J.H. Janssen 325 
The spring is compressed more or less and in turn excites the mass. The well- 
known equivalent electrical circuit is also shown. The ratio of v, (input velocity) 
to v,, (velocity of the mass) depends only on the ratio: forcing frequency f to 
resonance frequency f. Let us now call 
20 log = By — Lym (10) 
Vy 
V, 
m 
the "isolation" for this situation. 
Clearly this isolation equals, approximately, the difference in impedance 
level for the mass and the spring, provided the frequency f is greater than f. 
For normal excitation and normal vibration, this statement turns out to be 
approximately valid if either the spring behaves less like a spring or the mass 
is replaced by a more general foundation; provided, again, that the impedance 
level of the spring is some 10 dblowerthan the impedance level of the foundation. 
Figure 17.3 shows the well-known wave effects [4,5,6] in the spring, the 
mass still simulating "rigid inertia." Figure 17.4 shows the effect of the foun- 
dation impedance on the isolation; simple theory agrees sufficiently with practice. 
In Fig. 17.5, however, an unexpected difference between two isolation curves is 
shown. For both curves the excitation was "normal"; the vibration, however, 
was not. Clearly, this simple fact is of great importance to the isolation. Many 
other experimental results indicate that besides normal excitation other—parallel 
or rotational—excitation must also be taken into account [7, 8]. 
4B O01 10 1O_kHz 
100 
90 
vm) 
80 
iN) 
(e) 
70 
isolation (Evia (L 
impedance level (Lz) 
+ 
(e) 
60 
50 
=1©) 40 
1 2 4 8 is se Gs) (25 e309) Seo) 1 2 4 8 6 32 63 
f Hz kHz 
Fig. 17.3. While hanging on two battens, one side of a 400-kgf nominal load rubber mount was excited 
normally (cf. Fig. 17.2); the other side was connected as rigidly as possible to a 130-kg steel mass, 
which was resiliently mounted as shown. Measured isolation figures for discrete frequency excitation 
(dots) and for half-octave-band noise excitation (squares) are shown in comparison with an approx- 
imate theoretical curve (solid line) including standing wave effects (dotted curve), Also shown are the 
computed impedance of mount and mass derived from their static stiffness and weight, respectively. 
