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

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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