra were measured

at about i m above the gear box (main propulsion).

Strong discrete frequency components occur due to the gear meshing frequencies and harmonics thereof.

centre frequency of i oct. bands

Fig. 5.08 Four "identical" geard turbo-generator pro_

duced thesespectra at0.7 m above the reductiongèarbx.

30

32 53 125 250 500 1000 20(X) 4000 8000

- _ centre frequency of L oct. bands

Hz

Fig. 5.09 Structure-borne noise (vibration) spectra at

the foundation of five main reduction gears on board

large. tankers.

§ 3 . The distributiòn of air-borne noise in the

engine room

Now that the air-borne and the structure-borne noise near the main sources in an engine room have been treated the next step is to consider the

paths flowed b

this noise to the other parts of

the ship..

The propagation of sound in the air was in-vestigated already years ago and still a simple de. scription of the distribution of air-borne sound in a room is rather complicated. There is, however, -a fairly representative mathematical model; it is supposed to be sufficiently detailed for noise con-trol purposes. For this reason no special experi-ments were performed in this respect, although certainly several poblems are unsolved viz, the radiation of low frequency noise or the radiation by large sources. It seems, however, worthwhile to treat this model briefly as follows in order to show how and how much noise -reduction may be achieved by applying sound absorbing materials (e.g. the well-known mineral wool slabs faced

with perforated plates).

In many situations the sound field due to a

source, which is supposed to be emitting -a station-ary acoustic power containing components of very

many frequencies, may be considered as being

composed of two contributions: the direct sound field and the reflected (a-ï' reverberant) sound

field;

the name "direct"

applies to the sound radiated by the Source immediately to the meas-uring point, whereas "reverberant" is used for the

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\,..

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110 -00 70 Go 50 63 125 23) -1000 2 40 8000 Hz 11 lo "E z o.

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C B w 7 6 5 110 100 90 80 E N 70 60 s, 50 4, 40

sound field resulting from the superposition of the infinitely many signals reflected by the boundary

of the room.

Let us now consider a general room which must not be small in one or in two directions, i.e. we

do not consider a shaft tunnel, a corridor or a

hangar deck. In this room be a sound source,

which must be small in comparison with the room.

The frequency range cf interest has to be such that the corresponding wavelenghts are small in

comparison with- the dimensions of che room. The respective sound pressures determining these

fields may be estimated as functions of the source and room properties. The mean square of the re-sulting pressure can then be found as the sum of the mean squares of the "direct" and the

"rever-berant" pressures.

In practice the noise due to a noise source, for

example an auxiliary dieselgenerator, might be

de-termined as follows. The engine is running under service load in a large hall. At a distance of say 2 m the sound pressure level is measured in eight octave bands. This level is determined by the

outward-going sound power radiated by the engine

but not by the reflections at the walls, floor and ceiling of the hall, approximately.. At greater

dis-tances, however, the reverberant field will be more

important compared with the direct field. This is due to the more or less spherical spreading of the sound power and the inherent reduction of the

direct sound pressure level with increasing distance to the source.

Let us assume that the pressure level L5 is known

at very many points on a surface S enclosing the

engine.

The points of this surface be always at a given distance d (e.g. 2 m as supposed before) from the nearest point of the engine. If the pressure s were

the same for all points the relation between this pressùre and the radiated sound power (in watts)

would be very simple, as can been seen by

remember-ing the formula for travellremember-ing waves

5.02a Ps = Qc y5

approximately (exactly for plane waves; is density

of air, c velocity of sound), and that power is equal to force times velocity VS. The force in this instance is the product of sound pressure Ps and area S, acting on the surrounding medium. So we obtain

5.02b P _{= Ps}S V (p2/ec) S

where P is the acoustic power within an octave band

radiated by the engine.

If the pressure_Psis not constant over the surface S the righthand side of equation 5.02b must be written in the form of an integral; it might be approximated of course by a sum of partial contributions over the surface. At greater distance x in a very large hail or

better in free air, the surface S may be considered to be a sphere. For this case one obtains

5.02c Q P = (P2/oc) 4ax2

Here Q is

called the directivity factor; Q P

gives the amount of power radiated in the direction

in question. Clearly the product of pressure p and distance to the source x is a constant then: at grçater distances smaller pressures. This well-known fact is called spherical spreading of sound;

it is an idealized model of course.

However in normal practice the sound pres-sure at greater distances will .depend also on the

reflections by the hail boundaries.

Let us therefore try and find a relation between the radiated sound power and the reflection prop

-erties of the walls.

The total sound power reaching the boundaries equals P. From this power part is absorbed, part is reflected. The average reflected power may be supposed to be (1 - a) P, where a is the average absorption coefficient for the boundaries. Due to this reflected power one may measure a rever-berant sound pressure, the mean square value of which Pr2. The name reverberant is used because this sound pressure due tO reflections is the sound one may hear decaying after the sound source is

stopped, as is well known.

In this connection a reverberation -time T is defined as the time required for a sound pressure level to drop 60 dB after stopping the source. One

finds that this time T is given by

5.02d T = 55 V/Ac V/6A

where V is the volume of the room in m3 and A

the total absorption in m2 (MKS units must be used at the righthand side of 5.02d).

This total absorption A divided by the totalarea

of the boundaries of theroom equals a, the absorption

coefficient. Under stationary conditions one may

describe the reflected sound power (1a) P

as

travelling into the absorption A instead of through

S into free space.

