# What Is Resonance? (Part 3)

In the previous two articles (What Is Resonance? (Part 1) & What Is Resonance (Part 2)) in this series we have looked at how we can identify a resonant frequency. Now we will discuss what happens next. What do we do when the resonant frequency of a structure has been found? We will also look at some potential ways of dealing with a resonance is in a structure, body or piece of equipment.

First, it is necessary to understand what a resonance is. A resonance occurs when the natural frequency of a structure is excited by an input. If the frequency of the input matches the natural frequency of the structure, that is the excitation frequency matches the natural frequency, then a resonance occurs.

Generally, performing a test like a hammer impact test on a structure or capturing a run-up or run-down will enable the natural frequency to be observed.

A natural frequency is the frequency of free vibration of a structure at which the structure vibrates to dissipate energy. The natural frequency ($\omega$) of a structure, expressed in radians per second, is a function of its stiffness ($k$) and its mass ($m$), as shown by the following equation:

$\omega_{n} = \sqrt{\frac{k}{m}}$

If either the ($k$) or ($m$) parameters are altered, then the natural frequency will change.

If you want to modify the natural frequency of a structure, then you need to change either the stiffness ($k$) or the mass ($m$). Increasing the mass or lowering the stiffness will lower the natural frequency while reducing mass or increasing stiffness will increase natural frequency.

In summary

• Increasing mass or decreasing stiffness will reduce the natural frequency
• Decreasing mass or increasing stiffness will increase the natural frequency

Sometimes it is not possible to change the mass or stiffness of a structure. So how can we solve a resonance problem?

Several options are possible, but there are two common and relatively simple solutions.

The first option would be to change the operating speed of the equipment. This will move the operational range away from the natural frequency. In basic terms, you are changing the excitation frequency and moving it away from the natural frequency. Depending on the natural frequency and the frequencies of operation of the equipment this may require only a small change in speed. In other cases it might require such a large change in speed that it is not possible for operational reasons.

For example, Figure 1 shows the response of the equipment (red curve) at a certain speed. The black curve shows the natural response of the structure when the equipment is at rest. It is clear that we are exciting the natural frequency of the equipment at around 400Hz.

By changing the running speed of the equipment we can change the frequency of the excitation. So by avoiding the natural frequency we reduce magnitude of the vibration. In figure 2 we see that by reducing the excitation frequency from 400Hz to around 365Hz we have significantly reduced the overall vibration.

The second solution is to install a dynamic absorber (as shown in Figure 3) . This significantly reduces the vibration levels. The dynamic absorber is usually a spring-mass system that is installed in series with the resonant system to create an out-of-phase exciting force to effectively counteract the initial excitation force.

### A Simple Frequency Response Function (https://blog.prosig.com/2009/10/19/a-simple-frequency-response-function/)

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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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7 years ago

James, can you please e-mail me copies of Parts 1 & 2? Also, can you please point out the “absorber” in Fig. 3?
Do you have any information on treating natural frequency related radial vibration problems in high speed rotating equipment?

Guilherme
7 years ago

Good article James!