What is Resonance? (Part 2)

This article is a follow on from What Is Resonance? (Part 1) and answers some of the issues not covered in that post.

How do you find the resonant frequency in the real world? What do you do when there is a situation with multiple peaks in the frequency domain data? How do you know the frequency you have found is a resonant frequency?

To answer any and all of the above questions can often be very simple, but sometimes, not so. Often there is a single clear peak in the frequency domain data that is easy to pick out, but sometimes there are many peaks. How do you find what you’re looking for in this case?

First, we have to explain what we are studying. In this article we will look at frequency response functions and how they are used to find a resonant or resonant frequencies.

For example, if we have a frequency response function from a hammer impact test, how do we find the resonance?

If we look at the magnitude or modulus part of the frequency response function in a raw format we’ll see something like that shown in Figure 1.

Modulus part of transfer function

Figure 1: Modulus part of frequency response function

There is only one peak in this case, but how do we know for sure this is the resonance?

From the signal shown in Figure 1 we cannot say. We can make a best guess based on our understanding of the structure or part under test, but that is all.

So what do we need to make a judgement? The answer is phase.

With both the modulus and the phase it is possible to make a decision upon which frequency is the resonant frequency.

If we look closely at the modulus and phase signals shown in Figure 2, we can see the frequency peak, but we can also see a peak in the corresponding phase.

Modulus & phase part of the transfer function

Figure 2: Modulus & phase part of the frequency response function

In Figure 3 we have zoomed in on the x scale to see the data more clearly. It is now possible to pick out the peak at 1758Hz. We have highlighted it using the DATS cursor marker function.

Modulus & phase of transfer function (x scale zoomed)

Figure 3: Modulus & phase of frequency response function (x scale zoomed)

Pay careful attention to the plots of the peak and it is clear to see that the peak at 1758Hz does have a corresponding phase switch of 180 degrees. This is a classic sign of a resonance, a large peak associated with a flipping in phase.

Generally, an engineer will not see data this clear or obvious, but this article is intended to show the concept of how you would find a resonance in a simple system.

Modulus & phase of transfer function (modulus shown on log scale)

Figure 4: Modulus & phase of frequency response function (modulus shown on log scale)

Further plots of this form would classically be shown on a logarithmic scale (or log scale for short). Figure 4 shows the same data on a log scale. Here both the resonance and the anti resonance are shown. The anti resonance was not visible at all on the linear scale, but shows itself and its phase inversion clearly in the log scale at 1689Hz. If not for viewing the data in the logarithmic form, this additional information would have been missed by visual inspection.

Further Reading & Viewing

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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.

12 thoughts on “What is Resonance? (Part 2)

  1. Tylor Liu

    Hello,

    Please tell me the reason it have to be 180 deg change when resonance?

    what if the amplitude peak is not with the phase change, what is the peak normal means in physical phenomenon?

    1. James Wren Post author

      Hello Tylor,

      Thanks for asking some questions on our blog.

      For your first question, actually it is a little more complex than that.

      As we detailed above if the frequency response function has a peak at a certain frequency and the phase shifts by 180 degrees, this indicates a natural frequency of the structure.

      The natural frequency is actually the frequency in the middle of the phase shift.

      If we assume a simple system, like a simple beam, then at frequencies below resonance the force and response are in phase.

      At resonance the force and response are 90 degrees out of phase, but above resonance the force and response are 180 degrees out of phase.

      The value of the natural frequency is determined by the dimensions of the structure and the wavelength of the excitations being reflected back onto themselves.

      For your second question, an amplitude peak with no phase changes would indicate a response that is not a natural frequency. This can often be caused by a high amplitude frequency component of the excitation force.

    1. James Wren Post author

      Hi Farid,

      Thank you for asking a question on our blog.

      Basically in a structure there will be a frequency at which if a force is applied at a particular point, this force will not cause any motion of the structure.

      These frequencies are known as the anti-resonances.

    1. James Wren Post author

      Hello Ryan,

      Thank you for asking a question on our blog.

      Sirens do not cause any sort of Resonance, so it is not applicable.

      Perhaps your confusing Resonance and the Doppler effect?

  2. Alan

    How does a phase shift of 90 degrees at the resonant frequency creat such a high response? What is the physical meaning of this? Cheers

    1. James Wren Post author

      Hello Alan,

      Thank you for asking a question on our blog.

      At a resonance the phase will shift 180 degrees. The centre of this shift will enable you to find the frequency of the resonance.

      The phase is the relationship between the input and the output basically. When they are opposites you have a resonance.

      The resonance occurs when the maximum potential energy is converted to the maximum kinetic energy, that is the input and the output are opposites at a particular frequency.

  3. Hao Lam

    Hello James,

    I found these articles are very useful for non-experienced vibration engineers.
    May I use your articles to trained our new engineers at my company.

    Regards,
    Hao Lam

    1. Prosig

      Hello Hao Lam

      James is away from the office for a few days so I will reply for him.

      We are pleased that you like the articles. You are welcome to use them for training purposes. We only ask that you state that they came from Prosig. And maybe encourage your engineers to read the blog themselves 🙂

      Regards

  4. Samruddhi Katkar

    When we are using an accelerometer and Impact hammer , FFT of Accelerometer signal(response to impact of hammer) represents Natural frequency? If yes then why to use FRF?

    1. James Wren Post author

      Hello Samruddhi,

      Thank you for asking a question on our blog.

      That is a good question, the answer is that where you only have the FFT of the response, you would be looking at just that, the response.

      You have no way of knowing what frequencies have been excited, there would be no coherence, so you would have not have any certainty in the validity of your results.

      Also we should be clear the FRF is a transfer function in this case. It shows the energy and frequency that transfers from one point to another. The FFT of the response will just show the frequencies of the response when excited by an unknown force and in an unknown frequency range.

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