Sound absorption and vibration suppression

The ability to damp vibration coupled with mechanical stiffness and strength at low weight makes an attractive combination. Automobile floors and bulkheads are examples of structures the primary function of which is to carry loads, but if this is combined with vibration damping and sound absorption the product quality is enhanced.

Metal foams have higher mechanical damping than the solid of which they are made, but this is not the same as sound absorption. Sound absorption means an incident sound wave is neither reflected nor transmitted; its energy is absorbed in the material. There are many ways in which this can happen: by direct mechanical damping in the material itself, by thermo-elastic damping, by viscous losses as the pressure wave pumps air in and out of cavities in the absorber and by vortex-shedding from sharp edges. Sound is measured in decibels, and this is a logarithmic measure, in accord with the response of the ear. The result is that - as far as human perception is concerned - a sound-absorption coefficient in the acoustic range of 0.5 (meaning that half the incident energy is absorbed) is not much good. To be really effective, the absorption coefficient must be exceed 0.9. The best acoustic absorbers easily achieve this.

Are metal foams good sound absorbers? Data described in this chapter suggest an absorption coefficient of up to 0.85 - good, but not as good as materials such as felt or fiberglass. More significant is that the high flex-ural stiffness and low mass of foam and foam-cored panels result in high natural vibration frequencies, and this makes them hard to excite. So while metal foams and metfoam-cored panels offer some potential for vibration and acoustic management, their greater attraction lies in the combination of this attribute with others such as of stiffness at light weight, mechanical isolation, fire protection and chemical stability.

12.1 Background: sound absorption in structural materials

Sound is caused by vibration in an elastic medium. In air at sea level it travels at a velocity of 343 m/s, but in solids it travels much faster: in both steel and aluminum the sound velocity is about 5000 m/s. The wave velocity, v, is related to wavelength Xs and frequency f by v = Xs f. To give a perspective: the (youthful) human ear responds to frequencies from about 20 to about 20000 Hz, corresponding to wavelengths of 17 m to 17 mm. The bottom note on a piano is 28 Hz; the top note 4186 Hz. The most important range, from an acoustic point of view, is roughly 500-4000 Hz.

Sound pressure is measured in Pascals (Pa), but because audible sound pressure has a range of about 106, it is more convenient to use a logarithmic scale with units of decibels (dB). The decibel scale compares two sounds and therefore is not absolute. Confusingly, there are two decibel scales in use (Beranek, 1960). The decibel scale for sound pressure level (SPL) is defined as

where prms is the (mean square) sound pressure and p0 is a reference pressure, taken as the threshold of hearing (a sound pressure of 20 x 10 ~6 Pa). The decibel scale for sound power level (PWL) is defined by

where W is the power level and Wo is a reference power (Wo = 10~12 watt if the metric system is used, 10~13 watt if the English system is used). The two decibel scales are closely related, since sound power is proportional to prms. In practice it is common to use the SPL scale. Table 12.1 shows sound levels, measured in dB using this scale.

Table 12.1 Sound levels in decibels

Threshold of hearing 0

Background noise in quiet office 50

Road traffic 80

Discotheque 100

Pneumatic drill at 1 m 110

Jet take-off at 100 m 120

The sound-absorption coefficient measures the fraction of the energy of a plane sound wave which is absorbed when it is incident on a material. A material with a coefficient of 0.9 absorbs 90% of the sound energy, and this corresponds to a change of sound level of 10 dB. Table 12.2 shows sound-absorption coefficients for a number of building materials (Cowan and Smith, 1988)

Table 12.2 Sound-absorption coefficient at indicated frequency

Material

500 Hz 1000 Hz 2000 Hz 4000 Hz

Glazed tiles

Concrete with roughened surface

Timber floor on timber joists Cork tiles on solid backing

Draped curtains over solid backing

Thick carpet on felt underlay Expanded polystyrene, 25 mm

(2 in.) from solid backing Acoustic spray plaster, 12 mm

in.) thick, on solid backing

Metal tiles with 25% perforations, with porous absorbent material laid on top 0.80 0.80 0.90 0.80 Glass wool, 50 mm, on rigid backing 0.50 0.90 0.98 0.99

12.2 Sound absorption in metal foams

Absorption is measured using a plane-wave impedance tube. When a plane sound wave impinges normally on an acoustic absorber, some energy is absorbed and some is reflected. If the pressure pi in the incident wave is described by

and that in the reflected wave (pr) by then the total sound pressure in the tube (which can be measured with a microphone) is given by the sum of the two. Here f is the frequency (Hz), t is time (s), x is the distance from the sample surface (m), c is the velocity of sound (m/s) and A and B are amplitudes.

The absorption coefficient a is defined as

It is the fraction of the incident energy of the sound wave which is absorbed by the material. The upper figure shows the value of a for a good absorber, glass wool: at frequencies above 1000 Hz the absorption coefficient is essentially 1, meaning that the sound is almost completely absorbed. The central figure shows absorption in a sample of Alporas foam in the as-received (virgin) state:

Frequency
Figure 12.1 Sound absorption, measured in a plane-wave impedance tube, for glass fiber, Alporas foam in the as-received condition, and Alporas foam after 10% compression to rupture the cell faces

a rises to about 0.9 at 1800 Hz. Compressing the foam by 10% bursts many of the cell faces, and increases absorption, as shown in the bottom figure. Similar results are reported by Shinko Wire (1996), Asholt (1997), Utsumo et al. (1989), Lu et al. (1999) and Kovacik et al. (1999). In dealing with noise, relative sound level are measured in decibels (dB):

Thus an absorption coefficient of 0.9 gives a drop in noise level of 10 dB.

The conclusion: metal foams have limited sound-absorbing ability, not as good as glass wool, but still enough to be useful in a multi-functional application.

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