# Natural frequency definition

1. Dec 1, 2011

### svishal03

Can I say that the natural frequency is the frequency of a system vibrating without effect of forces and including all parameters of damping that could occur on the system?

Resonance would occure when the forcing frequency equals the antural frequency.

2. Dec 1, 2011

### JHamm

Yes, the natural frequency of a system is the frequency it will vibrate at if left on its own in deep space. And yes resonance will occur if there is some external periodic force on the system varying with the system's natural frequency :)

3. Dec 1, 2011

### sankalpmittal

Natural frequency is the number of vibrations executed by a body on being disturbed from its mean position by application of external force in vacuum or space.

Emphasize on the bold words. If you are considering damped vibrations made by a body then you might consider friction. Natural frequency is the word used in absence of friction of atmosphere.

Remember that there has to be external force applied for frequency be it frequency made by damped vibrations or natural frequency. In case we don't apply force still body executes very slight damped vibrations due to external force by wind or air.

Yes because we generally neglect other forces like viscosity of air , friction etc. except the one which is applied on a body. We assume the body to be vibrating in vacuum.

"Resonance occurs when frequency of the external periodic force of a vibrating body becomes equal to (or matches) or becomes the integral multiple of the natural frequency of a given body."

4. Dec 1, 2011

### svishal03

Let us consider the plot of campbell/ stoke diagram.

Campbell diagram is a plot of natural vs exciting (forcing) frequiencies.

It predicts the resonant frequencies and the corresponding modes when resonance occurs.

On the horizontal axis in the Cambell diagram, I ahve the engine speed starting from zero at the left to maximum speed as I move towards to the right on the horizontal axis.

On vertical axis I have the frequencies.

I know how the exciting force varies which are the lines coming from the origin of the Cambell diagram.

Coming from the vertical axis are another series of lines representing natural frequencies of various nmodes (flexural or torsional modes). Here, I mean naural because it is the frequency of a system based on its own characteristics NOT the forcing characteristics. RIGHT?

when theese lines coming from vertical axis intersect with the lines from origin we get resonance.

Now,

My question is:

In computing the natural frequencies, shouldn't we include damping BOT due to FRICTION as well as structural damping ?

Of course the natural frequency is WITHOUT effect of foprces according to me.

sankalpmittal- how can you bring external foirce here? IT is the frequency due to a disturbance not force-Right?

5. Dec 1, 2011

### svishal03

Anyone-pls help?

6. Dec 3, 2011

### sankalpmittal

Here is your Campbell diagram :-

Yes...

Yes...So...

Ok.

Right..

Yes...

See my previous reply and also the second reply by JHamm. When a body executes free vibrations , then the vibrations made per unit time gives its natural frequency. Free vibrations are the vibrations which a body executes in absence of outside interference i.e in vacuum or deep space.

In computing natural frequency we neglect any kind of damping , be it damping BOT due to FRICTION as well as structural damping.

If we include damping then we will have to compute friction of air , etc which are perhaps very difficult to. Also the frequency of a body will be different due to varying interference.

Look here : http://www.cs.wright.edu/~jslater/SDTCOutreachWebsite/nat_frequency.htm [Broken]

Yes.. without the effect of external periodic forces of other bodies..

Wow !! So you mean "resonance" has nothing to do with forced vibrations.

How about this : Tell me what you know about resonance and natural frequency. Also tell me the difference between "external force and external periodic force." Moreover tell me how a body is said to be in resonance with an example , and differentiate between resonance and forced vibrations.

Please do not copy from any website because I want your "own" explanation.

Last edited by a moderator: May 5, 2017
7. Dec 3, 2011

### svishal03

Sankalpmittal,

Thanks.

Now,

(I'm copying and pasting your questions below as I couldn't use quotes properly- my answers are against my name)

You said;

1) In computing natural frequency we neglect any kind of damping , be it damping BOT due to FRICTION as well as structural damping.

Vishal- But, then, resonance occurs when exciting/forcing frequency equals natural frequency. And, natural frequency varies with damping of course.

So, how will the prdiction of resonance be correct if we neglect damping?

Next, you said:

2) Of course the natural frequency is WITHOUT effect of foprces according to me.

Yes.. without the effect of external periodic forces of other bodies..

