Modal Analysis: Which mode shapes to review?

[cpfmarvin]

I implemented a frequency analysis for a specific structure to determine the natural frequencies. My general understanding of modal analysis is that in most cases, a first or second mode near an operating frequency may cause vibration amplification. For other designs, I have verified that the first mode shape is higher than the operating frequency.

If my operating frequency is much higher than the natural frequency (mode 1), how do I assess the higher mode shapes at the operating speed. I know this is a common scenario; turning on a grinding wheel often experiences a resonance as the wheel passes thru its natural frequency. But at the operating frequency, things are OK. There may exist some mode shape (lets say 50) that has the same frequency as the final wheel speed. Why are there no problems at this mode, even though the frequencies may be similiar? How do I evaluate such systems. Most examples compare the lower mode shapes.

I understand that lower mode shapes illustrate "natural" behaviors and are usually compared to operating frequencies, but what information can I gain from detecting higher mode shapes than correlate with an operating frequency?

What can be evaluated by a typical modal analysis? What might indicate possible resonance problems or the need for further investigation, like a dynamic model?

I have the following notes: "If the modal study indicates that there are no natural frequencies near the operating speed, then a frequency response analysis may not be required." Since systems actually have an infinite number of natural frequencies (= number of DOF), do I compare the operating frequencies to the lowest modes only? Sorry for the various questions, I'm just looking for a short summary.

Thanks for any help.

 

[tomirvine]

Each mode has a "participation factor." This value is obtained by integrating the mode shape along the mass of the structure.

The participation factor is a method for comparing the relative response of modes.

The relative response of a mode is proporational to its participation factor. Modes with high participation factors can be readily excited.

The lower modes tend to have the higher participation factors.

On a related note, higher modes tend to be more localized.

A good example is a cantilever beam. Apply an impulse to the end of a cantilever beam. The response is dominated by the first mode since it has the highest participation factor.

Sincerely, Tom Irvine

http://www.vibrationdata.com

 

The higher modal frequencies are also interesting because they may not cause high amplitude vibrations but they may cause a noise that is not wishfull to hear. So it is also interesting to stay out of there neighbourhood.
It is however not really necessary to make a dynamic model since it will always be a model and not the real thing. So I suggest just trying to calcute them by hand with heuristic formulas.
You must also evaluate if your system has enough damping. If a system has very little damping then even high frequencies can cause very high amplitudes.In the other case these frequencies will have almost no effect.