Hence, analogous to 5.02b.

5.02e

(ia) P=Pr7/c) aA

where "a" is a correction factor which may be found by means of a theoretical model - or by experiments; "a" equals approximately 0.25.

Implicitly the required relations are found now. Let us consider for more detail the example of an

auxiliary dieselgenerator again.

Suppose acoustic measurements are performed on the engine located in a large hail at the engine works. At several points of a surface (area S) the sound pressure level L5 in eight octave bands is

14

determined. The shortest distance between this

imaginary surfáce and parts of the enginê radiating

ñoise be approximately 2 m. For low frequencies this distance is rather small, at larger distances,

moreover, the results may be spoiled by reflections

against the hall boundaries (if

not by other

sources!).

-If this engine 'will be installed later on in a ship's

engine room, what wilt be the sound pressure level, L9

at small distances and what at greater distances? An answer to the former question is simple: for.

most purposes the measured spectrum is a

sufficient-ly accurate approximation .of the. required one. For the latter question we fiñd, using equation

2.0 1, 2.03, .02b, 5.02c and 5.02e.

5.02f

pr2=QcP.4(.1-a)/A

It follows from this relation that the mean square

of the pressure at a distance x from the source inside the room is given by the general expression

5.02g

P'2 + p2= cP [Q/4 't x2 ± 4 (1- a)/A]

which expression was given in a slightly different form also in [.3] chapter 8; it will only seldpm be

used, because the corresponding accuracy is either not required or spoiled by other causes. From.5.02b

and 5.02f, however, a very useful expression fpr

ship noise control may be derived:

5;0 L9 = L9s + 10 log 4 (1 - a) S/A

L9s should be given by thé engine works, S ditto

(may be estimated), a and A are proporties to be

determined for the engine room.

For the data of figures 5.01, 5.02 and table SI one may assume L9s is. the spectrum as resulting from relation 5.01 and these figures, wheras S must

be estimated.. For an enginç of 3 m length this

area S will be 60 in2 approximately. Sometimes the

quotient A/ (1 - a) is called the room constant;

uñreliable or unknown)

TABLE SII

here A equals the total absorption 2' a S, i.e. the

sum of all sound reflection surfaces, each individual

area in the sum multiplied, however, by the ap-propriate absorption coefficient a.

It will be understood that the sound pressure level in the engine room due to a source of air-borne floise can be lowered by an increase in the

total absorption A.

Clearly, always some absorption is present,

other-wise the noise level in engine rooms would be infinitely high or the reverberation time would

be infinite. That means, however, that the

re-duction in L9 (the improvement) will depend upon

the absorption already present before any special

material is applied.

By measuring the reverberation time the ab-sorption in the engine room of several ships was

determined. A typical example will be given below

in table 5.11. The measuring locations are indi-cated in figure 5.11 as T1 inside .the casing at bridge-deck 'height, T2 insi4e the casing at main deck height and T:i near the auxiliarly engines just below the platform deck. Moreover, location

T2 is shown in figure 5.12. The reverberation times

for the higher frequencies are rather long; they should be halved. Therefore - the total absorption

already present (Ao) must be increased. This could

be done by applying absorbing material for ex-ample only on the free boundaries, i.e. on bulk-heads, deck-heads and hull plates. For the engine room mentioned this free area is about 200 m2, for the casing 400 m2. This allows for not more than the indicated amount of square meters "ab-sorption". The result in theoretical noise level

reduction 4 L9 is also giv.en. The maximum re-duction is seen to be not greater than 6 dB for this

instance. In other ships the reduction might be more.

To explain this, it may be instructive to show how the figures in the A L9 columns are arrived at. From relation 5.03 one may derive that the noise

reduction 4 L9 = L91 - L90 is given approximately

Frequency (Hz) Absorbing material coefficient Engine room (V 900. m3 -extra absorbing area = 200 m2)

Casing

(.V 900 m3 -extra absorbing area = 400 m2)

73 A0 _Aa ¿1 L9 T1 T2 A0 A 4L (s) (m2) (m2) (dB) (s) (s) (m2) (ma) (dB) 63 0. 1 1.2(?) 125 20

-0.S

2.0 (?) (?) 75 40

-2.0

125 0.1 1;6 94 20

-1.0

1.2 0 8 i SOE 40

-1.0

250 0.2 2.0 75 40

-2.0

1.0 1.2 136 80

-2.0

500 0.5 1.9 79 100

-3.5

1.3 1.5 107 200

-4.5

1000 O,.8 1.7 88 160 1.3 1.6 104 320

-6.0

2000 0.9 1.5 100 180

-4.5

1.3 1.3 116 360

-6.0

4000 0.9 1.1 136 180

-3.5

1.0 1.1 142 360

-5.5

8000 0.8 0.7 .214 160

-2.0

0.7 0.8 200 320 -c--4. O

centre frequency of . er - oct. bande

Fig. 5.10 Air-borne noise levels inside the casing of two motorships. Comparison of normal untreated casing (left) and .a casing lined with sound absorbing material; accord-ing to measurements. Cross-sections are drawn to the same scale.

by 10 log (A0/A1), neglecting the term (1 - a). Now A1 the total absorption after applying ad-ditional absorbing material, may be approximated in the fraction by A0 + Aa.

Thus the practically attainable noise reduction depends on the absorption already present and on

the amount of absorbing material that can be

installed.

