Metal Foams: A Design Guide

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Sound absorption and vibration suppression 177
Figure 12.3) it stores elastic strain energy per unit volume, U; in a complete
loading cycle it dissipates 1U, shaded in Figure 12.3, where
� max
U D dε D 1
2
�
max
and 1U D dε ⊲12.11⊳
2 E
s
s max
Area = ∆u
ε max
ε
Area = u
Figure 12.3 The loss coefficient measures the fractional energy dissipated
in a stress–strain cycle
The loss coefficient is the energy loss per radian divided by the maximum
elastic strain energy (or the total vibrational energy):
D 1U
⊲12.12⊳
2 U
In general the value of depends on the frequency of cycling, the temperature
and the amplitude of the applied stress or strain.
Other measures of damping include the proportional energy loss per cycle
D D 1U/U, the damping ratio , the logarithmic decrement υ, the loss angle
, and the quality factor Q. When damping is small (