68 : Lecture 4 
+40 
F = 6 
v0 
Ww 
“N 
uw 
e 
= 
s a 
a 
o 
F a 
7 u = -40 
g 
c¢ 
2-S/M = 
Wo = 
-80 
0.1 10 100 
(a) (b) 
Fig. 4.1. The idealized simple mounting system and its transmissibility curve. 
If the forces concerned are sinusoidal, with amplitudes F and F, and frequen- 
cy #/27, the transmissibility as a function of w is as given in Fig. 4.1b. No 
isolation is achieved unless o> ¥2o,. At high frequencies T varies as 1/o?, as 
in Eq. (8), i.e., decreases at 12 db per octave. It is therefore necessary that 
@ 9 fall below all significant frequency components present in the spectrum of 
the exciting force F. If it is not practicable to make the springs soft enough to 
achieve this—and Eq. (3) shows that irrespective of the nature of the spring, so 
long as it is linear and frequency-independent as stated, a low natural frequency 
necessarily requires a large static spring deflection—then w, must fall between 
and not close to any strong low-frequency spectrum components. The process 
of isolation is of course a purely reactive one, and no means of absorbing 
vibrational energy is necessarily involved. 
4.2, ADDITIONAL CONSIDERATIONS 
The foregoing simple theoretical predictions are in general well borne out 
by measurements on mountings of a mechanically simple character [1]. Effects 
of finite damping, to be discussed below, of course modify the transmissibility 
