- Email: [email protected]
Some aspects of the performance of acoustic hoods
J. Sound VS. (1966) 3
(I),
82-94
SOME ASPECTS OF THE PERFORMANCE
OF ACOUSTIC
HOODSt
R. S. JACKSON A.E.I. Power Group Research Laboratory, Manchester, 17, England (Received 26 May
I 965)
The paper summarizes some previously reported investigations made into the performance of acoustic hoods for enclosing noisy machinery, and outlines how differing applications require their own particular solution. The importance of having sealed acoustic enclosures is stressed but some of the problems involved with unsealed enclosures are also discussed. I. INTRODUCTION
Many instances occur in practice with machinery noise where it is more fruitful to place an enclosure around it rather than try to reduce the noise by treating the machine itself. Enclosures of this kind, known as acoustic hoods, pose many problems for the designer. For example, space and weight are often at a premium insofar as the hood is concerned, and access to the machine may be frequently required. Ideally, the walls of an enclosure should be as massive as possible, e.g., a brick building with a concrete roof, and it is also desirable that the enclosed item should be hermetically sealed from free space by the hood. Unfortunately, for various practical reasons many machines cannot be sealed in this way, and in some applications, particularly on ships and other vehicles, the hood must be as light as possible. Hence the need often arises for a close-fitting “tailor-made ” lightweight hood, elements of which may be removable for inspection of the enclosed machine. The problem then resolves itself into choosing a construction for the walls of the enclosure which is both practicable from an operating point of view (e.g., high temperatures may be involved) and suitable from an acoustical point of view. In the case of machinery noise, it should be borne in mind that discrete sinusoidal components of sound may predominate rather than broad-band sound, and the approach adopted for the enclosing of, say, a power transformer, which is predominantly a low frequency sound generator, may be different from that adopted for a gearbox, which generates discrete components at higher audio frequencies. Consideration must also be given to the nature and size of any openings which may be necessary in an enclosure, since there is little point in having hood walls with high transmission loss if sound is by-passed to free space via the openings. z. SEALED 2.
ENCLOSURES
I. BASIC CONSIDERATIONS The
foremost
consideration
which must be given to a machine
before an enclosure
is
placed around it is to ensure that it is completely isolated mechanically from its surrounding environment. This entails not only placing antivibration mountings between the
machine and its base but also ensuring that any connections such as pipes or electrical cables are so flexible that they do not transmit appreciable vibration from the machine and detract from the hood performance. A typical arrangement for the enclosing of a transformer is illustrated in Figure I where it can be seen that these precautions have in fact been taken. t Presented as a lecture in June 1964 at the conference on “Planning and design for protection from noise” organized by the Society of Acoustic Technology
at the Lanchester 82
College of Technology,
Coventry.
PERFORMANCE
83
OF ACOUSTIC HOODS
For the purposes of analysis it may be considered that a vibrating source and enclosure take the form of “pulsating boxes ” whose dimensions increase and decrease in a periodic manner, but whose sides remain plane throughout these excursions. This model is illustrated in Figure 2. If the sound pressure at some nearby point, P, is measured both Enclosure
Flex
couplings
Concrete “picture
Resilient
Figure
/
I. Acoustic
enclosure
for a transformer.
(motion,
y= waves
6
sin ht
t +)
radiated
(b)
Figure 2. Models for analysis of hood performance. equivalent of (a). Solution of (b) : 2 sin ~(XCOS ~9-
(a) Ideal sealed enclosure;
(b) plane wave
R sin 0) + sin2 0(X2 + R2) -U2
1 ’
S, M, R are plate “ stiffness “, “mass ” and “ damping “.
before and after the hood has been erected, the ratio of these two quantities will give the attenuation of sound produced by the hood (i.e., an “insertion loss”). An exact analysis of the model in Figure a(a) is a very complicated business, involving wave propagation and reflection in three dimensions. However, in the case of a close-fitting hood, where the spacing between the machine surface and the hood wall is small, a
R. S. JACKSON
84
sufficiently good approximation is obtained by considering that the hood walls are subjected to plane waves at normal incidence, since the large radiating surfaces of a machine will encourage these conditions. It is then possible to simplify the analysis to the one-dimensional case shown in Figure z(b). In evaluating this model a most important assumption, one which influences the whole philosophy of acoustic hood theory, is made. This is the assumption that the presence of the enclosure does not in any way affect the oscillatory motions of the surfaces of the machine. Hence, in Figure a(b), it is assumed that the driving plate A has a forced displacement amplitude YO which is the same whether plate B is present or not. The amplitude ratio, Y,/ Y,,, calculated (I) for the plane wave model of Figure a(b) is also shown in Figure 2 and Figure 3 shows graphs of the corresponding attenuation. This attenuation is a function of the mass, damping and elastic restraint of the attenuating plate and also of the distance between the plates. The three full curves illustrate how this function behaves for three values of elastic restraint, SO. The dashed curve shows the familiar “mass law” curve for a plate of the same area density.
I
60 IO
I
I
I 111111
I
I
100
Frequency
IllIll
I
II
IO00
(c/s)
Figure 3. Theoretical curves for attenuation derived from equation of Figure 2. M= 1.6 g/cm2: IOO c/s, Q=30 at 105 c/s. C:fO=475 c/s, Z=Igcm(7iin.).A:fo=oc/s,Q=30at33c/s.B:fo= Q = 30 at 475 c/s.
