WHAT IS RESONANCE?
By James Wren, Application Engineer, Prosig
First, in order to explain resonance we have to explain the terms we will use.
• A resonance is a particular frequency.
• 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
• A single Hertz is equal to one cycle per second.
In technical terms, resonance is the tendency of a structure or material to oscillate at maximum amplitude at a certain frequency. This frequency is known as the structure’s resonant frequency. A dictionary 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 damping is small, the resonant frequency is approximately equal to the natural frequency of the structure, which is the frequency of free vibrations of the molecules of the material itself.
Further, resonance is the condition when the natural frequency of a structure or material and the frequency at which it is operated are equal or very nearly equal. This makes the structure or material become very excited; this is the classical resonance state. This resonance state can often lead to unexpected behaviour of the structure or material.
The natural frequency, often called the fundamental frequency, is related to the size of the structure and the material it is made of. This is because the larger the structure the lower the frequency and therefore a larger waveform can exist inside the structure or material. The natural frequency is also related to the speed the 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 much fewer free molecules and is much denser, therefore the waveform moves much more slowly.
In order to measure the 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 exert 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, whilst not connected to anything else like the vehicle suspension or wheel rim as these other parts would 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. The excitation must be an acceptable representation of the normal working frequencies applied to the structure or material. If this structure has a resonance in this frequency range there will be a large peak. This large peak is the resonant frequency of the structure or material. If no peak is detected then the resonant frequency is outside the operating range of the structure or material. In order to find the resonant frequency of the structure or material it is then required to apply a wider range of frequency excitation until the resonance is found.
Figure 1
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
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 , its resonant frequency would not be excited. And therefore the structure would behave as expected.
