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7.6 ACOUSTIC ENCLOSURES

Back

In a room containing a source of noise, such as a piece of machinery,

acoustic treatment of the walls of the room may not reduce the sound

level in the room sufficiently. This is especially true when the direct field

predominates over the reverberant field at the receiver location. When a

reduction in the sound level of more than about 10 dB is required, an enclosure

for the noise source is often the most practical solution to control noise

of an existing machine. Reductions in the noise levels by 20–30 dB are

common with complete or full machine enclosures. Noise reductions as

high as 50dB may be achieved with special isolation treatment for the

enclosure.

Generally, the only inherent disadvantage, if accessibility to the

machine is not required, is the initial cost of the enclosure. If accessibility

to the machine is required (to feed in material, to make adjustments, etc.),

then a partial enclosure must be used, and careful attention must be directed

to the design of the openings in the enclosure.

Examples of enclosures are shown in Fig. 7-10 (enclosure for an automatic

press) and Fig. 7-11 (enclosure for a saw).

Room Acoustics 299

FIGURE 7-10 Enclosure for an automatic press.

7.6.1 Small Acoustic Enclosures

An enclosure is considered to be ‘‘small’ if the bending wavelength of the

enclosure wall is large compared with the largest panel dimension and if the

wavelength of the sound inside the enclosure is large compared with the

largest interior dimension of the enclosure. The wavelength of the bending

wave is a function of the frequency:

_b ј

_cLh ffiffiffi

3p f

_ _1=2

(7-74)

The quantity cL is the speed of longitudinal waves in the enclosure wall

material, see Eq. (4-156), and h is the thickness of the enclosure wall. For

practical purposes, the enclosure may be considered to be ‘‘small’’ if the

following condition is met:

Lmax

_ ј

fLmax

c _ 0:1 (7-75)

The quantity Lmax is the largest interior dimension of the enclosure, and c is

the speed of sound for the air in the enclosure.

The enclosure acts to reduce the acoustic power radiated from the

system, as shown in Fig. 7-12. If the acoustic power radiated from the

300 Chapter 7

FIGURE 7-11 Enclosure for a gang rip saw for wood. The cover is 3-inch thick

plywood lined with 1-inch thick polyurethane foam. (From Handbook of Acoustical

Enclosures and Barriers, R. K. Miller and W. V. Motone, 1978. Used by permission

of the Fairmont Press, Inc.)

enclosure is denoted by Wout, the insertion loss (IL) for the system is defined

by the following expression:

IL ј 10 log10рW=WoutЮ ј LW _ LW;out (7-76)

For a small enclosure, the air space and the enclosure walls are acoustically

coupled. In this case, the surface absorption and wall transmission

loss have little effect on the performance of the enclosure. The most important

factor is the stiffness of the enclosure walls. The power ratio for a small

sealed (no openings) enclosure may be calculated from the following expression

(Veґ r, 1973):

Wout ј 1 ю

_oc2_Cwj

" #2

(7-77)

The quantity Vo is the volume of air in the enclosure, _o is the density of the

air in the enclosure, c is the speed of sound in the air in the enclosure, and

Cwj are the volume compliances of each of the walls.

The volume compliance of a homogeneous panel with fixed (clamped)

edges is found from the following expression (Timoshenko and Woinowsky-

Krieger, 1959):

Cw ј

S3w

Fр_Ю

_2B

(7-78)

The quantity Sw is the surface area of the panel; _ ј a=b 1 is the aspect

ratio for the panel, where a is the larger edge dimension of the panel, and b is

the smaller edge dimension of the panel. The quantity B is the flexural

Room Acoustics 301

FIGURE 7-12 Nomenclature for an enclosure.

rigidity for the panel. For a homogeneous panel of thickness h, with

Young’s modulus E and Poisson’s ratio , the flexural rigidity is given by

the following expression:

B ј

Eh3

12р1 _ 2Ю

(7-79)

The flexural rigidity for a two-layer panel is given by Eq. (4-184), and the

flexural rigidity of a rib-stiffened panel is given by Eq. (4-190).