The most important consequence of the above-mentioned assumption is now clear: this is that a plate (or machine) vibrating with a constant amplitude is not a constant sound energy generator. This is best illustrated by the curve for zero stiffness where it can be seen that at low frequencies the sound energy radiated from the system is greater after the enclosure has been inserted than before. Clearly, the “mass law” concept based on energy considerations is not valid for acoustic hoods. The behaviour indicated by the family of curves of Figure 3 may be summarized as follows. At low frequencies, plates A and B and the air trapped between them form a massspring system which resonates at some low audio frequency. Even when plate B behaves as a pure mass a resonance still occurs due to the stiff cushion of air trapped between the plates. To lower this resonant frequency out of the working range either the mass of plate B or the spacing between plates must be increased. To increase the resonant frequency for a plate of given mass, and thereby increase the attenuation at low frequencies, the mechanical stiffness associated with the plate must be increased. To reduce the resonant build-up requires the introduction of mechanical damping into plate B. At high frequencies, more particularly at frequencies where the plate spacing is an integral number of half wavelengths of sound in air, standing wave resonances occur
PERFORMANCE
OF ACOUSTIC
HOODS
85
in the air between the plates. These resonances can be suppressed only by soundabsorbent material between the plates. These effects will be discussed in more detail later. 1
,t:
:
10
.L=
sj 20
5 Q 40
z
50 30 60
1 ____--I
IO
I
I
Illlll!
I
I
lllllll
100
II
1000
Frequency
(c/s)
Figure 4. Attenuation produced by steel box 30.5 cm x 152 cm x 14.0 cm deep. Wall thickness = a.03 mm; mass per unit area= 1.6 g/cm* of volume of air enclosed= 4750 cc. Dotted curve theoretical from curve C in Figure z.
Long Vibrating source (displacing volume K of fluid per plate width.)
Equotion for oir a5 ax2
of
_
I
flat
plates
clamped to rigid framework, each plate displacing V, of fuid to free space
motion A
Equation
of
motion
a2y
-227
Section of flat
of a plates
practical clomped
hood arrangement consisting in CI rigid framework
Figure 5. Models for analysis of framed hood performance. Approximate solution:
2 = [l+&~q], where
e =
WI C'
s
* = PC’ al ’ 2
cr(coth cra + cot
aa)
-a
1 ,
Ep = “ plate ” modulus of elasticity of plate material, d = density of plate material.
To illustrate how these theoretical expectations are confirmed in practice, measurements have been made on a number of small boxes. In Figure 4 the agreement between theoretical concepts and practical measurement is shown for a small steel box of the dimensions indicated. The resonance in the 500 c/s region is due to the walls of the box, and that at
86
R. S. JACKSON
900 c/s to standing waves inside the box. The curves also illustrate that good attenuation is obtainable at low frequencies with a stiff-walled construction. Often a more practical arrangement for a larger sized acoustic hood is to erect around the machine a rigid framework to which the walls of the enclosure can be bolted (or welded) to form a complete hood. A section of such an arrangement is shown schematically in Figure 5. The behaviour of this construction can be readily analysed mathematically (2), especially if the plates are considered to be infinitely long. What is required from the analysis is the ratio of the volume displacement of a plate to the volume displacement of a corresponding area of the source. The approximate solution for this ratio is included in Figure 5 and in Figure 6 the corresponding attenuation function has been plotted for a & in. thick aluminium plate clamped at its edges. This new analysis illustrates the significance of plate stiffness better. For example, at low frequencies the sound attenuation is positive because, although the mass reactance of the plate in this range is negligible, its volume displacement is now controlled by its
Frequency
k/s)
Figure 6. Theoretical curve for attenuation of &in. thick (0.635 cm) aluminium plate (unlimited length, clamped at edges). Distance between supports = a = 76 cm (30 in.) ; distance between source and plate = I= 19 cm (7fi in.).
ability to resist flexure, and hence with rigid supports a flexurally stiff plate will provide more attenuation than a limp one of the same mass. As the frequency is increased a peak is approached at a frequency approximately equal to that of the “fundamental mode” of vibration of the (clamped) plate, the frequency of the peak being increased somewhat because of the trapped air stiffness. As the frequency is increased still further a succession of troughs and peaks is seen, being caused by flexural modes of vibration of the plate, and interspersed with these, at 900 c/s and multiples of this frequency, standing wave resonances due to the air between the plates occur. Hence two distinct kinds of resonant conditions exist: plate resonances and air resonances. A closer examination of the nature of the plate resonances reveals the behaviour shown in Figure 7. At the “fundamental” resonant frequency the plate bends approximately as shown, and at any instant of time all points on the plate move in the same direction. In this case plate curvature is comparatively small, so that plate damping treatments are least effective for this mode. Above the fundamental mode frequency the plate no longer moves unidirectionally since the outer regions now start to move in the opposite direction to the centre regions. Consequently, the net volume of fluid displaced by the plate decreases as the frequency is
PERFORMANCE
OF ACOUSTIC
HOODS
87
increased until a condition is reached whereby as much fluid is drawn inwards as is displaced outwards and a sharp trough appears in the curve. Slightly above this frequency the next resonant mode is reached, but in this case the plate is flexing much more sharply than for the fundamental mode and so is more amenable to damping. Similar arguments hold at progressively higher frequencies. As regards the air resonances, if the plate spacing is chosen to be 74 in. for example, it follows that standing waves occur at approximately goo c/s and multiples of this frequency.
Large displaced volume low flexure, not easily damped
Large plate but no net displacement
motions volume
Large net volume displacement, higher flexure, more amenable to damping
Figure 7. Motions of clamped plate subjected to uniform sound pressure.
Frequency
(c/s)
Figure 8. Build-up of sound pressure due to presence of enclosure (plane wave model with I = 74 in. (19 cm). Curve A : No acoustic absorption between plates ; Curve B : 2 in. crown zoo surfaced with 2 in. Superfine Fibreglass at hood surface.
Had the spacing been chosen larger than this then the lowest standing wave frequency would have been correspondingly lower, in accordance with the usual plane wave theory. Analysis shows that at these preferred frequencies of air resonance the trapped air behaves (ideally) as an infinite impedance, coupling the two plates together. In other words the “attenuating” plate must move with the same motion as the driving plate since theoretically it would require an infinite force to move one relative to the other. Clearly, this form of resonance can be suppressed only by applying absorbent treatment in the trapped air itself. Any amount of mechanical damping may be applied to the attenuating plate without making the slightest difference to any of these air resonances.