Vishal- Why periodic , why not non periodic?

Vishal- As I said above, resonance occurs when natural frequency = forcing frequency

Natutal frequency is number of vibrations per second/unit time based on the systems own/natutal characteristics

Resonance occurs when natural frequency = forcing frequency

Forcing frequency is cycles of force per second- i.e. number of times a force repeats per second.

Since, natural frequency will definitely vary with damping then if resonance is to be predicted then natural frequency computation should include damping- according to me.

4) Also tell me the difference between "external force and external periodic force."
Periodic forces have a periodicity that is, they repeat in same manner after a certain time/period. Non periodic forces are random and do not exhibit any repettion of a kind.

Moreover tell me how a body is said to be in resonance with an example
Vishal- At resonance the amplitude of vibration increases may fold as natural frequency= forcing frequency

5) and differentiate between resonance and forced vibrations

I have explained above the terms

8. Dec 3, 2011

### olivermsun

The "natural frequency" is defined as the frequency that would present itself in the absence of damping. A real system would have damping, so the frequency would be different from the natural frequency.

If the damping is weak then the frequency will be close to the natural frequency. As the damping increases then so does the deviation. If the damping is too large then the natural frequency becomes relatively unimportant, but then again the system won't do much "oscillating" either.

9. Dec 3, 2011

### svishal03

Thanks oliversun.

Yes, I was trying to say the same.

However, coming to the last point you said;

If the damping is weak then the frequency will be close to the natural frequency. As the damping increases then so does the deviation. If the damping is too large then the natural frequency becomes relatively unimportant, but then again the system won't do much "oscillating" either.

Assume, that damping is not weak but at the same time does not arrest oscillation 100% just reduces the frequency to considerable value than what it was without damping, then, in such a case, is the prediction of resonance correct using (undamped) natural frequency?

10. Dec 3, 2011

### sankalpmittal

Post #8 by olivermsun is just the repetition of my previous replies just in little detail. He gave the same definition as natural frequency as I had in previous posts.

Suppose you are driving a bike and at a particular speed you here a loud sound. This is because the natural frequency of the frame of bike is equal to or is the integral multiple (you missed this point about resonance) of the frequency of the engine at that time.

But the question arises about damping , right ? Imagine that the vibration of bike frame is of very high velocity than the force constant applied by outside surroundings on it. So it nearly reaches its natural vibrations which matches with frequency of external periodic force of engine. This resonance is determined as nearest approximation. It is not 100 % correct demonstration but is enough to experimentally understand resonance.

Understood ?

To quote a user just click on quote button at the bottom of his/her post.

Last edited: Dec 3, 2011
11. Dec 3, 2011

### svishal03

sankalpmittal and oliversum:

Ok, but I repeat my last question again- ok-I agree that natural frequency does not include damping.My question is again (as stated in post to oliversum- I would also be grateful if oliversum replies to this):

Assume, that damping is not weak but at the same time does not arrest oscillation 100% just reduces the frequency to considerable value than what it was without damping, then, in such a case, is the prediction of resonance correct using (undamped) natural frequency?

12. Dec 4, 2011

### sankalpmittal

Sorry to say but you repeated same question again. Have you read my previous post i.e. post #10 ? I illustrated your answer to question with the help of an example even...

I highly recommend that you again go through the post 10.

Now let me explain with another example :

Strike an odd piece of cutlery with a spoon. You will notice that at one particular force a very loud sound will be heard. This is because natural frequency of cutlery becomes equal to or is the integral multiple of the vibrations of the periodic external force of spoon.

If damping is very less , then you may predict resonance perhaps easily. As damping increases the prediction of resonance will perhaps become a lot difficult. You may then have to strike cutlery with much greater force for resonance to be predicted due to "unison".
Note that you will predict the resonance as nearest approximation which will not be cent percent correct demonstration. Perhaps it will be enough to fundamentally understand resonance.

Explaining the above mathematically is beyond the scope of my knowledge. You can as well try these sites :
http://en.wikipedia.org/wiki/Damping
http://www.newagepublishers.com/samplechapter/000591.pdf
http://www.lightandmatter.com/html_books/lm/ch18/ch18.html#Section18.3 [Broken]