Hello,

I am trying to determine if my system's operating frequency is adequately far from it's natural frequency (as determined by solidworks frequency analysis.) I cannot find any concrete formulas that tell us how far a natural frequency should be above the operating frequency.

I have been told the "frequency limits criterion" can be used (fn > 1.6*6*fo), however I have no way to validate this formula and cannot find any source for it other than the one linked.

Another formula I have been made aware of is:

[(Fres-Fop)/sqrt(Fres*Fop)]>>1/Q

where Q - system mechanical quality factor

but i have no idea what it is called, or how reliable it is.

I've been stuck on this for weeks, and I'd love if someone has an answer! basically I want to know if either of these formulas are trustworthy, or if there are any other metrics anyone knows of to determine the safety or otherwise of an operating frequency in a system.

P.S.

my system has lowest natural frequency fn = 17.86 Hz and operating frequency 6Hz. Damping is assumed to be around 0.03 (3%) as it is an aluminum mechanical structure.

You can always use the dynamics capability to figure that out for you. Run a static analysis and get a result. Run a dynamic frequency sweep for the same load and see what the dynamic amplification is. Then you will know how it responds when the excitation is at a frequency relative to your natural frequency. The attached plot may also be informative.