The function f р_Ю in Eq. (7-78) for a panel with clamped edges may be

estimated from the following expression:

Fр_Ю ј р3:50=_8Юf1 ю 1:033 tanhЅр_=2Юр_ _ 1Ю_g (7-80)

If all of the panels of the enclosure are made of the same material and

have the same thickness h, the summation for all the walls of the enclosure in

Eq. (7-78) may be written as follows:

_Cwj ј

12р1 _ 2Ю

Eh3 _рS3w

j=_2j

ЮFр_jЮ (7-81)

It may be observed from Eq. (7-77) that the insertion loss for a small

enclosure is increased if the enclosure walls are made stiffer, since an

increase in the flexural rigidity results in a decrease in the panel volume

complaince. A very small volume compliance of the enclosure panels results

in a large value of the power ratio, W=Wout, or a small value of the power

radiated from the enclosure, Wout, relative to the power radiated by the

noise source, W.

A geometry that exhibits higher stiffness than the rectangular box

geometry is a cylindrical body with two hemispherical end caps (Beranek

and Veґ r, 1992). Insertion losses of as high as 50 dB have been achieved with

this geometry using no absorbing material on the interior of the enclosure.

Another approach to achieving small enclosure wall compliance is to

use a composite material consisting of a honeycomb core between two plates

(Fuchs, et al., 1989). In the research reported by these authors, the plate

facing the noise source had circular openings over each honeycomb cavity,

which produced a resonator element to absorb energy. The plate containing

the holes was covered with a thin membrane to prevent contaminants from

entering the cavities and to provide additional energy dissipation. Insertion

loss values on the order of 20 dB were obtained with a 100-mm thick wall for

the frequency range from 31.5 Hz to 8000 Hz.

Example 7-7. A small motor is to be enclosed in a rectangular enclosure

having dimensions 200mm long _ 100mm wide _ 100mm high (7.87 in_

302 Chapter 7

3.94 in _ 3.94 in). There is no sound transmitted through the floor of the

enclosure, so only the two end walls and three side walls are considered. The

enclosure is constructed of 14-gauge steel sheet, 1.9mm (0.0747 in) thick.

The air volume within the enclosure is 1.50 dm3 (91.5in3), and the air is at

308C (868F), for which _o ј 0:859 kg=m3 (0.0536lbm=ft3) and c ј 349 m/s

(1145 fps). Determine the insertion loss for the enclosure for a frequency of

125 Hz.

From Appendix C, we find the following property values for steel:

Young’s modulus, E ј 200 GPa р29 _ 106 psi)

Poisson’s ratio, ј 0:27

Speed of longitudinal waves, cL ј 5110 m/s (16,770 fps)

Let us check the condition given by Eq. (7-75) to determine the applicability

of the ‘‘small-enclosure’’ analysis:

fLmax

c ј р125Юр0:200Ю

р349Ю ј 0:0716 < 0:10

Next, let us check the condition given by Eq. (7-74) to determine the wavelength

of bending waves in the panels of the enclosure:

_b ј р_Юр5100Юр0:0019Ю ffiffiffi3p р125Ю

_ _1=2

ј 0:375m ј 375mm > 200mm

The panel dimensions do meet the conditions for the ‘‘small-enclosure’’

analysis.

