Vibration of low, harmless level cannot be avoided because they are linked to the working principle of the machines. Mechanical risks due to excessive amplitudes are avoided by separately keeping every single source of vibration within acceptable limits. The respective design principles used are specific for the different mechanisms of vibration and, accordingly, quite different.
Some risks can be dealt with by avoiding resonance (i.e. by ensuring sufficient difference between exciting frequencies and natural frequencies); however, this does by no means hold for all kinds of problems (see the page What is the role of resonance?).