88
R. S. JACKSON
Sound absorbent material of the rock- or glass-wool kind is thus clearly beneficial at standing wave frequencies. At frequencies removed from these preferred values little advantage is to be gained from such treatment, particularly at low frequencies. This is best illustrated by the curves of Figure 8. In these curves the plane wave sound pressure at the hood wall has been plotted for the models of either Figure z(b) or Figure 5, assuming the motion of the hood wall to be much less than that of the source. The curves thus show the build-up of sound pressure due to the presence of the enclosure, and since it is under the action of this pressure that plate B moves, this must be reduced if the absorbent treatment is to be of any value. Curve A shows that in the absence of any absorbent there are standing wave resonances at the appropriate frequencies. Furthermore, in this case there is a build-up of pressure at 50 c/s 15 dB. of approximately Curve B was computed from absorption coefficient data obtained experimentally. In this example, a 2 in. thick layer of Crown 200 Fibreglass faced with a further + in. thick layer of Superfine Fibreglass was assumed to be on the hood internal surface. It can be seen that at the standing wave frequencies the absorbent material suppresses the resonances but away from resonance, as, for example, at one octave below the fundamental frequency the benefit is negligible even though the absorption coefficient of the material at this frequency is approximately 0.7. 2.2.
TEST ARRANGEMENT FOR PANELS
To investigate experimentally how particular panels behave the test arrangement shown in Figure 9 was constructed. In this arrangement a battery of twelve 5 in. diameter loudspeakers was mounted in a sealed box as shown and connected in series electrically. The inside of the speaker box was tightly packed with glass wool thus making the impedance
0 0
0 00
00 0 0
0 ,P!an view wlthout panel
0 0
Optional Fibreglass sheet on speaker surface to suppress air resonances \
Accommodation /for panel
‘,
\\\\\\\\\\\\\\\\\\\
Figure
\
9. Arrangement
\\
for testing panels.
,Fibreglass
PERFORMANCE
OF ACOUSTIC
HOODS
89
behind the cones so high that their motions were substantially independent of the air loading on the front surface. The rigid steel outer frame then housed this speaker unit for accommodating test panels. Panels together with the “picture frame” arrangement normally 30 in. square (effective) could be tested, and the microphone was situated approximately 6 ft above the panel in an acoustically absorbent room. The test procedure consisted of measuring the sound pressure with and without the panel inserted, the ratio between the two thus giving the insertion loss. As an optional condition, a sheet of Fibreglass with holes corresponding to the cone positions was laid on the speaker front surface. This had the effect of suppressing standing wave resonances between the source and panel and thereby simulating “mass law” conditions for high frequencies. By using a suitable correction curve (very similar to curve B of Figure S), it was then possible to approximate to mass law theory (at normal incidence) over quite a wide frequency range. 2.3.
SOME RESULTS
ON PANELS
Experimental confirmation of the theory outlined was attempted for an undamped steel panel. The full curve in Figure IO is the theoretical one for a flat steel plate & in. thick, 30 in. wide and of unlimited length, with the space between source and panel, which was 74 in., having no acoustical absorption. The dashed curve was obtained experimentally,
601-
10
I
I
,
I IllIll
/ I
100
Frequency
I!l!j 1000
(c/s)
Figure IO. Flat steel plate, -& in. (0.16 cm) thick. () Theoretical for plate 30 in. (76 cm) wide, unlimited length; (---) practical for plate 30 in. (76 cm) square. Distance between source and plate=7+ in. (19 cm).
the plate used being 30 in. square. It can be seen that the general prediction on theoretical grounds of resonances and anti-resonances is confirmed experimentally and also that a peak occurs at 900 c/s due to standing waves. The low values of plate resonant frequencies in the practical case, compared with the approximately equivalent theoretical case, were attributed to the fact that the supports were not truly built-in. In Figure I I the effects of mechanical and acoustical damping are illustrated. Curve A is for the undamped steel plate & in. thick with no mechanical or acoustical damping in the system. Consequently the plate resonances and the air resonance at 900 c/s are clearly in evidence. Curve B, however, shows the results when the plate was damped mechanically by means of a pB in. thick layer of Aquaplas antidrumming compound. It can be seen that this treatment reduces the magnitude of the plate resonances but leaves the air resonance,
90
R. S. JACKSON
Frequency
k/s)
Figure I I. Flat steel panel, 76 cm square, 1.6 mm thick. Curve A: panel alone, M= 1.25 g/cma; curve B : panel coated with 1.6 mm layer of Aquaplas, M= 1-5 g/cm2; curve C: as B, but with z-5 cm thick internal layer of Fibreglass, M = I ‘5 g/cm2.
$---\-___ 20
50
100
200
Frequency
500
KJoo
2000
51 10
(c/s)
Figure 12. Flat panels 76 cm square. No Fibreglass. Curve A: Two 1.6 mm steel plates with I mm MV 5 35 varnish between ; Curve B : 3.2 mm steel plate coated with 3.2 mm Aquaplas F 1o2B ; Curve C: 1.6 mm lead and 0.8 mm aluminium plates with I mm MV 535 between.
For the measurements shown by curve C, a I in. thick layer of Fibreglass was inserted on the internal plate surface and it can be seen that this reduces the 900 c/s air resonance. Figure 12 shows three examples of the behaviour of mechanically damped plates. The alternative damping treatment of having two outer parent layers with a viscous material
9’
PERFORMANCE OF ACOUSTIC HOODS
between them produces the results shown in curve A. It can be seen that by using the correct viscous material for the shear layer superior mechanical damping can be obtained especially at low frequencies. This is evident since curve B is for a single plate of equivalent thickness damped with Aquaplas. Curve C shows the effect of including a very heavily damped combination of lead and aluminium. Basic theory has indicated that high attenuation is possible at low frequencies if the plate stiffness is made high. In Figure 13 this is illustrated experimentally, using aluminium honeycomb panels. These panels exhibit a high stiffness-to-mass ratio by virtue of the fact that two outer skins are rigidly spaced apart from each other by a honeycomb core, to
4050-20
, 50
I 100
I 200
/ 500
Frequency
I 1000
I 2000
101JO
k/s)
Figure 13. Aluminium honeycomb panels 76 cm square. Curve A : 9.5 mm thick, 9.5 mm mesh, M=o*16 g/cmz; curve B: 16 mm thick, 9.5 mm mesh, M=0.62 g/cmz; curve C: 25 mm thick, g-5 mm mesh, M= o-67 g/cm*; Dashed curve, Aquaplas and Fibreglass, M= 0.7 g/cm*; curve D : 50 mm thick, 38 mm mesh, M=0*63 g/cm*. Full curves, no mechanical or acoustical damping.