It is interesting to compare the figures of table 5 II with those published by Shearer in [33] for

the engine room of a tanker. In the latter case

the engine room treatment consisted of 5 cm thick mineral wool faced with flattened expanded metal fixed between the frames. For a comparable ma-tena1 the absorption coefficient a in table 5 II was given The agreement between the results of table S II an4 figure 3 of [33] is rather good.

Apart from silencing the engine - the noise

source should always be considered. first more

reduction of the air-borne noise level can be ob-tained by freely suspending separate absorbing

units in the engine room (c. f. [34]), if the walls

are not available.

For the computed noise reduction in table 5 II

it was assumed that the casing was closed com-pletely. Usually, however, the engine room proper and the casing are connected by free air paths. Moreover, the auxiliaries mostly produce a high noise level. It is interesting to note that the sound

pressüre level in the casing due the sound pressure

level in the engine room is given by

5.05

= - 10 log (1 + K/4 S)

where R = A/(1 - a) is the room constant for

the casing and S the open area connecting engine

room and casing. Clearly, the noise level in the casing

can be reduced by an increase of the total absorption and by a decrease in connecting area. Of course, the

insulation by a deck between engine room and

casing limits the attainable reduction and, moreover, nO noise sources inside the casing are assumed.

Concluding this section, a comparison between

the noise spectra inside a casing of the Willem Kuys

[23], with special absorbing material applied at

the inner casing, and the noise spectra as measured

inside the casing of a motorship not acoustically

treated are given.

Figure 5.10 clearly shows the large difference

be-tween the spectra at nearly the same height (D and G) although the engine room spectra do not differ appreciably (A and E). This favourable noise reduction in the casing has an important

bearing on the noise control problem in ships.

Fig. 5.11 Part of the engine room of the ships «296" and «297" (c.f. figure 5.12). The points indicated are

referred to iñ the text (measuring positions).

o s .

\

o . F E o

I.

I_

o.

_I

G11

u._

o n 11.11' ILIIIIIIIIII1P 'lIllIIlllIIIIIIIlIIII -LO O- -32 63 125 250 am 50) 4 8 .Hz .11 9

16

4. Structure-borne noise in engine room

boundaries

For the two sister ships "296" and "297" mentioned

before a detailed study was made on the

distribu-tion of vibradistribu-tion levels in the

steel structures

forming the boundaries of the engine room.

In this paragraph measurements carried out

dur-ing builders' trials will be reported upon (propeller shaft at approximately 115 rpm). In figure 5.11 the measuring locations are indicated; figure 5.12

more-over shows a part of the engine room just above

the main deck. In figure 5.13 the velocity spectra as measured in the shell are given; in figure 5.14 those

for a column. The decrease in vibration level for higher decks is shown in figure 5.15. In general, shell or casing plates are found to vibrate more than the stiffeners or frames, as may be seen in figure 5.16 for the casing and figure 5.17 for the hull plating.

The vibrations in the shell plating between floor

and platform deck are due probably to the auxilia-ry diesel engines (also shown in figure 5.11). The difference between the structure-borne levels as measured at the seating of the nearest diesel (loca-tion 9) and in the shell plates (loca(loca-tions 13 and

16) is shown in the spectrum of figure 5.18.

The structure-borne noise spectra as measured

on the bulkheads are shown in figure 5.19, 5.20 and

5.21 (see also figure 5.22); moreover, in the

for-ward bulkhead the distribution was given in figure

5.22, 5.23 and 5.24.

I

Fig. 5.12 Part of the engine room including measuring

position T2 (c.f. figure 5.11) of the ships "296" and

"297". 60 E C -C .! 3 w t,

t

1 a 60 E r-w 0 o >-w 32 63 125

250 s 1

2 4

centre frequency f + oct bands

H

Fig. 5.14 Structure-borne noise velocity spectra as

meas-ured in a column (c.f. figure 5.11); same conditions as for fig. 5.13.

i'

N:

32 63 125 250

s

i 2 atoe Hz

centre frequency of + oct. bands

Fig. 5.13 Structure-borne noise velocity spectra as

meas-ured (during a trial trip, propeller 115 revs/mm) in shell plating and related points as shown in figure 5.11 (c.f.

figure 6.09); ship: "297".

g

o 80 70 60 :0 E C 40 f 4 30 > > ti 20 o 10 o 32 63 125 250 500 1000 2 4 8 Hz

centre frequency of + oct. bands

Fig. LI-5 Structure-borne noise velocity spectra as

meas-ured in different decks (c.f. figure LI 1); sime coisditions

as for figure 5.13. gô 80 70 60 50 o, E N 40 f

t

30 s L o' 5 20 o w 10 o 32

s

- Centre frequency of + oct. bands

Fig 5.16 Structure-borne noise velocity spectra as

meas-ured (same condition as fòr figure 5.13) oncasing plating

(upper curve) and on stiffeners (lower curve). As ex

pected plating shows a higher level.

90 80 70 60 50 E 40 f

t

c 30 20 O s 10 o * 30 w +20 C 32 63 125 250 500 10m 20m 40m 80m Hi

centre frequency of + oct. bands

.Fig. 5.17 Structure-borne noise velocity spectra as meas-ured (same conditions as for figure 5.13) on casing plating

(upper curve) and on frames (lower curve). As expected

plating shows a higher level.

