# Natural frequency determination

I have estimated some transfer frequency functions of complex mechanical suspension. It is shown the gains reach a very high value at a 0.8Hz. How could i know if the 0.8Hz isthe suspension natural frequency?

This question does not even make sense, do you know what a natural frequency is? Also, what is a transfer frequency functions? Do you mean you have a transfer function, obtained analytically via frequency sweeps?

Side:
Please capitalize the word "I" in sentences.

This question does not even make sense, do you know what a natural frequency is? Also, what is a transfer frequency functions? Do you mean you have a transfer function, obtained analytically via frequency sweeps?

Side:
Please capitalize the word "I" in sentences.

I have applied a frequency sweep and then i have measured the accelleration at fixed frame (called a) and at the suspended frame (called b). After that i have calculated the ration (b/a) from fourier transform of a and b. is f1 a natural frequency of suspension if the phase of B/A=90° in f1? Now the question is more clear?

Capitalize "I" when you use it in sentences. Goodness, gracious .

The word for (b/a) is ratio, not ration. Fourier is named after someone, it is capitalized as well. When you type in a proper English sentence, I will try and help you.

berkeman
Mentor
I have estimated some transfer frequency functions of complex mechanical suspension. It is shown the gains reach a very high value at a 0.8Hz. How could i know if the 0.8Hz isthe suspension natural frequency?

It does sound like it is a resonant frequency, if you are getting amplitude gain there. Is it the only resonant frequency you have found in your sweep? You should be able to start to calculate the resonant frequency based on the spring constant and the unsprung mass, I would think.

It does sound like it is a resonant frequency, if you are getting amplitude gain there. Is it the only resonant frequency you have found in your sweep? You should be able to start to calculate the resonant frequency based on the spring constant and the unsprung mass, I would think.

thank you for your answer. The question is my suspension isn't so simple and so it is difficult to say if it is a real resonant frequency. So I would want to know if there is a general way to estimate a natural frequency suspension.

Resonance occurs when the bode magnitude plot reaches a peak.

Resonance occurs when the bode magnitude plot reaches a peak.

Is it always true? Moreover does resonance occur when the bode phase plot reaches 90°?

berkeman
Mentor
Is it always true? Moreover does resonance occur when the bode phase plot reaches 90°?

Why would you say 90 degrees?

Is it always true? Moreover does resonance occur when the bode phase plot reaches 90°?

Rather than give you the answer, I want you to arrive to it on your own. Reflect on the derivation of terms when we define the natural frequency, damping ratio, etc, for any classic single input, single output (SISO) system. Hint: look at the equations of motion in those cases. What can you say about them? How does that apply to your complex system?

When I don't know the values in my system (ie mass compliance, damping), I often modify a known value (ie mass) and observe the effect. For a second order system, it's easy to ascertain the baseline mass based upon the added mass and frequency shift.

Then, knowing the baseline mass and the baseline resonance, you can compute the compliance.

Of course it gets much more tricky if you're coupled into another system....

When I don't know the values in my system (ie mass compliance, damping), I often modify a known value (ie mass) and observe the effect. For a second order system, it's easy to ascertain the baseline mass based upon the added mass and frequency shift.

Then, knowing the baseline mass and the baseline resonance, you can compute the compliance.

Of course it gets much more tricky if you're coupled into another system....

You are getting close to what I'm hinting at.

Why would you say 90 degrees?

http://mechatronics.technion.ac.il/rotordynamics/pdf/lesson_1b.pdf [Broken] page 6. For w=wn the phase is 90°. Is it true also for a MIMO system?

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When I don't know the values in my system (ie mass compliance, damping), I often modify a known value (ie mass) and observe the effect. For a second order system, it's easy to ascertain the baseline mass based upon the added mass and frequency shift.

Then, knowing the baseline mass and the baseline resonance, you can compute the compliance.

Of course it gets much more tricky if you're coupled into another system....

i think i have understood. I take a siso system and i apply it a frequency sweep. After that i try to increase the mass and apply another time a frequency sweep. Then with a system identification method i can estimate the natural frequency, isn't it?