72 Lecture 4 
+40 
-40 
RESPONSE RATIO (db) 
0.1 | 10 100 1000 
Fig. 4.5. Response ratio of a mount on foundation with multiple resonances (schematic). 
trum. A more generally significant feature of the response-ratio curves is the 
presence of any upward or downward shift of general level. 
A third way in which Fig. 4.1a is anoversimplification is in that the mounted 
item will not in general behave as a pure mass except at low frequencies. This 
effect has not been widely studied in the literature, but might be expected to 
produce effects qualitatively rather similar to those of nonrigid foundations. 
Three main directions are apparent in which the performance of a simple 
spring isolator of given static stiffness couldbe improved. The first is to reduce 
its resonance frequency with a given mass. This can only be done by making 
the dynamic stiffness decrease with increasing frequency or with increasing 
load. Unfortunately, in all real materials where stiffness varies with frequency, 
the change is in the undesired direction and so merely detrimental. Systems 
can, however, be devised which are nonlinear in such a way that the dynamic 
stiffness for small vibratory motion is well below the average stiffness con- 
trolling static or quasi-static deflection. One such system is a strut which is 
buckled under the load of the machine; another employs two conventional springs, 
one tending to pull the mass away from its equilibrium position due to the other 
[2]. One difficulty with such systems is that of making them effective for motion 
in more than one direction. 
