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American Society of Heating and Ventilating Engineers Guide, 1936
of accuracy. Table 4 gives the values of c and r for a number of commonlyused flexible materials.
In general; there are two principal points to observe in the design of a flexible support for any piece of equipment, namely, the material should have a relatively large compliance and it should be loaded to nearly the Upper safe limit of loading. Several flexible metallic supports have recently been developed.
; Example 2. A machine weighing 1000 Ib-has a base area of 20 sq ft. Assume that the
principal vibration of the machine has a! frequency of 100 cycles per second (most machinery vibrations are less than 150 vibrations per second; and the assumed frequency
of 100 is quite representative of typical machines). Suppose that a 1-in. slab of corkboard, weighing 1:10 lb per. board loot ibe placed between-the machine and the.floor.
The loading on the cork will then be only 50 lb per square foot, or slightly more than lb per square inch. (It is assumed that the compliance c in centimeters per dyne for a
specimen 1 in. thick arid 1 sq cm in cross-section is 0.25 X 10-6 and the resistance r in mechanical ohms is 0.15 X 10s.)
The transmissilrility is calculated in the following manner:
- Mass of\machine in grams = 1000. Xv 454 4.54 X 10s. ;
Area of base in square centimeters = 20 X 144 X
2A4 X 2154 = 1.86 X 10*.
1
.;
Therefore, the compliance of the entire support, 1 in. thick and 20 sq.ft in cross
section, is 0.25 X i(T* it on v
^ 6:134 X 10"10 cm per dyne, and the resistance of
. Table 4- Compliance and Resistance-Data for Typical Specimens of
.;
Flexible Materials^ V
The compliances, and resistances given in (He table are for specimens1 in.thick and 1 sq cm in cross-section
y Material ,
Description op Material
Approximate Upper
Sape Loading in
. Compliance c in
^ Pounds per Square
;. Centimeters per Dtne'
Inch..
Resistance r in Absolute Units
Corkboard
1.10 lb per
. 12
board foot
Corkboard
0.70 lb per
8
board foot
Fiber Board
.1.35 lb per
4.to 6 .,
Fiber Board
board foot Carpet lining; :
\ 10
Fiber Board '
Insulating
12
board
Fiber board
Insulating
15
board
Fiber Board
Insulating
15
board
Anti-Vibro-Block
:5 .
Sporige Rubber
25 lb per
T to 3
cubic foot
Soft India Rubber 55 lb per
3 to 6
. cubic foot
Hairfelt
10 lb per . . 1 to 2
. cubic foot
0i25 x lO"6
o: 15 x 10s
0.50 x 10^
0.25 x10s
0.60 x lO"5
0.50 x 10s
0.40 x 10-6 0.18 x 10-
0.16 x 10-
0.12 x 10-
0.60 x 10- . 1.5 x 10s 3.0 x 10-6 .
1.2x10- 1.5x10"
V'
.
eFrom Architectural Acoustics, by V. 0. Knudsen.p. 278. 336
Vq
Chapter- 18--Sound Control
the entire support is 0.15 X 10s X 1.86 X 10* ; = 0.28 X 10s mechanical ohms (or absolute
units). Therefore,
<.
-i
"V-
10" (0.28 X 10s)2 4-
4# X 100 X (0.134)8 :
= 0.93
(0.28 + 10)J + ^2x X. 100 ,X 4.54 X 10s
10" r
2x X 100 X 0.134
Consequently, it is seen that the transmissUnlily is nearly equal to unity, and that the support therefore is not satisfactory for insulating 100 or fewer vibrations per second.
If the amount of cork be reduced so that it is loaded to 10 lb per square inch', the total area of the supporting cork will be dnly 100 sq in. or 645 sq cm: The compliance of the
entire support will now be 0.25. X. ICC X . = 0.39 X . HU cm per dyne, and the
resistance will be 0.15 X 1W X 645 = 0.97 X 107 mechanical ohms (or absolute units).
Therefore .
. - . ..
101S (0.97 X.107)7 + 4x2 X 100 -X (0.39)* ~
(0.97 X 107j* + (2x X 100 X 4(54 X 10s
- 10s y
2x X 100 X; 0.39 /
0.037
It is seen, therefore, that with the bearing surface on the cork reduced to 100 sq in. (that is, with'the cork loaded to 10 lb per square inch), the transmissibility is reduced to. 0.037, or the amplitude of vibration transmitted to' the flpor will be only about 1/27 of what it would be) if the machine were mounted directly upon the floor. These two numerical examples ..will serve to show; , not only the manner of making the calcu lations, but also the importance of selecting the,proper type and design of flexible supports for insulating1 the-vibrations of a machine from the rigid structure of a building.
CONTROL OF NOISE TRANSMISSION THROUGH DUCTS
The most troublesome sources of noise from ventilating and air con ditioning equipment. are fan and motor noises which are transmitted through the ducts. The reduction, in decibels, of noise transmitted through a duct,, neglecting reflection from ends and bends, is proportional (1) directly to the length of the duct, (2) directly to the perimeter of the duct, (3) inversely to the area of cross-section of the duct, and (4) directly, (or at least approxirnately so) to the coefficient of sound absorption of the material which comprises the interior surface of the- duct.. It is apparent therefore, thatdong, narrow ducts, lined with highly absorptive material, will provide a high degree of insulation against the "transmission of noise through ducts. In fact,-small ducts"(4 in. x 6 iii.), made of material having a coefficient of sound-absorption of 0.50, will provide a noise reduction of slightly more than 1 db per linear foot..
As can be seen from an inspection of. Table 2, noises of low frequency are difficult to absorb; on the other hand, these frequencies are easily reflected by elbows, branches, arid duct ends whereas higher frequencies are little affected. Furthermore, the reflection effects are more pro nounced in small ducts than in large ducts. Hence, by introducing into a duct a sufficient length of small, absorptive channels together with a number of elbows or other; reflecting elements it is possible to -reduce the
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