1032 - 63 125 250 500 10m, 20m 40m - 6000 Hz

-

-centre frequency of 1 oct. banth

Fig. 5.18 The auxiliary engines cause their foundations and the adjacent shell to vibrate. This situation is repre-sentative for the structure-borne sound excitation of the hull by the engines. The difference in level between the locations 9 (auxiliary foundation) and the average of 13

and. 17 (shell plating) is shown in this.figure,; ship: "297".

-_\

---

. \'\

\

45

\

_-.

'\

N

\\\47\ \' .\

5\

63 125 250 1D 2 40m 8 Hz

18 .0 E C g 75 71 o .0 E C C o w O

iuiuiiuuuiuuilIUIIHhIIIIIIIuIIhuui...is

¶ 80 boat deck bridge deck shelter deck main deck platform deck

Fig. 5.-19 Structure-borne noise has been measured on the engine room bulkheads; the various measuring locations

are indicated in this figure (c.f.: figures 5.11 and 22). A kind of vibration pattern is shown in figure 5.20; ship: "297" (conditions as for figure 5.13).

- 4g

48 a

41

41 a

Fig. 5.22 The forward bulkhead of the engine room (ship: "297"; c.f. figures 5.11 and 19) with measuring

locations on the plating indicated.

G' .0 E J C C o ¶ ¶7 G) B E J C C o e o boatdeck bridgedeck shelterdeck maindeck platforn,deck floor tanktop velocity level in dB re 47 nm/s

Fig. 5.23 Representation of a "vibration pattern" (c.f.

figures 5.20 and 21) of the forward bulkhead; the meas-uring locations are indicated in figure 5.22.

f114!

-

\

¡

i

-

I__

r._¡Ii

--VE

-

r-w

go 70 80 0 10 -20 30 40 50 50 velocity level in dB re 47 nm/s

Fig. 5.20 For normal operating conditions (115 revs!

mm) octave band velocity levels (abscissa; centre

fre-quency as parameter) are. shown as- a function of the

location (see figure 5.19) on the forward bulkhead.

80 go 70

0 10 20 30- 40 50 50

-- - velocity level in dB 4 47nm s

Fig. 5.21 Representation of a "vibration pattern",

analogous to that of figure 5.20, as measured on the engine

room after bulkhead (see figure 5.19).

go 70 BO 0 10 20 30 40 50 50 50 - 70 80 go 0 10 20 30 40 50 velocity level in dB re 47 nm/s Fig. 5.24 Analogous to- figure 5.23.

60 50 40 20 Q 032 _{5.3 125} 250 503 1 2 4 8 Hz

- centre frequency f + oct ban

Fig. 5.25 At four locations in the engine room casing the air-borne-noise level L and the structure-borne nóise

level of the plates L-i. were measured uñder the same operating conditions as before (ship.: "297"; 115 revs!

mm). The (averaged) difference L1) - L is plotted in

this figure because it seemed very probably that thç casing is excited by air-borne noise rather than by structure-borne

noise transmitted from the engine foundations (cf. figure 7.09).

In the course of the investigatioñs it was sup-posed that the vibrations, in the casing might be caused by air-borne sound prevailing- there (i.e.

the plates are excited by the alternating air pres-sures). For that reason in figure 5.2 the average

difference is shown between the air-borne sound

pressure level at various locations inside the casing and the structureborne velocity level as measured

-on the casing plates abovç the shelter deck. It is

-interesting tó compare the results of this paragraph

with those of the transmission experiments in

chapter 6 and those of chapter:7.

CHAPTER 6. TRANSMISSION EXPERIMENTS § 1. Transmission in vertical - direction

In three ships the transmission of structúre-borne sound in a direction parallel to the frames

(vertically) was investigated with the aid of 'a 6 mm pl.

40 w 30 - 20_w > o 32

I

10

..

.. ,nciter

Fig. 6.01 A tapping machine excited a steel deck (c.f. 'figure 6.03) of "Prinses Beatrix". The structure-borne

sound propagation in the vertical direction was measured;

the points -on the shell plating where the velocity- level was determined are indicated.

-A

63 .125 250 50) 1 2 4000 9000 Hz

-

centne frequency of. + oct. bands

Fig. 6.-02- The average structure-borne noise -level, at A

and B (see figure 6.01) relative to that at 0, due to a

tapping machine on the lowest deck. Some details about

frames and plating are given in figure 6.03. The

attenua-tion "per deck" of pure structure-bOrne sound may be estiñiated for similar constructions with the aid of this

data. f-rame no 145 frame spacIng 610 mm 6 mm. L 150 X 75 x 8.5 L115x65x8' 9.5mm l5Òx75x7.5. 2.30 m - 7.5mm

L100x75x9

5mm pI. -i'

iR1:

..L130x6

9.5m /' 11J5 mm pl.

A 14.5 mm 11.75 mm pl.

o

tappinq mach. B 6 mm

Fig. 6.03 Details about plating and frames of M.S.

20

tapping machine (see figure 2.05). By means of piezo-electric accelerometers the velocity, level of parts of the ship structure could be measured.

In figure 6.01 the location n the firstship (Prinses Beatrix) is shown. The tapping machine was placed

on the deck near the hull. The result is shown in

Fig. 6.04 Analogous experiments were performed on

board M.S. "Randfontein" to investigate the propagation of structure-borne sound in four. different directions (as

indicated); see also figures 6.05, 17 and 18).

frame no's 133/134 frame. spacing 840 mm

Fig. 6.06 Details ibout plating and frames. of M.S..