which the skins are cemented with epoxy resin. Consequently the skins are spaced well away from the neutral axis of bending and a stiff light panel results. The four curves refer to four differing thicknesses of panel and it can be seen that at frequencies below IOO c/s more than 30 dB of attenuation is obtainable. It should be pointed out, however, that in a practical hood arrangement the supporting framework for such panels must also be very rigid. An alternative means of obtaining a high stiffness-to-mass ratio is by the use of certain of the expanded plastics. If no temperature problems exist then expanded rigid P.V.C. may be used to advantage. This can be seen from the curves of Figure 14, where curve C, which is for a 3 in. thick panel faced with aluminium, shows over 40 dB attenuation obtainable below IOO c/s. Another virtue of this material is that it can, if necessary, be
92
R. S. JACKSON
moulded to any particular shape desired, thus obviating the use of a framework for smaller sized enclosures. A profitable means of utilizing available mass is to use a double skin construction of two plates separated by an air space. This provides an extremely efficient method for “free plate ” construction on an architectural scale. However, with finite sized panels some ._
1%:____L_Y_____ 30 -
$
____*&_____
e
,____&-----
iii
50
20
100
200
Frequency
500
1000
2000
5oc10
k/s)
Figure 14. Expanded rigid P.V.C. panels, 76 cm square (Plasticell). Curve A: IO cm thick low density material, M= 0.46 g/cm2 (Plasticell D40) ; curve B : 8 cm thick high density material, M = 0*8z g/cm2 (Plasticell DIOO) ; curve C : as B, but with 1.0 mm aluminum sheet on each surface, M= 1.36 g/cm2. c 30 .s .; zoF g I:
IO-
Resonance due to air trapped
between plates
\ 0
60I 10
I
I Illlll 1000
100
Frequency
k/s)
One sheet 24 02 Figure 15. Double glazing : effect of having windows too close together. -, glass, 30 in. (76 cm) square; ---, two sheets 24 oz glass spaced 2% in. (5.7 cm) apart. (Air resonances between source and panel suppressed.)
difficulties are involved and the example of a double glass window illustrates this best. In Figure 15 the two attenuation curves are, respectively, for a single sheet of 24 oz glass 30 in. square (full curve), and for two sheets of the same material spaced 2$ in. apart. It is evident that for frequencies below 160 c/s no benefit is to be derived from having the extra sheet and in fact at 90 c/s conditions are worsened by double glazing. This is because at this frequency a resonance occurs due to the two plates reacting with each other through the
PERFORMANCE
OF ACOUSTIC
HOODS
93
stiff cushion of trapped air. Clearly in the case of glass, this cannot easily be damped without affecting transparency, so resonances of this kind must be reduced in frequency out of the working range by either increasing the spacing or increasing the mass of both panels. In the case of non-transparent constructions, Fibreglass and rock wool have been used to advantage between the sheets, an arrangement which also provides thermal insulation. 3.
UNSEALED
ENCLOSURES
As mentioned previously, many machines cannot be sealed off completely from free space and where a considerable quantity of air must be passed through the enclosure a conventional splitter arrangement must be used on both the inlet and outlet. Enclosed
air
Oreo A, equivalent
At low frequencies,
3 = VI
L
viz d
I--)+w2 C2A
V,
2
is reloted
to
L(
by
42
1
12
(b)
Figure 16. Model for analysis of Helmholtz resonator effect. (a) Ideal unsealed enclosure; (b) typical response for small enclosures.
It is essential to avoid the Helmholtz resonator effect which can occur if there are small inadvertent openings in small enclosures. The effects of this are illustrated in Figure 16. If the machine behaves as a pulsating box as before but there is an opening in the enclosure around it, then, by analysis, the volume of fluid displaced to free space compared with the volume displaced by the machine is given by the equation shown in Figure 16. When the corresponding attenuation is plotted a resonance can be seen occurring at the Helmholtz frequency. Consequently, the area and length of the opening and the volume of enclosed air should be chosen so that this frequency lies below the working range.
R. S. JACKSON 94 To illustrate the effect experimentally the curves shown in Figure 17 were obtained using a glass box 29.2 cm long, 14 cm wide and 14.6 cm deep with a sound source inside (I). Measurements were made for two different conditions of outlet. In the first case, by inserting strips of steel 0.32 cm thick between the longer walls and the bedplate, the whole box was raised by 0.32 cm leaving two outlets each 14 cm wide and 0.32 cm deep. The second condition was obtained by raising the box 2.54 cm with appropriate packing pieces, a vent at one end then being constructed having a section of 14 cm by 1.27 cm and length 3.2 cm. The curves show that at the Helmholtz frequency sound magnification can in fact occur. The particular system chosen for the experiments was designed to illustrate the effect, and resulted in resonant frequencies of the order of IOO c/s, which are probably much higher
Frequency
k/s)
Figure 17. Attenuation produced by glass box having outlets of known dimensions. Curve A : one outlet, 14 cm x 1.27 cm x 3.2 cm long; curve B: two outlets, each of section 14 cm x 0.32 cm formed by raising box from bedplate ; curve C : sealed box. than would be the case if large enclosed volumes were involved. However, when absorbentlined air ducts are to be used to introduce cooling, precautions should be taken to ensure that the resonant frequency of the damped resonator thus produced occurs at a frequency below the range under consideration. In this way, in addition to the attenuation produced by the absorbent lining, some benefit can also be derived from the low pass filter formed by the duct and the enclosed volume. ACKNOWLEDGMENTS
The author wishes to thank the Director of Research, Associated Electrical Industries Limited, Power Group, for permission to publish this paper. REFERENCES I. R. S. JACKSON1962 Acusticu 12, 3. The performance of acoustic hoods at low frequencies. 2. A.E.I. Research Report No. T.P./R. II, 213.
