# Natural frequency determination

• serbring
In summary: 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.... will the resonance still happen?
serbring
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.

Cyrus said:
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.

serbring said:
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.

berkeman said:
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.

Cyrus said:
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°?

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

Why would you say 90 degrees?

serbring said:
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...

Mike_In_Plano said:
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.

berkeman said:
Why would you say 90 degrees?

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

Last edited by a moderator:
Mike_In_Plano said:
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?

## 1. What is natural frequency determination?

Natural frequency determination is the process of identifying and measuring the frequency at which an object or system naturally vibrates without any external force. It is a fundamental concept in the field of mechanics and is used to study the behavior of structures, machines, and other physical systems.

## 2. Why is natural frequency determination important?

Understanding the natural frequency of a system allows scientists and engineers to design and build structures and machines that can withstand vibrations and avoid resonance, which can cause damage or failure. It also helps in predicting the behavior of a system under different conditions and making necessary adjustments to ensure safety and efficiency.

## 3. How is natural frequency determined?

Natural frequency can be determined through experiments or mathematical calculations. In experiments, the system is excited with a known force, and the resulting vibrations are measured and analyzed to determine the natural frequency. In mathematical calculations, the properties of the system, such as mass, stiffness, and damping, are used to calculate the natural frequency.

## 4. What factors affect natural frequency?

Several factors can influence the natural frequency of a system, including its mass, stiffness, and damping. The shape and size of the system also play a role, as well as the material it is made from. External forces, such as wind or earthquakes, can also affect the natural frequency of a structure.

## 5. Can natural frequency be changed?

Yes, the natural frequency of a system can be changed by altering its properties, such as its mass, stiffness, or damping. For example, adding weight to a structure will decrease its natural frequency, while increasing its stiffness will increase the natural frequency. Additionally, applying external forces can also change the natural frequency temporarily.

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