"Randfontein" in connection with figures 6.04 and 05.

40 "30 C 20 s 10 o 32 63

--

125 250 5CC 1 4 8 Hz

centre frequency of . oct. bands

Fig. 6.05 For the vertical direction the average level difference between O and A is shown as indicated in

figure 6.04. It is comparable to curve A of figure 6.02. In figure 6.10 two analogous curves for "296" are shown.

The influence of different constructions on the shell

plating level reduction due to adjacent decks clearly can

be recognized.

figure 6.02, whereas figure 6.03 presents more details

about the structure. For the second ship (Rand-fontein) the experimental results and the location

details are shown in figures 6.04, 6.05 and 6.06. For the third ship (296) some transmission experiments

in the vertical direction have been reported in chapter 4 (propeller noise). Moreover, in § 4 of chapter 5, some measuring results about the struc-ture-borne noise in engine room boundarIes have been shown as far. as originating in the engines

(figures 5.11, 13, 14, 20, 21, 23 and 24).A tapping

machine, was also used in this ship; figure 6.07 shows

QI _o

iuiiii

_1ULIW

0 10 -20 30 40 50 60 70 80 go

velocity level in dB re 47 nm/s

Fig. 6.07 In .the engine room of "296" a tapping

machine excited tank top (see figures 6.11 and 5.11). The structure-borne sound propagation in the vertical

direc-tion was investigated; the measuring points are indicated

'in figure 5.11. In this figure a "vibration pattern" is

shown. 51 t-46 E C C 4.4 o a 2 ¶

c 30

o 20

0 B

the results. For easy comparison, in figure 6.08 some

velocity levels are shown as measure4 at the same

points when an auxiliary diesel engine was running

only, and in figure 6.09 during the trial trip (c.f. figure 5.13 which is identiçal in principle). The differences between the curves are obvious.

Espe-cially a comparison of figure 6.09 with figure 6.08 is

interesting. The slopes of the various correspond-ing curves differ considerably, thus indicatcorrespond-ing that the ship's structure is being excited also at other places than the foundation when the main -exgine

is running.

In figure 6.10 curves analogous to those of figures

6.02 and 6.05 are shown. These . differences in

velocity level as measured in thç shell at plates below

and above a deck vary considerably among

com-parable situations in different ships.

In figures 6.12,13 and'14-(c.f. figure 5.14.)

veloc-ity levels as measured in a column (H-beam; see figures 5.11 and 6.15) are presented'. As could be

frame no 80 frame spacing 760mm -_r2&5mm pl. Longt #203x25.4 spacing 980mm 2.85m --10.5mrn pl. tapping mac1 1254x102 12m 12 - 17mm

I601

DO ç7.5mmpl. 23mm pl. L 229x9.7 17mm pl. 12mm pl. 17mm pl. = _12mm 13.5 mm pL1 16.5 mm PL

Fig. 6.11 Details about plating and frames of'M.S. "296"

("297") iñ connection with figures 5.12, 6.07, 08, 09

and 10). 175mm pl. N

I

o - --N --N N SN

III. II-II

000.00

00

N N ii T -. -N

I

--N N

I I

II

N N

I

N

I

N N 4

-'

iii

D

3,

32 125

250 s -

i 2 4 8 Hz

-- centre frequency of - oct. bands

Fig 6.10 Structure-borne sound level reduction in shell plating due to adjacent decks for excitation on tank top

in engine room of "296". The level difference between 13

and 30 is shown in curve A, between 13 and 44 ('see

figure 5.11) in curve B'(c.f. figures 6.02 and 05). Some constructional details are given in figure 6.11.

0 10 20 30 40 50 60 70 80 90

.- velocity level In dB re 47 nm/S

Fig. 6.09 The data of figure 5.13 rearranged into a "vibration pattern for normal operation of the ship

("297"). Comparison with figures 6.07 -and 08 suggests

air-borne sound excitation of casing directly and, may-be,

of adjacent decks indirectly, the level at 51 and 54- being relatively high in this figure.

o - 10 20 '30 40 50 60 70 BO 9

- velocity level, in dB re 47 nm/s

Fig. 6.08 "Vibration pattern", analogous to figure 6.07, as measured while an auxiliary engine was running only.

51 E C C .2 9 5 5 E g3 1

22

w n E J C 42 o + 30

I

Fig. 6.15 The vertical column investigated; experimen-tal results are shown in figures 6.12, 13 and 14. One may

infer that sometimes a column may be an important

transmitter of structure-borne noise, depending on the relative amount of vibrations and noise produced by the engines or by other noise sources.

A.

4

AIÌi

125 250 5 1 2 4 8 Hz

centre frequency o _foct.

Fig. 6.16 The level difference of structure-borne noise between points in shell (resp. casing) plating and in ad-jacent decks for normal operating conditions of the ship ("297"; 115 revs/mm of propeller shaft). The rather

small difference in level between the curves A and B of

figures 6.10 agrees very well with the relatively high

level of the structure-borne noise in the main deck

(location 45 in figure 5.11). The lower curve of the

"44-45" differeñce was measured in "296" during exci-tation by means of a tapping machine on tank top. Except for the lower frequencies the curves are nearly identical. This suggests that the excitation of this part of the hull is mainly due to structure-borne sound coming directly

from the sources.

i.u,1I1.