(I),
82-94
SOME ASPECTS OF THE PERFORMANCE
OF ACOUSTIC
HOODSt
R. S. JACKSON A.E.I. Power Group Research Laboratory, Manchester, 17, England (Received 26 May
I 965)
The paper summarizes some previously reported investigations made into the performance of acoustic hoods for enclosing noisy machinery, and outlines how differing applications require their own particular solution. The importance of having sealed acoustic enclosures is stressed but some of the problems involved with unsealed enclosures are also discussed. I. INTRODUCTION
Many instances occur in practice with machinery noise where it is more fruitful to place an enclosure around it rather than try to reduce the noise by treating the machine itself. Enclosures of this kind, known as acoustic hoods, pose many problems for the designer. For example, space and weight are often at a premium insofar as the hood is concerned, and access to the machine may be frequently required. Ideally, the walls of an enclosure should be as massive as possible, e.g., a brick building with a concrete roof, and it is also desirable that the enclosed item should be hermetically sealed from free space by the hood. Unfortunately, for various practical reasons many machines cannot be sealed in this way, and in some applications, particularly on ships and other vehicles, the hood must be as light as possible. Hence the need often arises for a close-fitting “tailor-made ” lightweight hood, elements of which may be removable for inspection of the enclosed machine. The problem then resolves itself into choosing a construction for the walls of the enclosure which is both practicable from an operating point of view (e.g., high temperatures may be involved) and suitable from an acoustical point of view. In the case of machinery noise, it should be borne in mind that discrete sinusoidal components of sound may predominate rather than broad-band sound, and the approach adopted for the enclosing of, say, a power transformer, which is predominantly a low frequency sound generator, may be different from that adopted for a gearbox, which generates discrete components at higher audio frequencies. Consideration must also be given to the nature and size of any openings which may be necessary in an enclosure, since there is little point in having hood walls with high transmission loss if sound is by-passed to free space via the openings. z. SEALED 2.
ENCLOSURES
I. BASIC CONSIDERATIONS The
foremost
consideration
which must be given to a machine
before an enclosure
is
placed around it is to ensure that it is completely isolated mechanically from its surrounding environment. This entails not only placing antivibration mountings between the
machine and its base but also ensuring that any connections such as pipes or electrical cables are so flexible that they do not transmit appreciable vibration from the machine and detract from the hood performance. A typical arrangement for the enclosing of a transformer is illustrated in Figure I where it can be seen that these precautions have in fact been taken. t Presented as a lecture in June 1964 at the conference on “Planning and design for protection from noise” organized by the Society of Acoustic Technology
at the Lanchester 82
College of Technology,
Coventry.
PERFORMANCE
83
OF ACOUSTIC HOODS
For the purposes of analysis it may be considered that a vibrating source and enclosure take the form of “pulsating boxes ” whose dimensions increase and decrease in a periodic manner, but whose sides remain plane throughout these excursions. This model is illustrated in Figure 2. If the sound pressure at some nearby point, P, is measured both Enclosure
Flex
couplings
Concrete “picture
Resilient
Figure
/
I. Acoustic
enclosure
for a transformer.
(motion,
y= waves
6
sin ht
t +)
radiated
(b)
Figure 2. Models for analysis of hood performance. equivalent of (a). Solution of (b) : 2 sin ~(XCOS ~9-
(a) Ideal sealed enclosure;
(b) plane wave
R sin 0) + sin2 0(X2 + R2) -U2
1 ’
S, M, R are plate “ stiffness “, “mass ” and “ damping “.
before and after the hood has been erected, the ratio of these two quantities will give the attenuation of sound produced by the hood (i.e., an “insertion loss”). An exact analysis of the model in Figure a(a) is a very complicated business, involving wave propagation and reflection in three dimensions. However, in the case of a close-fitting hood, where the spacing between the machine surface and the hood wall is small, a
R. S. JACKSON
84
sufficiently good approximation is obtained by considering that the hood walls are subjected to plane waves at normal incidence, since the large radiating surfaces of a machine will encourage these conditions. It is then possible to simplify the analysis to the one-dimensional case shown in Figure z(b). In evaluating this model a most important assumption, one which influences the whole philosophy of acoustic hood theory, is made. This is the assumption that the presence of the enclosure does not in any way affect the oscillatory motions of the surfaces of the machine. Hence, in Figure a(b), it is assumed that the driving plate A has a forced displacement amplitude YO which is the same whether plate B is present or not. The amplitude ratio, Y,/ Y,,, calculated (I) for the plane wave model of Figure a(b) is also shown in Figure 2 and Figure 3 shows graphs of the corresponding attenuation. This attenuation is a function of the mass, damping and elastic restraint of the attenuating plate and also of the distance between the plates. The three full curves illustrate how this function behaves for three values of elastic restraint, SO. The dashed curve shows the familiar “mass law” curve for a plate of the same area density.
I
60 IO
I
I
I 111111
I
I
100
Frequency
IllIll
I
II
IO00
(c/s)
Figure 3. Theoretical curves for attenuation derived from equation of Figure 2. M= 1.6 g/cm2: IOO c/s, Q=30 at 105 c/s. C:fO=475 c/s, Z=Igcm(7iin.).A:fo=oc/s,Q=30at33c/s.B:fo= Q = 30 at 475 c/s.
The most important consequence of the above-mentioned assumption is now clear: this is that a plate (or machine) vibrating with a constant amplitude is not a constant sound energy generator. This is best illustrated by the curve for zero stiffness where it can be seen that at low frequencies the sound energy radiated from the system is greater after the enclosure has been inserted than before. Clearly, the “mass law” concept based on energy considerations is not valid for acoustic hoods. The behaviour indicated by the family of curves of Figure 3 may be summarized as follows. At low frequencies, plates A and B and the air trapped between them form a massspring system which resonates at some low audio frequency. Even when plate B behaves as a pure mass a resonance still occurs due to the stiff cushion of air trapped between the plates. To lower this resonant frequency out of the working range either the mass of plate B or the spacing between plates must be increased. To increase the resonant frequency for a plate of given mass, and thereby increase the attenuation at low frequencies, the mechanical stiffness associated with the plate must be increased. To reduce the resonant build-up requires the introduction of mechanical damping into plate B. At high frequencies, more particularly at frequencies where the plate spacing is an integral number of half wavelengths of sound in air, standing wave resonances occur
PERFORMANCE
OF ACOUSTIC
HOODS
85
in the air between the plates. These resonances can be suppressed only by soundabsorbent material between the plates. These effects will be discussed in more detail later. 1
,t:
:
10
.L=
sj 20
5 Q 40
z
50 30 60
1 ____--I
IO
I
I
Illlll!
