G. G. Parfitt 79 
It may be seen that at high frequencies there is a large gain in the effec- 
tiveness of the isolation if a mass comparable with the supported mass is added 
to the beam. For the simple case of the single-resonance foundation used in 
Fig. 4.4 the response ratio at high frequencies is given by 
M+MA/oo\" 
nf) aa 
This equation also describes the high-frequency behavior in Fig. 4.9 tolerably 
well when mis appreciable. In particular it shows that when m=M, then R = (@/w)’, 
which is the value for an undamped mount on a rigid foundation. The process 
at work here is of course simply that in which the inertia of the mass m relieves 
the beam of much of the force transmitted through the mount. 
Another very apparent effect is that the effective foundation resonance is 
brought down in frequency by the mass m, in this case from some 70 cps to 
8 cps for m=M. (More exactly, the mass largely nullifies one effect of the spring 
mount in detaching the mass M from the beam and allowing the foundation reso- 
nance to rise from its loaded value of5 cps to 70 cps.) This could be detrimental 
if there are strong excitation components in the low-frequency region, such as 
the rotor frequency of a machine. Figure 4.10, where the mass M is ten times 
the beam mass M;, and the beam damping factor has been increased to 0.1, shows 
the same general effects, but the frequency shifts are of course smaller and 
the resonant peaks due to beam resonance lower. 
It will be observed that the curves for m/M =1.0 show no indication of beam 
resonances other than the lowest, and in fact at higher frequencies agree closely 
with the transmissibility curve for a mount on a rigid foundation. This should 
not be taken to imply that the amplifying effects of the higher-order resonances 
have been eliminated from the system, but only that they are similar with and 
without the spring mount and mass inserted. Other results of Snowdon show that 
applying the same additional mass distributed along the foundation beam is less 
effective than adding a concentrated mass under the mount. 
The third possible position for additional mass in the system is at a point 
subdividing the isolator spring, typically into two equal sections. The isolator 
can then be regarded as atwo-stage unit and has been termed a compound mount- 
ing (Fig. 4.1la). Being a two-degree-of-freedom system, it has two natural 
resonances, and typical transmissibility curves will appearasin Fig. 4.12 [6,9]. 
These are calculated for a typical vulcanized rubber (hevea). As the ratio 6 of 
the secondary mass halfway down the spring to the main supported mass M in- 
creases, the secondary resonance frequency moves down towards the first. Above 
the secondary resonance, the isolation (for little or no damping) increases as 
o* instead of w? as for the simple mount (6 = 0). If strong damping is applied to 
the springs to suppress the resonances, some penalty is paid in high-frequency 
loss, just as for the simple mounting. It will be seen that unless the secondary 
mass is of a magnitude comparable with the main mass, any advantage of the 
compound system over the simple is not realized until a frequency is reached 
where the isolation of either is already very good. 
When used on a nonrigid foundation the effect of adding extra mass in a com- 
pound mounting is broadly similar to that of adding it at the base of a simple 
