G. G. Parfitt 69 
curves, and an additional feature in practice is the presence at high frequencies 
of so-called "wave effects." These are the result of standing waves within the 
body of the resilient material and lead to some loss in isolation. They are not 
usually large in rubber mounts, but may be serious in, say, steel coil springs 
with very low damping. For this reason it is common to insert a rubber pad 
under a coil spring mount to give additional high-frequency isolation. 
In spite of the fact that it forms a very useful starting point for discussion, 
the system of Fig. 4.la is nevertheless a substantial oversimplification of a 
practical mounting system in several respects. First, practical mechanisms 
do not normally have only one degree of freedom, but many degrees. There will 
thus be many natural modes of oscillation, and hence many resonances; in gen- 
eral there will be coupling between them. These effects are likely to complicate 
rather than invalidate the discussion which follows, and they will be ignored 
henceforth. They are of course extensively dealt with in standard texts [2 to 5]. 
Secondly, the foundation on which the isolator rests will never be infinitely 
rigid, particularly in marine applications, and this will modify the transmissi- 
bility. In such cases of nonrigid foundations, it is often more instructive to use 
in place of T some other measure of isolation describing the extent to which the 
motion of the foundation is reduced by the isolator. One which has been used [6] 
is the so-called response ratio R, namely, 
R= : amplitude of foundation under isolator : (4) 
amplitude of foundation with M rigidly attached to it 
The same exciting force at the same frequency is assumed applied to M in each 
case. "Amplitude" here may refer to the displacement, velocity, or acceleration 
of the foundation, or even to the force upon it, for at a given frequency force 
will be proportional to motion. If the mechanical impedance of the foundation is 
at all frequencies very large compared with that seen looking into the base of 
the mount, then R is identical with Tas shown in Fig. 4.1b. 
If the foundation consists of a pure mass MM, or a pure spring of stiffmess 
S;, the resulting response-ratio curves are those shown in Figs. 4.2 and 4.3, 
respectively. The curve for the mass foundation is of the same form as Fig. 4.1b, 
but the resonance frequency is increased, leading to a reduction of isolation 
(increase in T) at high frequencies in the ratio 
M+M; 5 
i (5) 
With an elastic foundation the resonance frequency is somewhat less than 
with a rigid foundation (negligibly sointhe case shown in Fig. 4.3), and the curve 
contains a trough due to removal ofthe original resonance of the main mass M on 
the elastic foundation [which gives a maximum for the denominator of Eq. (4)]. 
Above this frequency the response ratio reaches the constant. value S/(S + S;). 
Thus, in both these cases the response ratio, i.e., the gain from inserting a 
spring mount, is less at high frequencies than it would be with a rigid foundation. 
However, it is worth noting that this is not so much due to an impairment of 
the action of the mount, but to the fact that before the mount is inserted the in- 
ertia of the body to be supported is already relieving the foundation of part 