I
I
lllllll
100
II
1000
Frequency
(c/s)
Figure 4. Attenuation produced by steel box 30.5 cm x 152 cm x 14.0 cm deep. Wall thickness = a.03 mm; mass per unit area= 1.6 g/cm* of volume of air enclosed= 4750 cc. Dotted curve theoretical from curve C in Figure z.
Long Vibrating source (displacing volume K of fluid per plate width.)
Equotion for oir a5 ax2
of
_
I
flat
plates
clamped to rigid framework, each plate displacing V, of fuid to free space
motion A
Equation
of
motion
a2y
-227
Section of flat
of a plates
practical clomped
hood arrangement consisting in CI rigid framework
Figure 5. Models for analysis of framed hood performance. Approximate solution:
2 = [l+&~q], where
e =
WI C'
s
* = PC’ al ’ 2
cr(coth cra + cot
aa)
-a
1 ,
Ep = “ plate ” modulus of elasticity of plate material, d = density of plate material.
To illustrate how these theoretical expectations are confirmed in practice, measurements have been made on a number of small boxes. In Figure 4 the agreement between theoretical concepts and practical measurement is shown for a small steel box of the dimensions indicated. The resonance in the 500 c/s region is due to the walls of the box, and that at
86
R. S. JACKSON
900 c/s to standing waves inside the box. The curves also illustrate that good attenuation is obtainable at low frequencies with a stiff-walled construction. Often a more practical arrangement for a larger sized acoustic hood is to erect around the machine a rigid framework to which the walls of the enclosure can be bolted (or welded) to form a complete hood. A section of such an arrangement is shown schematically in Figure 5. The behaviour of this construction can be readily analysed mathematically (2), especially if the plates are considered to be infinitely long. What is required from the analysis is the ratio of the volume displacement of a plate to the volume displacement of a corresponding area of the source. The approximate solution for this ratio is included in Figure 5 and in Figure 6 the corresponding attenuation function has been plotted for a & in. thick aluminium plate clamped at its edges. This new analysis illustrates the significance of plate stiffness better. For example, at low frequencies the sound attenuation is positive because, although the mass reactance of the plate in this range is negligible, its volume displacement is now controlled by its
Frequency
k/s)
Figure 6. Theoretical curve for attenuation of &in. thick (0.635 cm) aluminium plate (unlimited length, clamped at edges). Distance between supports = a = 76 cm (30 in.) ; distance between source and plate = I= 19 cm (7fi in.).
ability to resist flexure, and hence with rigid supports a flexurally stiff plate will provide more attenuation than a limp one of the same mass. As the frequency is increased a peak is approached at a frequency approximately equal to that of the “fundamental mode” of vibration of the (clamped) plate, the frequency of the peak being increased somewhat because of the trapped air stiffness. As the frequency is increased still further a succession of troughs and peaks is seen, being caused by flexural modes of vibration of the plate, and interspersed with these, at 900 c/s and multiples of this frequency, standing wave resonances due to the air between the plates occur. Hence two distinct kinds of resonant conditions exist: plate resonances and air resonances. A closer examination of the nature of the plate resonances reveals the behaviour shown in Figure 7. At the “fundamental” resonant frequency the plate bends approximately as shown, and at any instant of time all points on the plate move in the same direction. In this case plate curvature is comparatively small, so that plate damping treatments are least effective for this mode. Above the fundamental mode frequency the plate no longer moves unidirectionally since the outer regions now start to move in the opposite direction to the centre regions. Consequently, the net volume of fluid displaced by the plate decreases as the frequency is
PERFORMANCE
OF ACOUSTIC
HOODS
87
increased until a condition is reached whereby as much fluid is drawn inwards as is displaced outwards and a sharp trough appears in the curve. Slightly above this frequency the next resonant mode is reached, but in this case the plate is flexing much more sharply than for the fundamental mode and so is more amenable to damping. Similar arguments hold at progressively higher frequencies. As regards the air resonances, if the plate spacing is chosen to be 74 in. for example, it follows that standing waves occur at approximately goo c/s and multiples of this frequency.
Large displaced volume low flexure, not easily damped
Large plate but no net displacement
motions volume
Large net volume displacement, higher flexure, more amenable to damping
Figure 7. Motions of clamped plate subjected to uniform sound pressure.
Frequency
(c/s)
Figure 8. Build-up of sound pressure due to presence of enclosure (plane wave model with I = 74 in. (19 cm). Curve A : No acoustic absorption between plates ; Curve B : 2 in. crown zoo surfaced with 2 in. Superfine Fibreglass at hood surface.
Had the spacing been chosen larger than this then the lowest standing wave frequency would have been correspondingly lower, in accordance with the usual plane wave theory. Analysis shows that at these preferred frequencies of air resonance the trapped air behaves (ideally) as an infinite impedance, coupling the two plates together. In other words the “attenuating” plate must move with the same motion as the driving plate since theoretically it would require an infinite force to move one relative to the other. Clearly, this form of resonance can be suppressed only by applying absorbent treatment in the trapped air itself. Any amount of mechanical damping may be applied to the attenuating plate without making the slightest difference to any of these air resonances.