The compliance for each of the enclosure walls may be calculated. For

the end walls, the aspect ratio is _1 ј 100=100 ј 1. The value of the function

defined by Eq. (7-80) is as follows:

Fр_1Ю ј р3:50Ю=р_8Ю ј 3:689 _ 10_3

There are two end walls, so the first term in the summation in Eq. (7-81) has

the following value:

2S3

w1Fр_1Ю

_21

ј р2Юр0:010Ю3р3:689Юр10_3Ю

р1:00Ю2 ј 7:378 _ 10_9 m6

The aspect ratio for the side walls is _2 ј 200=100 ј 2:

Fр_2Ю ј р3:50=_8Юf1 ю р1:033Ю tanhЅр_=2Юр2:00 _ 1Ю_g ј 7:183 _ 10_3

Room Acoustics 303

There are three side walls, so the second termin the summation in Eq. (7-81)

has the following values:

3S3 w2Fр_2Ю

_22

ј р3Юр0:020Ю3р7:183Юр10_3Ю

р2:00Ю2 ј 4:310_10_9 m6

The summation of the compliances for the walls of the enclosure may

be calculated from Eq. (7-81):

_Cwj ј р12Юр1_272Юр7:378ю4:310Юр10_9Ю

р200Юр109Юр0:0019Ю3 ј 94:79_10_12 m5=N

(or m3=PaЮ

The sound power ratio may be found from Eq. (7-77):

Woutј 1 ю р1:50Юр10_3Ю

р0:859Юр349Ю2р94:79Юр10_12Ю

" #2

ј р1ю151:2Ю2 ј 23,179

The insertion loss is found from its definition, Eq. (7-76):

IL ј 10 log10р23,179Ю ј 43:7dB

7.6.2 Large Acoustic Enclosures

An enclosure may be considered to be ‘‘large’’ when the enclosure volume

exhibits a large number of resonant modes of vibration. A large enclosure

usually meets the following condition:

fV1=3

c 1 (7-82)

The quantity Vo is the volume of air in the enclosure, f is the frequency of

the sound in the enclosure, and c is the sonic velocity in the air in the

enclosure.

There are several paths along which sound may be transmitted from

the noise source within the enclosure to the space outside the enclosure,

including (a) through the enclosure walls, (b) through openings in the enclosure

walls, and (c) through solid structural supports. The magnitude of the

sound transmitted through the walls of the enclosure is a function of the

sound power transmission coefficient at of the walls, as discussed in Chapter

4. The magnitude of the sound leaking through openings in the enclosure

can also be expressed in terms of an equivalent sound power transmission

coefficient (Mechel, 1986). By using proper vibration isolation, the transmission

of sound through solid supports should be reduced to a negligible

contribution for the enclosure to be effective in noise control.

304 Chapter 7

It is important that a large fraction of the acoustic energy radiated

fromthe noise source inside the enclosure be dissipated within the enclosure.

But, it is equally important to block the transmission of sound through the

enclosure walls. To achieve this condition, the enclosure walls are usually

constructed of a composite material, with the inside layer having a large

surface absorption coefficient and the other layer or layers having a large

transmission loss or small sound power transmission coefficient.

The acoustic power radiated by the noise source W is equal to the

sound power absorbed or dissipated at the wall surface plus the energy

transmitted through the walls:

W ј Wtr юWabs ј р_Sjatj=SoЮWinc юр_Sj_j=SoЮWinc (7-83)

The quantity Winc is the acoustic power incident on the enclosure walls from

the noise source, Sj is the surface area of the jth component of the enclosure

walls, and So is the total surface area of the enclosure. The power radiated

from the surface of the enclosure to the surrounding space is the power that

has been transmitted through the walls:

Wout ј р_Sjatj=SoЮWinc (7-84)

The sound power ratio for the enclosure may be found by dividing the

power from Eq. (7-83) by the power from Eq. (7-84):

Wout ј 1 ю

_Sj_j

_Sjatj

(7-85)

The insertion loss is defined by Eq. (7-76).

The acoustic pressure within the enclosure may be determined from

Eq. (7-10):

Winc ј 1

4DRcSo ј

p2cSo

4_oc2 ј

p2So

4_oc

(7-86)

The incident power Winc may be found from Eq. (7-83) and combined with

Eq. (7-86):

_oc ј

_Sjatj ю_Sj_j

(7-87)

For partial enclosures or enclosures with openings, the absorptivities

and sound power transmission coefficients for the openings are required.

Some typical property values for materials used for covers of openings are

given in Table 7-4.

