Metal Foams: A Design Guide

Sound absorption and vibration suppression 175
˛ 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):
1⊲SPL⊳ D 10 log 10
� �2 B
D 10 log10 ⊲1 ˛⊳ ⊲12.5⊳
A
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.
12.3 Suppression of vibration and resonance
Consider the linear single degree-of-freedom oscillator shown in Figure 12.2(a):
amassm attached by a spring and a damper to a base. Assume that the base
vibrates at a single frequency ω with input amplitude X, so that its displacement
is x D Xe iωt . The relative deflection of the mass is y D Ye iωt is then given by
the transfer function H⊲ω⊳:
H⊲ω⊳ D Y
X D
⊲ω/ω1⊳ 2
1 ⊲ω/ω1⊳ 2 C i ⊲ω/ω1⊳
⊲12.6⊳
where ω1 is the undamped natural frequency of the oscillator and is the
damping constant. The magnitude of H⊲ω⊳ is shown in Figure 12.2(b).
y = Y e iωt
Spring
Mass
x = X e iωt
Viscous
damper
Y
X
1
(a) (b)
1
ω/ω 1
Figure 12.2 (a) Single degree of freedom oscillator subject to seismic input
x at frequency ω. (b) The transfer function for the relative displacement y