# How do we design or modify a system to avoid resonance?

##### After finding the natural frequency of a system, what could be done to stop or reduce the systems resonance being excited? Basically put, how do we avoid resonance

This is simple in theory, but not always so simple in practice.

If the natural frequency is $f_n$

Then,

$f_n = \left(\frac{1}{2\pi}\right)\sqrt{\frac{k}{m}}$

And where the undamped natural frequency is $w$,

$w=\sqrt{\frac{k}{m}}$

Where k is stiffness and m is mass.

Therefore to avoid resonance being excited we must change either k or m or both. In general, the fundamental consideration for an example SDOF system is to make the system as stiff as possible, increase k, but keeping the mass as low as possible, decrease m. This will have the effect of raising the natural frequency, the objective is to raise it enough that it is outside of the working range or out of the excitation range.

So, in practice how could this be carried out?

As a guide the general rules of thumb are

1. Stiffening without adding mass raises the natural frequency.
2. Adding mass without stiffening lowers the natural frequency.
3. Increasing damping lowers the response, but widens the range of the response.
4. Decreasing damping raises the response, but in a narrower range.
5. Reducing the forcing function reduces the response.

You may be dealing with one or any combination of the above list with an initial design. However, modifying a design after can be more complex. For example, if the stiffness is increased, but the change adds mass, it is possible the resonance would not have changed as the two changes could have cancelled each other out.

When working with new designs, or modifying existing designs, simulations can be left wanting. In all situations it is best practice to test the system before and after changes.

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#### James Wren

Former Sales & Marketing Manager at Prosig
James Wren was Sales & Marketing Manager for Prosig Ltd until 2019. James graduated from Portsmouth University in 2001, with a Masters degree in Electronic Engineering. He is a Chartered Engineer and a registered Eur Ing. He has been involved with motorsport from a very early age with a special interest in data acquisition. James is a founder member of the Dalmeny Racing team.

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Dave Yantek
6 years ago

In practice, there are usually several natural frequencies that could present a problem. Shifting the problem natural frequency by changing the mass or stiffness can sometimes move the original problem natural frequency so that it is not a problem, but then shift a different natural frequency so that it lines up with the excitation frequency. In the case of fixed-operating-speed machinery where the operating speed can be adjusted slightly without affecting performance, sometimes a few hundred RPM change in operating speed can reduce the response enough to eliminate the problem.

6 years ago

I need to avoid the resonance between a pressure vessel and the steel structure which support this equipment.
The resonance range is very low ( from 0,5 to 6 hz.) so the best solution is to isolated this pressure vessel of structural steel in order to reduce this range.
I am thinking about to use cable supports in order to reduce the resonance range to 0,5 – 3 hz.
Do you have experience whit this low resonance experience?

5 years ago

What about a continuous system?? What should be the relation between excitation frequency and first modal frequency.??

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MW
4 years ago

Isn’t it fn = 1/2pi root(k/m) not 1/pi

4 years ago

Now corrected. Thanks for the spot, MW.

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AJK
3 years ago

My question is, why is it absolutely necessary to use impact hammer, rather frequency response function to determine the natural frequency of the system? If use accelerometer and excite the object by any means , lets say by wood or something, it should be regarded as a natural frequency.

3 years ago

[…] ) must-see videos:                                                                                                                       Tacoma Narrows Bridge collapse — https://www.youtube.com/watch?v=j-zczJXSxnw ; https://www.youtube.com/watch?v=6LbkM1AhxNM ; the physics behind it — https://blog.prosig.com/2014/04/10/how-do-we-design-or-modify-a-system-to-avoid-resonance/ […]

3 years ago

If there’s a known set of problem frequencies, like from walking or wind gusts on a pedestrian bridge, is there another frequency in the same kind of range that’s least resonant to both of them? I don’t know anything about engineering, I’m just being curious.

Kevin
2 years ago

I have a fantastic 25 pound inch thick aluminum elbow bracket for mounting test units on a vibration table on my lab, I don’t want to get rid of it.

However it resonates at 90/180/270/360 hz. The noise at 270 and 360 is ear splitting.

Can I fix it bolting on heavier blocks or better yet drilling holes in it or milling channels into its surface?

Fazwan Musa
2 years ago

Hi
My objective is to shift the natural frequency of a thin rectangular plate, by adding a rib/stiffeners. But after adding it, my mode shapes are completely change into a new deformations in each modes. Is that valid? Second question is how much percentage should i shift natural frequencies?

thanks.

Ari
1 year ago

Hi James,

For the second question,

I believe the actual request was:
What margin of safety should the F-natural be outside the F-excitation?
E.g. F-natural should be +/- 5% outside the F-excitation

(Or at least, this is my question!)

Thanks

dave
2 years ago

I am a audio hobbyist designing exciter speaker 5mm thick plywood sound boards. To fit my room they are suspended from the rafter at about 8 feet height, and for clear headroom they cannot exceed 50cms height, I have about 80cms width to play with. For best level freq response from about 100hz to 12khz I learn that the boards must dimensions must cause resonance above or below audible frequency. I can change dimensions easily, thickness and density would be tricky.
Dayton audio suggest the boards width be 4/5 its length and the exciter be placed at 3/5 of the width and 3/5 of the length. Is this correct if peaks and troughs in the freq spectrum are to be minimised ?
For my next step I have to think about a 20hz to 100hz woofer exciter sound board.

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