Single Degree Vibration Isolation

In many industrial applications, one may find the vibrating machine transmit forces to ground which in turn vibrate the neighbouring machines. So in that contest it is necessary to calculate how much force is transmitted to ground from the machine or from the ground to the machine.

 
   A vibrating system

It is a system subjected to a force   and vibrating with  .

This force will be transmitted to the ground only by the spring and damper.

Force transmitted to the ground

                                                     
It is known that for a disturbing force  , the amplitude of resulting oscillation

 
Substituting and defining

The transmissibility TR as the ratio of the force transmitted force to the disturbing force one obtains

 
It can be noted that

 
When damping is negligible

 
to be used always greater than

Replacing 

 
To reduce the amplitude X of the isolated mass m without changing TR, m is often mounted on a large mass M.

The stiffness K must then be increased to keep ratio K/(m+M) constant. The amplitude X is, however reduced, because K appears in the denominator of the expression

 
                                          Transmissibility ~frequency ratio plot

The variation transmissibility with frequency ratio and it can be noted that vibration will be isolated when the system operates at a frequency ratio higher than .

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