## 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

Solutions Engineer and Sales & Marketing Manager at Prosig
James Wren is a Solutions Engineer and the Sales & Marketing Manager for Prosig Ltd. 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 special interest in data acquisition. James is a founder member of the Dalmeny Racing team.

## 22 thoughts on “How do we design or modify a system to avoid resonance?”

1. Dave Yantek

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.

1. James Wren Post author

Helo Dave,

Thank you for posting on our blog and thank you for your comments.

I agree with what you have said 100%, your point is valid and very clear, thank you for your suggestion. The article did not focus on this point, the fact that you can adjust the excitation frequency by varying things like RPM is a very sound engineering practice and potentially much easier than a re-design.

2. Francisco

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?

1. James Wren Post author

Hello Francisco,

Thanks for posting on our blog.

That is indeed a low frequency, but generally these are low frequency issues.

You idea seems sound, however we could not comment further without a detailed knowledge of your structure.

If you understand the structure, the frequencies and the masses involved you should be able to use the cable supports as anti-vibration mounts. If you are unsure then further research into the anti-vibration mounts is required.

If it is something of interest Prosig have several engineers with many years experience designing anti-vibration mounts and Prosig systems and software can be used for the evaluation of these design issues.

Please feel free to make contact if you so desire.

1. James Wren Post author

Hello BloggingPanda,

Thank you for posting on our blog.

I am not sure your questions are completely clear to understand.

In practical terms excitation should generally be broadband if your trying to excite a structure with the objective of finding a particular or all resonances.

There will be a relationship between the excitation and the first mode, but to find that one would perform some practical test or mathematically model the system, for example in a simulation.

We would recommend practical test to find a mode rather than a mathematical process as structures more complex than a simple beam tend to be rather difficult in terms of finding boundary conditions and free states.

1. James Wren Post author

Hello MW,

Thank you for posting on our blog.

I can confirm you are indeed correct, it would appear when we transcribed the formula to our blog the ‘2’ went missing.

I would like to thank you for bringing this mistake to our attention.

3. AJK

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.

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5. sinksmith

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.

1. James Wren Post author

Hello Sinksmith,

Thank you for asking a question on our blog.

I understand your question.

If you have a structure like a bridge for example, it will have a natural frequency.
The engineers who design the bridge, will calculate what this should be from their design, the good engineers will validate this guess once the bridge is constructed.

In any case the bridge will have a natural frequency. The affect of wind, will again cause excitation of the bridge. The engineers will have designed the bridge in such a way that the natural frequency and the frequency excited by t he wind will be different.

The engineers do this by changing the mass or the stiffness of the bridge.

In short, you design the structure so that it’s natural frequencies do not overlap with the frequencies that will be excited by normal usage.

I hope this clarifies the issue for you, feel free to ask if you have further questions.

6. Kevin

I have a fantastic 25 pound inch thick aluminum elbow bracket for mounting test units on a vibration table on my lab, I donâ€™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?

1. James Wren Post author

Hi Kevin,

Thank you for posting on our blog.

The short answer to your question is ‘Yes’.
The long answer is more complex, to change the natural frequencies you have to change the mass or the stiffness of the structure.

You can change the mass by adding the heavy blocks you mention, or by changing the structure itself, milling or drilling, but the milling or drilling will also change the stiffness.

So I recommend adding additional mass, then the stricture is unchanged and you can always go back to your current configuration.

It really depends on the testing your doing however, if you change the behaviour of the bracket, you are in effect changing the behaviour of the vibration table.

So please think about it like this, are the natural frequencies of the bracket, frequencies of interest to the test? If so additional thought maybe required, for example you would have to consider where you measure the input force to the structure.

You could also consider some form of damping to the bracket, something that could absorb a lot of the energy that is creating the noise. Perhaps a very tough rubber mount for example, this is in effect changing the stiffness. But again the force and frequency that the test piece is then subject to has to be considered.

Perhaps you could suggest the frequencies of interest for your test? Are they outside the natural frequencies you have mentioned?

Please feel free to post back if you so desire.

7. Fazwan Musa

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.

1. James Wren Post author

Hello Fazwan,

Thank you for posting on our blog.

We understand your objective, please understand if you have a simple structure and then redesign the structure, the mode shapes will most likely change. It would appear you have significantly changed the structure, therefore one would expect a significant change to the mode shapes. If you are unsure, perhaps you could check the equipment you use to capture and analyse the mode shapes.

Regarding your second question, only you can answer. The natural frequency should be outside the range of frequencies normally excited by the standard operation of the equipment. That could mean a 2% shift or a 500% shift. It depends on the operating conditions of the equipment and the natural frequency.

Please fee free to ask if you have further questions at all.

1. Ari

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

8. dave

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.

1. James Wren Post author

Hello Dave,

Thank you for posting on our blog.

The issue here will be related to wavelength I believe, hence the dimensions being critical, 100Hz to 12kHz is a wide range and would give you a range of wavelengths from 3.43m down to 0.028m. If you could design the sound board to have a natural resonance outside the human auditory range, that would be perfect, but might be a challenge.

I would suggest testing the initial build and then refining the design with further iterations as you approach your desired goal, probably best to test with a swept sine wave, across the range of your interest.

You could then sweep through the frequency range and test to ensure that you do not have any resonances in the range you desire. If you did have to move a resonance, only mass and stiffness of the structure will provide any variables that could shift the resonance significantly.

I hope this helps and good luck!

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