The design value for the ‘‘absorptivity’’ of a simple opening is

_ ј 1:00. Although the sound power transmission coefficient for an opening

Room Acoustics 305

would also be equal to 1, there is a directional effect for the opening, as far

as the operator is concerned. In this case, the transmission coefficient should

be modified for the directivity and diffraction effects on the opening. The

following values are recommended for the effective transmission coefficient

for simple openings (no cover) in an enclosure (Faulkner, 1976), assuming

that the operator is located in front of the enclosure:

(a) Front opening, at ј 1

(b) Side or top opening:

no reflective surfaces nearby, at ј 1=3

with reflective surfaces nearby, at ј 2=3

306 Chapter 7

TABLE 7-4 Acoustic Properties for Some Materials Used for Covers of Openings

in Enclosures

Material

Octave band center frequency, Hz

125 250 500 1,000 2,000 4,000

Surface absorption coefficient, _

Glass 0.18 0.06 0.04 0.03 0.03 0.02

Polyvinyl chloride (PlexiglasTM) 0.20 0.07 0.05 0.04 0.04 0.03

Leaded vinyl curtain 0.33 0.88 0.79 0.69 0.53 0.26

Sound power transmission coefficient, at

Glass, 1

4 in thick 0.020 0.0050 0.0032 0.0020 0.0016 0.0013

Double glass, 1

4 in _ 1

2 in _ 1

4 in 0.005 0.004 0.004 0.002 0.0016 0.0010

Polyvinyl chloride film:

0.0015 in thick, 1 layer 0.95 0.90 0.63 0.170 0.043 0.013

0.0015 in thick, 2 layers 0.90 0.70 0.17 0.043 0.013 0.013

Polyvinyl sheet (PlexiglasTM),

4 in thick

0.025 0.020 0.0063 0.0016 0.0005 0.000063

Polyvinyl sheet (PlexiglasTM),

2 in thick

0.0079 0.0050 0.0025 0.00063 0.00063 0.00020

Leaded vinyl curtain,

0.064 in thick

0.050 0.025 0.010 0.0025 0.0008 0.0003

Leaded vinyl curtain,

2 in thick

0.063 0.025 0.0050 0.0005 0.00016 0.00013

Polycarbonate film (LexanTM),

0.25 in thick

0.063 0.016 0.0040 0.0020 0.0020 0.0020

PC film, 0.50 in thick 0.016 0.0040 0.0020 0.0020 0.0020 0.0020

PC film, 2 layers, each 0.25 in

thick with 2-in space

0.013 0.0020 0.00063 0.00025 0.00010 0.00006

no reflective surfaces nearby, at ј 1=6

with reflective surfaces nearby, at ј 1=3

If there are ventilating ducts or ‘‘sound traps’’ connected to the enclosure,

an equivalent sound power transmission coefficient may be related to

the decrease in the sound power level from the duct inlet to outlet, _Lw:

at;eff ј 10__Lw=10 (7-88)

The change in the sound power level in the ventilation duct may be estimated

according to the material presented in Sec. 5.11.

Example 7-8. A production machine has a sound power level spectrum

given in Table 7-5. The machine is operated in a room having dimensions

of 20m_20m_4m high (65.6 ft _65:6ft_13:1ft high). The room has an

average surface absorption coefficient as given in Table 7-5. The directivity

factor for the machine is unity, and the operator is located 3m (9.8 ft) from

the machine. It is desired to reduce the noise from the machine by placing

the machine inside an enclosure having a width of 1.80m(5.91ft), a length of

1.20m (3.94 ft), and a height of 1.00m (3.28 ft). To allow for material flow

into and out of the enclosure, there are two openings (one in each side)

300mm _ 200mm (11.8 in _ 7.87 in), as shown in Fig. 7-13. The enclosure

is constructed of 25mm (1 in) thick plywood, covered with a 1-in layer of

acoustic absorbent material on the inside. The transmission loss and absorption

coefficients for the materials are given in Table 7-5. Determine the

sound pressure level at the operator’s location both with and without the

enclosure in place.

