We hear the word used a lot, but what is resonance? First, in order to explain we have to explain the terms we will use.
A period is the amount of time it takes to complete one cycle
The number of cycles in one second is the frequency of an oscillation.
Frequency is measured in Hertz, named after the 19th-century German physicist Heinrich Rudolf Hertz
One Hertz is equal to one cycle per second.
What Is Resonance?
A resonance occurs when a structure or material naturally oscillates at a high amplitude at a specific frequency. This frequency is known as a structural resonant frequency. Typically a structure will have many resonant frequencies.
A dictionary definition of resonance gives us –
“the state of a system in which an abnormally large vibration is produced in response to an external stimulus, occurring when the frequency of the stimulus is the same, or nearly the same, as the natural vibration frequency of the system.”
When the damping in a structure is small, the resonant frequencies are approximately equal to the natural frequencies of the structure, which are the frequencies of free vibrations of the molecules of the material itself.
Furthermore, an individual resonance is the condition when a natural frequency of a structure or material and the frequency at which it is being excited are equal or very nearly equal. This results in the structure or material vibrating strongly and is the classical resonance state. This resonance state can often lead to unexpected behaviour of the structure or material.
The lowest natural frequency, often called the fundamental frequency, is related to the material of which the structure is made. The greater the mass or density of the material the lower the fundamental frequency of vibration. The natural frequency is also related to the speed that a waveform can propagate through the structure. This is determined largely by the molecular make up of the material. Gas, for example, has many free molecules with high kinetic energy, so the waveform can move quickly through the material. A solid has far fewer free molecules and is much denser, therefore the waveform moves more slowly.
In order to measure a resonance of a structure or material with a Prosig P8000 data acquisition system and DATS Professional signal processing software it is necessary to attach an accelerometer to the structure. It is then required to excite or stimulate the structure with the frequencies that it is normally exposed to in its working life. For example, an automotive car tyre would need to be subject to the frequencies it would encounter whilst in use. This would normally be accomplished by use of a shaker or a large heavy hammer. The tyre for example would need to be tested in isolation, and not connected to anything else like the vehicle suspension or wheel rim as these other parts have their own resonant frequencies and would make the capture and analysis of the tyre resonant frequency difficult.
The measured response from the accelerometer will be relative to the excitation and will only exhibit frequencies that are present in the excitation. The excitation must be an acceptable representation of the normal working frequencies applied to the structure or material. If the structure has a resonance in this frequency range there will be a large peak in the response spectrum. The frequency of this peak will correspond to one of the resonant frequencies of the structure or material. If no peak is detected then the resonant frequencies lie outside the operating range of the structure or material. In order to find the resonant frequencies of a structure or material it may be necessary to apply a wider range of frequency excitation.
Figure 1 shows a frequency spectrum, this spectrum is a response of a structure to its excitation. A large spike can clearly be seen at approximately 250 Hz.
Figure 2 shows a frequency spectrum, this spectrum as in Figure 1 shows a frequency response. However, Figure 2 shows, using cursors, the exact frequency of the resonance. In this case the resonant frequency is 245 Hz.
This means that this structure should probably not be used if in its working life it will be exposed to this frequency. Figure 2 also shows that if this structure was to be used, and only exposed to 300Hz to 400 Hz or perhaps 0Hz to 200Hz , this particular resonant frequency would not be excited, and therefore the structure would not vibrate abnormally.
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.