88
R. S. JACKSON
Sound absorbent material of the rock- or glass-wool kind is thus clearly beneficial at standing wave frequencies. At frequencies removed from these preferred values little advantage is to be gained from such treatment, particularly at low frequencies. This is best illustrated by the curves of Figure 8. In these curves the plane wave sound pressure at the hood wall has been plotted for the models of either Figure z(b) or Figure 5, assuming the motion of the hood wall to be much less than that of the source. The curves thus show the build-up of sound pressure due to the presence of the enclosure, and since it is under the action of this pressure that plate B moves, this must be reduced if the absorbent treatment is to be of any value. Curve A shows that in the absence of any absorbent there are standing wave resonances at the appropriate frequencies. Furthermore, in this case there is a build-up of pressure at 50 c/s 15 dB. of approximately Curve B was computed from absorption coefficient data obtained experimentally. In this example, a 2 in. thick layer of Crown 200 Fibreglass faced with a further + in. thick layer of Superfine Fibreglass was assumed to be on the hood internal surface. It can be seen that at the standing wave frequencies the absorbent material suppresses the resonances but away from resonance, as, for example, at one octave below the fundamental frequency the benefit is negligible even though the absorption coefficient of the material at this frequency is approximately 0.7. 2.2.
TEST ARRANGEMENT FOR PANELS
To investigate experimentally how particular panels behave the test arrangement shown in Figure 9 was constructed. In this arrangement a battery of twelve 5 in. diameter loudspeakers was mounted in a sealed box as shown and connected in series electrically. The inside of the speaker box was tightly packed with glass wool thus making the impedance
0 0
0 00
00 0 0
0 ,P!an view wlthout panel
0 0
Optional Fibreglass sheet on speaker surface to suppress air resonances \
Accommodation /for panel
‘,
\\\\\\\\\\\\\\\\\\\
Figure
\
9. Arrangement
\\
for testing panels.
,Fibreglass
PERFORMANCE
OF ACOUSTIC
HOODS
89
behind the cones so high that their motions were substantially independent of the air loading on the front surface. The rigid steel outer frame then housed this speaker unit for accommodating test panels. Panels together with the “picture frame” arrangement normally 30 in. square (effective) could be tested, and the microphone was situated approximately 6 ft above the panel in an acoustically absorbent room. The test procedure consisted of measuring the sound pressure with and without the panel inserted, the ratio between the two thus giving the insertion loss. As an optional condition, a sheet of Fibreglass with holes corresponding to the cone positions was laid on the speaker front surface. This had the effect of suppressing standing wave resonances between the source and panel and thereby simulating “mass law” conditions for high frequencies. By using a suitable correction curve (very similar to curve B of Figure S), it was then possible to approximate to mass law theory (at normal incidence) over quite a wide frequency range. 2.3.
SOME RESULTS
ON PANELS
Experimental confirmation of the theory outlined was attempted for an undamped steel panel. The full curve in Figure IO is the theoretical one for a flat steel plate & in. thick, 30 in. wide and of unlimited length, with the space between source and panel, which was 74 in., having no acoustical absorption. The dashed curve was obtained experimentally,
601-
10
I
I
,
I IllIll
/ I
100
Frequency
I!l!j 1000
(c/s)
Figure IO. Flat steel plate, -& in. (0.16 cm) thick. () Theoretical for plate 30 in. (76 cm) wide, unlimited length; (---) practical for plate 30 in. (76 cm) square. Distance between source and plate=7+ in. (19 cm).
the plate used being 30 in. square. It can be seen that the general prediction on theoretical grounds of resonances and anti-resonances is confirmed experimentally and also that a peak occurs at 900 c/s due to standing waves. The low values of plate resonant frequencies in the practical case, compared with the approximately equivalent theoretical case, were attributed to the fact that the supports were not truly built-in. In Figure I I the effects of mechanical and acoustical damping are illustrated. Curve A is for the undamped steel plate & in. thick with no mechanical or acoustical damping in the system. Consequently the plate resonances and the air resonance at 900 c/s are clearly in evidence. Curve B, however, shows the results when the plate was damped mechanically by means of a pB in. thick layer of Aquaplas antidrumming compound. It can be seen that this treatment reduces the magnitude of the plate resonances but leaves the air resonance,
90
R. S. JACKSON
Frequency
k/s)
Figure I I. Flat steel panel, 76 cm square, 1.6 mm thick. Curve A: panel alone, M= 1.25 g/cma; curve B : panel coated with 1.6 mm layer of Aquaplas, M= 1-5 g/cm2; curve C: as B, but with z-5 cm thick internal layer of Fibreglass, M = I ‘5 g/cm2.
$---\-___ 20
50
100
200
Frequency
500
KJoo
2000
51 10
(c/s)
Figure 12. Flat panels 76 cm square. No Fibreglass. Curve A: Two 1.6 mm steel plates with I mm MV 5 35 varnish between ; Curve B : 3.2 mm steel plate coated with 3.2 mm Aquaplas F 1o2B ; Curve C: 1.6 mm lead and 0.8 mm aluminium plates with I mm MV 535 between.
For the measurements shown by curve C, a I in. thick layer of Fibreglass was inserted on the internal plate surface and it can be seen that this reduces the 900 c/s air resonance. Figure 12 shows three examples of the behaviour of mechanically damped plates. The alternative damping treatment of having two outer parent layers with a viscous material
9’
PERFORMANCE OF ACOUSTIC HOODS
between them produces the results shown in curve A. It can be seen that by using the correct viscous material for the shear layer superior mechanical damping can be obtained especially at low frequencies. This is evident since curve B is for a single plate of equivalent thickness damped with Aquaplas. Curve C shows the effect of including a very heavily damped combination of lead and aluminium. Basic theory has indicated that high attenuation is possible at low frequencies if the plate stiffness is made high. In Figure 13 this is illustrated experimentally, using aluminium honeycomb panels. These panels exhibit a high stiffness-to-mass ratio by virtue of the fact that two outer skins are rigidly spaced apart from each other by a honeycomb core, to
4050-20
, 50
I 100
I 200
/ 500
Frequency
I 1000
I 2000
101JO
k/s)
Figure 13. Aluminium honeycomb panels 76 cm square. Curve A : 9.5 mm thick, 9.5 mm mesh, M=o*16 g/cmz; curve B: 16 mm thick, 9.5 mm mesh, M=0.62 g/cmz; curve C: 25 mm thick, g-5 mm mesh, M= o-67 g/cm*; Dashed curve, Aquaplas and Fibreglass, M= 0.7 g/cm*; curve D : 50 mm thick, 38 mm mesh, M=0*63 g/cm*. Full curves, no mechanical or acoustical damping.
