74 Lecture 4 
+20 
-40 
TRANSMISSIBILITY (db) 
-80 
0.1 0.3 1.0 
=e 
w 3 10 30 100 
®o 
Fig. 4.6. Transmissibility curves of simple mounts with various types and degrees of damping. (a) 
5=0.1, (b) 6=1.0, (c)6 =0.5, (d) modulus and damping as in Fig. 7c. 
Equation (8) represents only a relatively small loss of isolation compared with 
an undamped mount, but Eq. (9) gives a serious loss due to the large viscous 
stress set up at high rates of shear (or high frequencies). The full transmissi- 
bility curves are shown in Fig. 4.6, curves b and c. High damping of the order 
of 6= 1 can be obtained in high polymers, and though there it may not be greatly 
frequency-dependent, it tends to be accompanied by an elastic modulus which 
increases with frequency. In fact, it can be shown [7] that in a typical polymer 
having a wide spread of viscoelastic relaxation times there is an intrinsic 
relation between the two, viz., 
: za(logs) 
Thus, for example, 5=1 implies an increase of some 19 times in stiffness over 
a frequency range of two decades. The increasing stiffness leads to a loss in 
isolation (relative to that of an undamped mount) which in practice is similar 
to that caused by large viscous damping (curve cof Fig. 4.6). Thus, for example, 
if in Eq. (7) $/S9 = @/w» and 6 is constant, then for w > wo 
P= (1-467) (0) (11) 
which has the same frequency dependence as Eq. (9). In addition, polymers with 
high damping are rather prone to show substantial creep or "compression-set" 
effects under a static load. 
The frequency dependence of viscous damping, such as may be obtained from 
a simple dashpot device, may be mitigated by the use of a multiple isolator 
element containing two springs and a dashpot, as in Figs. 4.7a or 4.7b. These 
two forms are identical in performance and have an effective stiffness and a 
