Natural frequencies occur on all mechanical systems. In most cases they are not a problem. However, if there is an exciting force that has a frequency near the natural frequency, the vibration response will be amplified as much as 100 times what it would be without the natural frequency. When this occurs, it is known as resonance. Resonances are rarely a good thing, and will often contribute to cracking in piping or other machine components
One the best tools for identifying and correcting resonances is impact testing. This is a fairly easy technique that can be as simple as bumping the machine with your hand (small machines, of course) or with large blocks of wood. We often use instrumented force hammers to load structures with known forces and record the vibration response. Examples of the impact hammers used are shown below:
Once a resonance has been identified, it is normally helpful to have some idea what the mode shape is of the natural frequency since that will often guide us to possible solutions for tuning the natural frequency away from the exciting frequency. The technique used for that is known as modal testing, or modal analysis. This test usually requires that the machinery be turned off for the test.
In some cases, an operating deflection shape test can be performed while the machine is operating to help understand the response of the machine to likely resonances.
Resonances can occur in mechanical systems like springs and masses, but also torsionally (twisting of shafting), acoustically (pressure pulsations in piping), as well as with control and electrical systems.