§ 88 888g_lO4 -N -NW W

III'

0u,c', U)JJC 0)

/

lì

0 10 20 30 40 50 60 70 80 g velocity level in dB re 47 nm/S

Fig. 6.12 "Vibration pattern" as measured on a column (see figures 5.11 and 6.15) for the conditions of figure 6.07 (tapping machine on tank top).

O IO 20 30 40 50 60 70 80 go

velocity level in dB re 47 nm/s

Fig. 6.13 Analogous 'vibration pattern" (c.f. figure

6.12) measured while an auxiliary engine was running (c.f. figure 6.08).

0 10 20 30 40 50 60 70 80 go

velocity vel in dB re 47nm s

Fig. 6.14 Analogous 'vibration pattern" (c.f. figure

6.12) measured during normal operation of the ship ("297"); comparison with figures 6.12 suggests again

air-borne noise excitation of the casing.

5 t n E J C e o 42 2 2 dl o C t o C t t 0 t +20 + Io 50e L E C 42

L

¶24

expected the differences in slope for the various corresponding curves are not important (columns

are not easily excited by air-borne sound). In

figure 6i6 the velocity level difference between adjacent vertical and horizontal plates (see figure

5.11) is given for two instances.

Transmission in horizontal direction

Apart from the data of- chapter 4 two other

figures may be given illustrating the gradual de-crease in velocity level with increasing distance to the tapping machine exciting a ship's hull. Meas-urements in three ships are reported upon. Finding a reasonable degree of regularity in the available data about transmission of structure-borne sound normal to the frames turned out to be very dif f

i-cult. Various ways of presentation have been tried. Finally figures 6.17 and 18 resulted as being the least

unpracticâl;. neither does the "distance-doubled" nor the "equidistant" representation allow for

sim-ple conclusions.

Damping

If a source of structure-borne sound is exciting a ship's hull, sound energy is distributed all over the ship. If now this source is suddenly stopped the vibrations of plates and beams do not cease

2 2 o .6 t 6I o 21

Fig. 6.17 For three ships (in this: graph from bottom

to top: "Prinses Beatrix", "Randfontein" and "296"; see

resp. figures 6.01, 04 and 4.01) the propagation of structure-ne sound in a horizontal direction through the side plating has been investigated. The results are

extremely complicated. Therefore many ways of

repre-sentation have been tried, the most "successful" being

the leveldrop per doubling of distance (this figure) and per 10 m increase of distance (figure-6.18).

C C s 20 s 4L 10 5m 032 _{63 t25 250 503} 1

- centre frequency of oct. bands

Fig. -6.18 From figure 6.17 and this one an "engineering estimate" about a structure-borne nòise level at a certain distance from a source may be derived. Especially the immediate neighbourhood of the source is however very

difficult. In "Randfontein" (see figure 6.04) as well

propagation in horizontal and vertical direction as "oblique

propagation" was investigated. It could be concluded that

the level reduction for "oblique propagatión is very nearly

equal to the sum of the corresponding horizontal and

vertical reductions (c.f. figures 4.04, 05, 06, 07, 08, 09 and 10 for "296"). Insufficient data were ávailable from

"Prinses Beatrix".

simultaneously. A gradually decreasing velocity

level is observed. Mostly one important- single decay rate will be found. In that case the quantity

reverbeEation. time may be defined easily: it is the

time T necessary for a level decrease of 60 dB. This reverberation time is related to the loss fac-tor (see for example [3] or chapters 7 and 8) by

6.01

T2.2/jf

where f is the frequency for which the reverber-atión time is being measured (e.g. the centre

fre-quency of an octave band). Only for one ship

(Rand font ein see figure 6.04) reverberation times of

a part of the hull structure were determined. The

resulting experimental values of T and are given in table 6 I. TABLE 61 20 Z512.m -10 rI 2o3o ,--. D

-.

o .,

n h 5P.lOrn 5I0m -Centre frequency of i/i octave band

Reverberation time T Loss factor 17 50 Hz 5.0 s 0.0088 100 Hz 5.0 s 0.0044 200 Hz 6.5 s 0.00 17 400 Hz 6.5 s 0.00085 800 Hz 6.0 s 0.00046 1600 Hz 5.0 s 0.00028 3200 Hz 4.0 s 0.0001-7 6400 Hz 3.5 s 0.000 10 125 2) iO 22D 4 .8 Hz

centre frequency of bands

63

32

4o 8030 Hz 2

24

CHAPTER 7. SOUND PRESSURE EXCITED

PLATE VIBRATIONS.

1. The coincidence model

The sound propagation in a ship is complicated:

air-borne sound may excite parts of the structure which in turn reradiate the vibrational energy. The hull of a ship consists mainly of plates and

beams. The acoustic behaviour of plates and beams

is thus of extreme importañce to noise control in ships. A fairly complete çlescription in

mathe-matical form is possible. E'ven very simple models

(i.e. with simple boundary conditions) like e.g.

infinite plates show complicated properties.

There are three instances, however, for which a theoretical consideration of more realistic models is useful, viz. first: the iñsulation of air-borne

noise by means of bulkheads or decks, secondly:

air-borne noise excitation of the engine room casing and consequently reradiation by adjacent decks, and thirdly: propeller-noise excitation of the shell and radiation, thus causing air-borne noise levels

sometimes 'being very high in the stern.

