All structures and materials have a resonant frequency, which can give rise to some unpleasant characteristics if vibrations of those frequencies occur with the thing you are riding on or in. Any exact multiple of those resonant frequencies also results in 2nd, 3rd 4th order etc harmonics, but at a lower amplitude.
That's pretty much it. Some engineers like me who have some history in working in NVH, will prefer to say 'natural frequency of vibration' rather than 'resonant frequency', though you are correct that you will find it in many texts. The word 'resonance' adds an unnecessary ambiguity, since we use the word 'resonance' is another more specific way. We also do not consider a material to have a natural frequency of vibration per se, since this has other dimensional variables and changes with the magnitude and direction of any applied forces.
To us, a system has a natural frequency of vibration. Further vibrations that are induced in the system by disturbing forces or energies may be at some other frequency which can be an unpleasant effect. This is more akin to 'resonance' and is the reason why that a resonator is required at a carefully determined and specific point along the length of the exhaust system. The Triumph Stag is a prime visual example. It has oversized exhaust tailpipes that schoolboys and motoring journalists got rather excited about. The truth is that
they were not a styling exercise, but rather that this position was the the optimal position of tuned length for the fitment of the resonator boxes.
Of course mass damping is a further method of tuning out or reducing resonant frequencies, but there is little point in making a system from a lightweight material only to need to add mass to tune its resonant length.
The second, third, etc are harmonics of the same frequency. An out of balance wheel that peaks at say 60 mph, will also peak again at 120mph with twice the intensity,
Anyway I think that's enough from me.