Let us first determine the sound pressure level if the enclosure were not

in place. The calculations will be made in detail for the 500 Hz octave band,

and the results for the other octave bands are given in Table 7-5. The surface

area of the room is found as follows:

So ј р2Юр20 ю 20Юр4:00Ю ю р2Юр20Юр20Ю ј 1120m2 р12,060 ft2Ю

The room constant (at 500 Hz) is found from Eq. (7-13):

R ј

__So

1 _ _ ј р0:051Юр1120Ю

р1 _ 0:051Ю ј 60:19m2

The sound pressure level at the operator’s location, without the enclosure

in place, is calculated from Eq. (7-18):

Room Acoustics 307

308 Chapter 7

TABLE 7-5 Solution for Example 7-8

Item

Octave band center frequency, Hz

125 250 500 1,000 2,000 4,000

Given data:

Room average absorption coefficient, __ 0.035 0.044 0.051 0.070 0.043 0.056

Sound power level, LW, dB 103 109 114 117 113 107

Room constant, R, m2 40.62 51.55 60.19 84.30 47.88 66.44

10 log10

ю 1

2_r2

_ _

; dB

_9.7 _10.6 _11.2 _12.5 _10.3 _11.6

Enclosure TL, dB 18.4 19.0 19.0 19.0 19.0 25.0

Enclosure _1 0.16 0.27 0.63 0.97 0.99 0.96

Without the enclosure in place:

Lop

(OB), dB 93.4 98.5 102.9 104.6 102.8 95.5

With the enclosure:

at1 0.0145 0.01259 0.01259 0.01259 0.01259 0.00316

S1at1, m2 0.1162 0.1012 0.1012 0.1012 0.1012 0.0254

S2at2, m2 0.0040 0.0040 0.0040 0.0040 0.0040 0.0040

_Sjatj, m2 0.1202 0.1052 0.1052 0.1052 0.1052 0.0294

S1_1 1.286 2.171 5.065 7.780 7.960 7.718

S2_2 0.120 0.120 0.120 0.120 0.120 0.120

_Sj_j, m2 1.406 2.291 5.185 7.900 8.080 7.838

W=Wout 12.70 22.78 50.29 76.10 77.81 267.6

IL, dB 11.0 13.6 17.0 18.8 18.9 24.3

LW;out, dB 92.0 95.4 97.0 98.2 94.2 82.7

Lp(OB), dB 82.4 84.9 85.9 85.8 83.9 71.2

p ј 114ю10 log10

60:19 ю

р4_Юр3:00Ю2

_ _

ю0:1

p ј 114юр_11:2Юю0:1 ј 102:9dB

The calculations for the other octave bands are given in Table 7-5. If

the octave bands are combined to obtain the A-weighted sound level, we

obtain the following value, without the enclosure:

A ј 108:4 dBA (without the enclosure)

According to Eq. (6-2), the maximum time per day that the worker could be

exposed to this noise level and be in compliance with the OSHA criteria is as

follows:

T ј

2р108:4_85Ю=5 ј 0:624 hours ј 37:4min

The volume of the enclosure, not considering the volume occupied by

the machine, is as follows:

Vo ј р1:80Юр1:20Юр1:00Ю ј 2:160m3 р76:28 ft3Ю

If we take the air temperature as 308C (868F), for which the sonic velocity

is 349 m/s (1145 fps), the left side of Eq. (7-82) may be calculated for a

frequency of 500 Hz:

fV1=3

c ј р500Юр2:160Ю1=3

р349Ю ј 1:85 > 1

Room Acoustics 309

FIGURE 7-13 Diagram for Example 7-8.