In this chapter the excitation of plates by

in-cident sound pressures will be investigated; it may

be called "area-excitation" in contrast to "line"-or "point-excitation" (occurring when sources of structure-borne noise are in contact with plates

or beams).

In figures 7.01 a sketch is given of a simple

situa-tion. An infinite plate is being hit by incident

plane waves, (effective pressure Pi angle of

inci-dence 6, sinusoidal motions). In the lower medium

the wavelength be 2. Travelling waves will be excited

in the plate. The "trace or print wavelength" will

be given by

7.01 = ¿/sin O

X

Fig. 7.01 Diagram of an incident sound "ray" Pi hitting a single leaf partition wall or panel. If the medium (e.g. air) at both sides of the wall is the same and if the wall is infinite in extent the direction of the transmitted "ray" P2 is equal to that of the incident one.

where the index B indicates the type of waves in

the wall viz, bending waves. For symmetry reasons

the direction of wave propagation in the upper medium will be the same if the velocity of sound there is equal to that in the lower medium (other-wise the principle of Huygens must be applied).

Of special interest for this chapter now is

the

'magnitude of the particle velocity y of the plate due to the incident sound. A plate may be con-sidered as a beam (of unusual width b, and of height h equal to the thickness of the plate). The

well-known differential equation for bending waves in a beam is given in 702:

54U

7.02 E t

4

+ O

= (Pi - P2) b

In this equation the right-hand side expresses the force per unit length exerted on the "beam" (plate),

whereas the left-hand side gives the bending stiff-ness and the inertial forces. The meaning of the symbols is: E the (complex: i + j ) modulus of elasticity, I = b h3/12, the density of the plate

material, O = b h and u the displacement of a plate

particle as a function of the coordinate x and the time t. After introducing the complex notation fo'r

the incident sound wave Pi =

i exp i w (ty/c,)

and rearranging, 7.02 may be read as

rn (1

Co2 Eh2 sin4 O)

12 c04 C, w3 Eh3 sin4 O

+

_cosO

+

_12c04

where in =

h kg/rn2, w

- 2

_{t f and P2 =}

e0 c0 v/cos O. The latter relation describes the fact

that for plane travelling waves the pressure equals

the product of the velocity component in the

direction of wave propagation and of the character-istic impedance , c0 of the fluid medium (for air

e c0 400 kg/rn2 s).

In principle relation 7.03 is the solution to the problem under consideration. Without going into detail some remarks may be made about its

pro-perties. Practically, the last term may be neglected.

The remaining terms at the right hand side show

a remarkable difference: the first term is frequency

dependent and imaginary, the second is not. For certain combinations of frequency f and angle of incidence O the first term may become zero. This

corresponds to a very high value of y for a given p.

This effect is called "coincidence" [35 because it turns out that the trace wavelength equals the length

of the "free bending waves" that may occur at the given frequency. The lowest frequency for which coincidence may occur is called the critical

fre-quency for.

It is found from 7.03 by putting sin O = i

(grazing incidence). Its value is given, by relation

7.04 = OJS c02/ci, h

where Cr. = 'ìT7, the velocity of longitudinal

waves in the plate material (for steel and aluminium

5000 rn/s. for wood 3500 rn/s approximately; see also [3]).

For frequences well belowf:rit follows from 7.03

that the velocity of a plate is approxiiñately given

by 7.05:

as if the plate were consisting of small masses without any elastic interconnection. In chapter 8 use will be made of this and a similar relation for deriving the so-called «mass law" of air-borne

sound insulation.

The low-frequency behaviour of the infinite plate as expressed in 7.05 must now be compared

with experimental results.,

2. Experimental facts

Are the preceding theoretical considerations suf-ficiently correct to describe or explain experimen-tal facts? Only a few measuring results are availa-ble to answer this question. The first case to be mentioned is that of underwater propeller noise, exciting stern plates of a ship. It was found that for a particular ship between 30 Hz and 1000 Hz the velocity level (re 47 nm/s; half octave band measurements) was fairly constant as a function of frequency, the levels being about 70 dB lower

than the corresponding water-borne pressure levels

(re 20 pN/m2) near the hull. Above 1000 Hz

this difference increased to about 90 dB at

10,000 Hz. Theoretically, one would expect

(equa-tion 7.05; below far) a difference of about 40 dB at 100 Hz and 80 dB at 10,000 Hz, because the steel plate. thickness was about 0.01 m. In this instance the velocity level of the 'hull was lower than expected theoretically fròm the simple model of equation 7.05. Indeed, the stiffened shell of a ship's hull cannot be imagined as consisting of small' masses without any elastic interconnection, except perhaps for high frequencies, "high" mean-ing that the correspondmean-ing bendmean-ing-wave lengths in the plates are small compared with the distance

between successive frames. This is indeed the case for frequencies above 5000 Hz.

For the audio-frequency range, moreover, the

coincidence effect is

not important for

water-borne sound excited steel plate vibrations.

Obvi-ously, the simple model of i turns out to be not very helpful for this instance; the construction of a more detailed model regarding low-frequency

stiffness seems inevitable if more knowledge about this type of excitation is wanted.

