G. G. Parfitt 75 
(a) 
DAMPING COEFFICIENT 
& MODULUS RATIO 
(b) 
RELATIVE FREQUENCY 
(c) 
Fig. 4.7. A damped spring system with a single relaxation time (a,b) and its modulus and damping 
spectra (c). 
damping factor both of which vary as in Fig. 4.7c. Stiffness still increases with 
frequency but does so now only over a limited range of frequencies. For a maxi- 
mum damping factor of unity the over-all increase of modulus between very 
low and very high frequencies is 5.8 fold. If such a system is arranged to have 
a maximum damping factor of magnitude unity placedat the resonance frequency 
of the mounting system, then the resulting transmissibility curve would be that 
given by curve d in Fig. 4.6. It isseento achieve a low resonant transmissibility 
with less sacrifice at high frequencies than the simple viscous damper or the 
high-damping polymer. The systems of Fig. 4.6 are compared on the basis of a 
common resonance frequency. A fairer basis of comparison would be that of a 
common static stiffness, as this determines the static stability of the equipment. 
In this case the relaxation curve d would be shifted to the right by a frequency 
factor of about 1.6. However, the curve for a high-damping polymer, at present 
indicated as coinciding approximately with the viscous-damping curve, would 
be shifted considerably more owing tothe larger ratio of high-frequency to static 
moduli. 
Snowdon [8] has studied the properties of a mount consisting of sections of 
a lightly damped natural rubber (hevea) and of a highly damped polymer placed 
mechanically in parallel. By suitable choice of material and relative cross 
section it can be arranged that the natural rubber provides most of the stiffness, 
which is therefore not strongly dependent on frequency and not too subject to 
static creep, while the other polymer contributes considerable damping. In this 
way a transmissibility curve combining substantial resonance damping with little 
loss in high-frequency performance can be obtained. Such a mount does not 
