That depends on your problem. Also what is a low or a high frequency depend on your problem.

Let suppose that we study the vibration of a beam, what is the difference if you have that the 1st mode natural frequency is 100 Hz for BEAM A.

for BEAM B the natural frequency is 1700 Hz (1st mode ) , same dimensions different material.

Interesting question!

In general and roughly speaking, for the same object (to be designed and/or tested=, there are many natural frequencies. Not all of them are equally important. Which ones will be important, depends on your problem.

Example 1- Frequency spectrum. If no external excitation are acting, the "free" or "natural" movement of your structure is the linear super-position of all the modes, meaning all modes participate. Generally, the lower the mode, the higher the participation. So you can say, low-frequency modes are "more important" in that sense.

Example 2- Resonance avoiding. Do you want to avoid vibration at a specific frequency? Then make sure your exciting frequency and the nearest natural frequency are sufficiently far from one another. This is called "separation margin" and should be 10-20% to design in a comfort zone, i.e. far from resonance. Resonance is when exciting frequency and natural frequency match. Although design engineers always try to avoid, test engineers know that it's not necessarily the worst-case scenario for your structure. If excitation magnitude is low, or acts close to a nodal point of your mode, or if there is enough damping to dissipate vibrating energy, the structure can operate in a resonant condition without too much pain.

Example 3 - If your problem is to compare natural frequencies on structures of different sizes, than you should define which order are you interested in, e.g. 1st bending mode. In general the smaller the structure, the higher is the mode.

I hope the three examples above help you a little bit.

Regards

Maurizio

Natural frequencies in structural analysis are the functions of the stiffness and mass of the component. Stiffer the component in any direction, higher is the corresponding mode frequency. Generally in structural analysis, the lower frequencies have higher displacement/deflection of the component, and that incurs higher fatigue damage damage to the component. Other aspect is whether the natural frequency (it maybe high also) is near to any excitation frequency, in which case also there will be higher fatigue damage to the component.

So basically lower frequencies should be avoided if the component is under forced vibrations, and also the resonance should be avoided which maybe at any frequency lower or higher.

The answers here are quite invaluable. @Maurizio, Please can you explain in clear terms the difference between excitation and natural frequencies?.

Thank you @ Maurizio