+3

C

-J

Fig. 7.02 For the model of figure 7.01 the "mass-law" (equation 7.05) indicates a theoretical vibration velocity

level L,, _,,,,,, which is mostly lower than the actually

measured L.,, meas. '

A second instance for experimental facts is. found

in air-borne sound excitation of panel vibrations. There are several differences with respect to the former case. In air, sound travels at a speed of

340 m/s, in water however at 1500 rn/s. This

means that in air for many practical panel

thick-nesses the critical frequency fer may occur within the audio-frequency range. One would expect, therefore, that velocity levels computed according to equation 7.05 will be smaller than the levels actuálly measured. This turns out to be true, even for panels, however, where the critical frequency is at the upper end of the audio frequency range!

This is illustrated in figure 7.02 for five rather thin

panels. It is very probable, in view of these ex-perimental reSults, that the coincidence model, as

leading to equations 7.03 and 7.05, is still too simple

for an adequate description of the acoustic

be-haviour of plates when excited by air-borne sound.

An obvious reäson for this seems to be the

com-plete neglect of resonance effects of 'the plates due to e.g.. clamping stiffness at the edges. This presents

a difficulty, however. On the basis of equation' 7.05, and some reasonable assumptions about the acoustic radiation behaviour of plates, a theoreti-cal expression for the transmission loss of single leaf partitions could be derived (see chapter 8 and e.g. [3] or for fundamental information [35]); this expression approximates the practical "mass

law" for sound insulation in the intermediate

frequency range. .

In checking 'the velocity level of a single leaf wall, however, one. will find that the measured level is much higher than predicted by equation 7.05 (see also [36]), just as already mentioned

above. The measured transmission loss nevertheless

can be computed approximately by means of the simple mass law. A typical example is shówn in figure 7.03; in chapter 8 more will be said about this. Suffice it to state that clearly a panel may

stoel

- plywo..

32 63 125 250 5W 1 2 4 B 4z

26

o

32 250 seo l 2

40

Hz

centre frequency of 4- oet. bands

Fig. 7.03 The vibration velocity level of a pressed-straw single leaf partition wall relatiÑe to the theoretical level according to: equation This wall was vibrating

appreciably more than expected. Its sound insulating pro-perties however agreed with sirrLple theory. The

explana-tion lies in amore complicated theory (c.f. figure 8.03).

vibrate more intensely than predicted by simple theory but at the same time it will radiate sound

less efficiently than simple theory supposes,

other-wise the simple "mass law" for sound insulation

would be completely useless.

Can this be explained?

3. A simple model of a finite plate

Of course, the answer to the last question must be somewhat complicated, due to the fact that not only the excitation of panels but also the sound radiation is involved. In view of books like

Timo-shenko's on vibration problems in engineering [37]

one will understand that noise cortrol on board

ships must consist of a great deal of guess-work

because time is not available for elaborate

compu-tation of all important vibration modes of plates and beams. Nevertheless, these modes determine

the amount of radiated noise.

For good guesses simple models of real structures

may be useful. The flat plate, being an important

noise radiator iñ ships, may be treated briefly. The theory underlying the formulae given below

may be found in excellent books like "Vibration

and Sound" bij Morse [38] or "Die Grundlagen dér Akustik" by Skudrzyk [39].

In this section the excitation of the flat plate

is given as an example; the theory might be applied

to beams or more complicated structures as: well. In chapter 8 the radiatìon of sound will be treated.

As the radiation mechanism depends upon the type of excitation it is necessary to distinguish between

different models. It is upposed for simplicity that a force acts normal to. the: surface of the plate. This force may be a "point force", in which

case a sinusoidally fluctuating pressure acts over a

very small area of the plate;

it may also be a.

"line force", in which case an oscillating pressure

is concentrated along a straight line in such a

manner that the force per unit lçngth is a constant.

The force may also act over the entire area of the

plate; in this case it

is called an «area force".

In any case, the forces are represented by the symbol their momentary value F benig given by

7.06

F= f ¡dScos2nft

whére p is a pressure (a function of the coordinates

on the plate) and S is the plate area. At a certain point (A) of the plate the velocity y (A) in a di-rection normal to the plate surface: can be .given

symbolically by

707

y (A) = Eu

In this relation Z, is called "mode impedance";

it says that the velocity can be considered as being built up from infinitely many contributions F/Z,.. The number u runs from O to oc. For every t,Z.

is given by

7.08

Z,, = q,. (A) .

(A){j 2 nf M + r + s/j 2 n f):»

In this equation the dimensionless factor q.. (A) is determined by the amplitude distribution over the plate for the vibration mode with number u.

It might be called a "quadratic amplitude transform

factor", because its value is given by

7.09 q.. (A) = 5 (û,2 dS) /û,,2 (A) S

Here, û is the 'amplitude of the displacement due to

mode ,u at an arbitrary point of the plate. For a given excitation 'frequency f the movement of that point is thus described by

7.10 u,, = û,, cos 2 n f t

as far as it is due to mode u. Of course, û,. is a function of the running coordinates of the point on theplate. The value of q,. (A) can be computed by integrating û,,2 over S. The example of figure 7.04 illustrates this integration which also can be

performed graphically for simple vibration modes. In this way approximate values may be obtained for

more complicated vibration patterns if theoretical or experimental data is available (see for. example

(1

k\ Z,,

Fig. 7.04 The integration required for relation 7.09

illustrated. The natural vibration mode (natural function) û,, as' a function of the coordinates is squared. The area

«under the. curve" is equal to the numerator of 709.