The enclosure meets the ‘‘large enclosure’’ criterion for frequencies of

500 Hz and higher, and is fairly close to meeting the criterion for the

250 Hz octave band. The insertion loss prediction, using the large enclosure

relationships, for the 125 Hz octave band would be questionable, because

р fV1=3

o =c ј 0:46 < 1Ю for this octave band. Generally, the 125 Hz octave band

does not contribute as much for the A-weighted levels as does the higher

octave bands, so the error (for the A-weighted sound level) is probably not

significant for this problem.

Suppose the machine base covers the floor of the enclosure, such that

the floor area is not involved in the calculations. The surface area of the

enclosure, excluding the floor area and area of the openings, is as follows:

S1 ј р2Юр1:20 ю 1:80Юр1:00Ю ю р1:20Юр1:80Ю _ р2Юр0:31Юр0:20Ю ј 8:04m2

The area of the two openings is as follows:

S2 ј р2Юр0:30Юр0:20Ю ј 0:120m2

The sound power transmission coefficient for the walls may be found

from the definition of transmission loss given by Eq. (4-90):

at1 ј 10_TL=10 ј 10_1:9 ј 0:01259

The openings are in the sides of the enclosure, and there are no reflective

surfaces nearby, so the effective transmission coefficient for the openings is

at2 ј 1=3. The summation of the transmission coefficients is as follows:

_Sjatj ј р8:04Юр0:01259Ю ю р0:120Юр1=3Ю ј 0:1052m2

The summation of the surface absorption coefficients for the 500 Hz

octave band is as follows, using _2 ј 1 for the openings:

_Sj_j ј р8:04Юр0:63Ю ю р0:12Юр1:00Ю ј 5:185m2

The sound power ratio for the enclosure is found from Eq. (7-85):

Wout ј 1 ю

_Sj_j

_Sjatj ј 1 ю

5:185

0:1052 ј 1 ю 49:29 ј 50:29

The insertion loss is found from Eq. (7-76):

IL ј LW _ LW;out ј 10 log10р50:29Ю ј 17:0dB

The sound power level for the sound radiated from the surface of the enclosure

in the 500 Hz octave band is as follows:

LW;out ј 114 _ 17:0 ј 97:0dB

310 Chapter 7

The corresponding sound pressure level for the 500Hz octave band is found

from Eq. (7-18):

Lp ј 97:0_11:2ю0:1 ј 85:9 dB

The sound pressure levels for the other octave bands are given in Table 7-5.

If these values are combined, the following values for the A-weighted sound

level is obtained:

LA ј 89:8dBA (with the enclosure)

This noise level is in compliance for 8-hour per day exposure, according to

OSHA criteria.

7.6.3 Design Practice for Enclosures

For satisfactory performance, there are several design guidelines for enclosures

that have been developed by manufacturers (Miller and Montone,

1978).

If the enclosure walls are constructed of a composite material, such as a

steel sheet and acoustic foam, the backing sheet should be at least 18-gauge

galvanized steel (0.0478in or 1.2mm thick). The perforated face sheet

should be at least 22-gauge galvanized steel, 0.0299 in (0.76mm) thick.

The perforations should be about 5/64 in (2mm) diameter on 5/32 in

(4mm) staggered centers. The thickness of the acoustic material between

the facings should be at least 2 in or 50mm thick for best performance.

All access doors should be provided with double seals and doubleaction

latches. Some typical door seal configurations are shown in Fig. 7-14.

The enclosure window, if access through the window is not required,

should be constructed of safety glass or plastic (such as a polycarbonate) at

least 1=2in (12mm) thick. It is important to provide gaskets for all windows

to prevent leakage of noise around the windows. If access is required

through the opening, then the openings can be covered with an acoustic

curtain, such as a couple of leaded vinyl sheets about 1/8 in (3mm) thick

with staggered slits for easier access.

In many cases, a fan system is required to provide ventilation (at least

one air change per minute), cooling, and particle removal from the interior

of the enclosure. Lined ducts or ‘‘sound traps’’ should be provided for both

the fresh air intake and the fan exhaust ducts. A typical design for a sound

trap is shown in Fig. 7-15.

Room Acoustics 311

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