## 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.

## 10 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.

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