How to Estimate Forces From an Experimental Vibration Analysis?

Use a decent computer, and matlab, and use all the data to calculate all the accelerations, and thereby the forces, and then apply summation of vectors/tensors as applicable, as per method #3.

hi there James Stewart, i think that my question was not clear, i have the response of the system in acceleration in a sampled 0 to 200 Hz frequency domain, i want to calculate the forces explicitly from this accelerations , i know the mass of the system, so i thaught i can use F=ma, but my problem is in which frequency should i take the acceleration, or which method from above should i use to take the right acceleration value.

there's a link of the data table.

https://drive.google.com/file/d/0B-w8NaeKir77dm15ZE5mLWpHYmM/view?usp=sharing

best regards.

jpfalt has responded clearly on your path to an answer. He has exceeded what I can offer you, and I offer jpfalt my kudos, congratulations, and thanks, as my brain was in danger of fatigue stress.

You need to decide what you are looking for. Specifically, if you want peak force, then you add them all up assuming that at some point, the structure resonates. If looking for deflection, the peak force is still used. If looking for fatigue life, you would need to work each frequency range and associated beat frequencies and then work them all into an alternating stress formula for projected life.

hi there Jpfalt, knowing that the system is a compressor which was turned on to work in normal conditions at 50 hz during the test, i wanted to evaluate the force of the compressor in work phase, so i don't know which method from above should i use.

best regards.

You still need to answer the question of whether you are looking for a structural failure due to overload or a fatigue failure over time.

Knowing that it is a structure on a compressor, I can only assume that you are looking at estimated fatigue life of the structure.

I also assume you have accelerations in several octave bands at several points in the structure. You need to reduce those accelerations to stresses in the structure at any identified critical junctions. What software tools to you have for stress analysis, or are you doing it the old fashioned way with a slide rule and ledger pad? Each frequency will have it's own stress value.

Once you have the stresses at critical joints identified for each octave band frequency, you must run a fatigue life calculation for the total combined frequency range and alternating stress level at each frequency. You will likely find that one frequency predominates, but each other frequency added will reduce the fatigue life further.

If it happens you are looking for a single critical structural failure event, then you simply use the frequency unfiltered peak acceleration to get a force and then reduce that force to stresses at the critical joints.