which the skins are cemented with epoxy resin. Consequently the skins are spaced well away from the neutral axis of bending and a stiff light panel results. The four curves refer to four differing thicknesses of panel and it can be seen that at frequencies below IOO c/s more than 30 dB of attenuation is obtainable. It should be pointed out, however, that in a practical hood arrangement the supporting framework for such panels must also be very rigid. An alternative means of obtaining a high stiffness-to-mass ratio is by the use of certain of the expanded plastics. If no temperature problems exist then expanded rigid P.V.C. may be used to advantage. This can be seen from the curves of Figure 14, where curve C, which is for a 3 in. thick panel faced with aluminium, shows over 40 dB attenuation obtainable below IOO c/s. Another virtue of this material is that it can, if necessary, be
92
R. S. JACKSON
moulded to any particular shape desired, thus obviating the use of a framework for smaller sized enclosures. A profitable means of utilizing available mass is to use a double skin construction of two plates separated by an air space. This provides an extremely efficient method for “free plate ” construction on an architectural scale. However, with finite sized panels some ._
1%:____L_Y_____ 30 -
$
____*&_____
e
,____&-----
iii
50
20
100
200
Frequency
500
1000
2000
5oc10
k/s)
Figure 14. Expanded rigid P.V.C. panels, 76 cm square (Plasticell). Curve A: IO cm thick low density material, M= 0.46 g/cm2 (Plasticell D40) ; curve B : 8 cm thick high density material, M = 0*8z g/cm2 (Plasticell DIOO) ; curve C : as B, but with 1.0 mm aluminum sheet on each surface, M= 1.36 g/cm2. c 30 .s .; zoF g I:
IO-
Resonance due to air trapped
between plates
\ 0
60I 10
I
I Illlll 1000
100
Frequency
k/s)
One sheet 24 02 Figure 15. Double glazing : effect of having windows too close together. -, glass, 30 in. (76 cm) square; ---, two sheets 24 oz glass spaced 2% in. (5.7 cm) apart. (Air resonances between source and panel suppressed.)
difficulties are involved and the example of a double glass window illustrates this best. In Figure 15 the two attenuation curves are, respectively, for a single sheet of 24 oz glass 30 in. square (full curve), and for two sheets of the same material spaced 2$ in. apart. It is evident that for frequencies below 160 c/s no benefit is to be derived from having the extra sheet and in fact at 90 c/s conditions are worsened by double glazing. This is because at this frequency a resonance occurs due to the two plates reacting with each other through the
PERFORMANCE
OF ACOUSTIC
HOODS
93
stiff cushion of trapped air. Clearly in the case of glass, this cannot easily be damped without affecting transparency, so resonances of this kind must be reduced in frequency out of the working range by either increasing the spacing or increasing the mass of both panels. In the case of non-transparent constructions, Fibreglass and rock wool have been used to advantage between the sheets, an arrangement which also provides thermal insulation. 3.
UNSEALED
ENCLOSURES
As mentioned previously, many machines cannot be sealed off completely from free space and where a considerable quantity of air must be passed through the enclosure a conventional splitter arrangement must be used on both the inlet and outlet. Enclosed
air
Oreo A, equivalent
At low frequencies,
3 = VI
L
viz d
I--)+w2 C2A
V,
2
is reloted
to
L(
by
42
1
12
(b)
Figure 16. Model for analysis of Helmholtz resonator effect. (a) Ideal unsealed enclosure; (b) typical response for small enclosures.
It is essential to avoid the Helmholtz resonator effect which can occur if there are small inadvertent openings in small enclosures. The effects of this are illustrated in Figure 16. If the machine behaves as a pulsating box as before but there is an opening in the enclosure around it, then, by analysis, the volume of fluid displaced to free space compared with the volume displaced by the machine is given by the equation shown in Figure 16. When the corresponding attenuation is plotted a resonance can be seen occurring at the Helmholtz frequency. Consequently, the area and length of the opening and the volume of enclosed air should be chosen so that this frequency lies below the working range.
R. S. JACKSON 94 To illustrate the effect experimentally the curves shown in Figure 17 were obtained using a glass box 29.2 cm long, 14 cm wide and 14.6 cm deep with a sound source inside (I). Measurements were made for two different conditions of outlet. In the first case, by inserting strips of steel 0.32 cm thick between the longer walls and the bedplate, the whole box was raised by 0.32 cm leaving two outlets each 14 cm wide and 0.32 cm deep. The second condition was obtained by raising the box 2.54 cm with appropriate packing pieces, a vent at one end then being constructed having a section of 14 cm by 1.27 cm and length 3.2 cm. The curves show that at the Helmholtz frequency sound magnification can in fact occur. The particular system chosen for the experiments was designed to illustrate the effect, and resulted in resonant frequencies of the order of IOO c/s, which are probably much higher
Frequency
k/s)
Figure 17. Attenuation produced by glass box having outlets of known dimensions. Curve A : one outlet, 14 cm x 1.27 cm x 3.2 cm long; curve B: two outlets, each of section 14 cm x 0.32 cm formed by raising box from bedplate ; curve C : sealed box. than would be the case if large enclosed volumes were involved. However, when absorbentlined air ducts are to be used to introduce cooling, precautions should be taken to ensure that the resonant frequency of the damped resonator thus produced occurs at a frequency below the range under consideration. In this way, in addition to the attenuation produced by the absorbent lining, some benefit can also be derived from the low pass filter formed by the duct and the enclosed volume. ACKNOWLEDGMENTS
The author wishes to thank the Director of Research, Associated Electrical Industries Limited, Power Group, for permission to publish this paper. REFERENCES I. R. S. JACKSON1962 Acusticu 12, 3. The performance of acoustic hoods at low frequencies. 2. A.E.I. Research Report No. T.P./R. II, 213.