How does Vibration Isolation work?
Introduction to Vibration Isolation
Note: This description of vibration isolation is intentionally simplified to help educate and inform.
The key here, is really very simple; if something wants to vibrate then, often, we should let it. Vibration is generally where something tries to move or bounce in one direction, then back again in the other direction – the force vectors generally add up to 0, that is to say they return to the same position (approximately).
To say the same thing in a different way, imagine a sine wave. This represents the vibratory forces moving one way then the other. The wave keeps coming back to the X-axis, or start point – it wants to return to the same place, but continuously ‘dance’ one way then the other.

Trying to stop this movement completely, and hold the vibrating item in place is hard work and results in all of the energy produced by the vibration being transmitted. The more you can allow the vibrating equipment to vibrate freely without letting it run away, the less energy is transmitted.
So, let’s say we allow 60-70% of the movement in each direction to occur, then the vibration related energy transmitted through to the surroundings is reduced by considerably more than the 60-70%.

So, how to we hold something securely but allow it to move just enough? Use a flexible connection – rather than bolting something firmly together, use a rubber (or other flexible material e.g. spring) product designed for the job.
Below is an example of a simple ‘rubber bobbin’ in different configurations. The metal fixtures are held together by the rubber, they are not directly connected, as can be seen in the third image with translucent rubber. They are flexibly connected and therefore ‘de-coupled’:

Why doesn’t a car engine vibrate the occupants to pieces? Why doesn’t a washing machine vibrate the whole building? The answer relate to flexible connections which de-couple the vibrating part from its surroundings.