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.
Dear James,
Your blog and explanations are really helpful – thanks. I’m a music student whose been asked to analyze and write about the Islamic call to prayer. During my research it became evident that in some countries the muezzin (caller) is being replaced by a pre-recorded version of the prayer (adhan). Hypothetically speaking, based upon the ‘sympatethic resonance’ effect might it be catistrophic if all 3,000 mosques in a a city (i.e. Istanbul) played the same adhan five times daily. If the sound was played collectively over loudspeakers could this produce a ‘walls of Jericho’ effect. Presently there is a ‘desynchronization’ of sound as various muezzin-s start calling at slightly different times, with different maqams (scales) and melodies, however I was just wondering…. Could a single call to prayer broadcasted across a city be problematic or when mosques and buildings are designed they automatically are damped so it won’t matter?
I’m a far better musician than I ever have been at physics or chemistry hence my question here…. your reply woud be most helpful.
Regards
Armani
Hello Armani,
Thank you for asking a question on our blog.
Your question is very interesting, it is however not possible for any damage to occur to a building structure from the co-ordinated playing of music.
From a structural point of view the buildings would not be affected for two reasons, the first reason is the frequency of the music is far too high to have any effect on structures of that sort. The sound waves would simply pass straight through.
Second, the magnitude of the sound wave would need to be very large to actually have enough power to excite a large structure.
With regards to constructive sound, this would happen if two points, or sound sources, had exactly the same music, and played it at exactly the same time. Exactly in between the two sound sources as the sound waves passed through each other there would be a constructive effect.
This is at that exact point the music would be louder.
I hope this answers your question.
Further to James’ comments I would add that structural damage is only likely to happen when there is high amplitude,low frequency excitation present(either impulsive or periodic. The “walls of Jericho” phenomenum is more likely to have been caused by the seismic impulses of the army marching in step around the city rather than due to the sound of the trumpets. The main contribution of the brass instruments was probably to improve the synchronisation of the marching soldiers.
Thank you very much. You have both been most helpful. Thanks.
HI,
I conducted a vibration test in a shaker machine. I applied 1 g acceleration and monitored the acceleration of the test piece. A linear sweep wave ranging from 30 Hz to 3500 Hz at 300 sec. The output acceleration curve shows some narrow peak points ( first one is acceleration peaked to 6g in a frequency range of 1110 Hz to 1130 Hz Hz. Second one is 5.16 g in a frequency range of 1325 Hz to 1500 Hz . Third one is 4.6 g in a frequency range of 1500 Hz 1650 Hz). But no significant increase in noise level is observed during this time. But a smoother increment in acceleration curve I observed was for 17 g in a frequency range of 2975Hz to 3495 Hz. Here there was a significant increase in noise level. I conducted a FEA for the same and found first natural frequency at 2900 Hz. My questions are, 1)What is the importance of noise curve? 2) How to interpret the narrow peaks? 3) Whether the first natural frequency is between 2975 to 3495 or prior to this peak like 1120 Hz? Kindly explain.
Benjamin Franklin,
Chennai, India.
Hello Benjamin,
Thanks for asking a question on our blog.
It sounds like the peaks your seeing are the natural frequencies of the structure your exciting.
Your Finite Element Analysis is giving you a natural frequency of 2700Hz, from the practical testing you have carried out it would appear to be inclusive. You say you have performed the test twice, but you have quite different results each time. Any practical test should be repeatable, no matter how many times you carry out the same test you should get the same results. I would suggest carrying out the practical tests again, perhaps repeating the test three times to make sure no experimental error is creeping into the testing.
Please feel free to come back and let us know your new results.
Dear James,
Thanks for your reply. I did not mention that I conducted the test twice. I intended to tell that those are the narrow peak curves I got when I swept the frequency from 30 Hz to 3500 Hz. Kindly draw a curve between Frequency and acceleration based on my values. Let the acceleration values for frequencies I did not mention be 1 g.I would like to ask you the significance of noise curve. Whether the narrow peaks makes sense even though there is no sign of noise level. Hope you understand my question. Kindly explain.
Hello Benjamin,
Thank you for asking another question on our blog.
I don’t think we can give you advise on your project exactly, we do not know what your structure is for example. Generally I would not expect to see very small spikes, that would mean there is very little energy in those bands and that the structure was only being excited in a very small band, which is not impossible, but unlikely. I would suggest looking again at your test procedure and the signal processing techniques you are using.
If you would like to discuss this further perhaps it would be best to contact us directly.
Hi James,I found your blog very helpful. I got a question to ask you. At one time of our testing, a resonant vibration at 2072 Hz and 34.26g in a valve had been found by some vibration measurements. We then measured in a separate test the natural frequency of one moving part by exciting the part by a special hammer which comes with a vibration measurement instrument. Its natural frequency is about 2000 Hz. I would like to know how I can find out the exiting frequency that caused the resonant vibration at 2072 Hz in our valve testing. Appreciate your help.
Hello Ricer,
Thanks for posting on our blog.
From what you have said you have a system which when tested had a resonant frequency of 2072Hz.
You then performed a separate test on a part of the system and found it had a resonant frequency of approximately 2000Hz.
And your question is that you are trying to find what had excited the system in the first place that then caused the resonance.
This is classical testing and analysis problem. I don’t know what your system is so I can’t offer you any specific advice, but generally if you have several inputs to a system you can simply remove them one at a time until you find the cause. There are more complex techniques but we would have to know more about your system to cover the more complex issues. You could for example consider something like Source Contribution Analysis, this could rank the inputs and show you which frequencies are being excited by which input.
If you would like to discuss this further perhaps it would be best to contact us directly.
Hi James, Thanks for the quick response. Let me simplify it to a more general question- if one has a vibration source in the system, say, 100 Hz. It can cause the resonances of 100, 200, 300 Hz,…. Is this correct? If there is a resonant frequency in the system in line with one of these frequencies, a resonant vibration would occur. Is this correct? As I observed a resonant vibration at 2072 HZ, could I say that what had excited the system had a frequency of 2072/n Hz (n is an integer)? Is it correct? Thanks again for your time. Appreciated your help.
Hello Ricer,
You have tested the system separately and found its resonance frequency to be 2072Hz, these results you deduced from hammer impact testing.
If the system had a resonance at 100Hz this would be excited by your 100Hz input. But if your system had a 200Hz resonance this would also be excited by your input of100Hz as one of the harmonics would fall at 200Hz and so on.
I hope this is clear for you and this information helps.
Sir,i wanted to know why we are going to find the fundamental natural frequency? (first mode of vibration) and which mode shape/ which frequency should be considered as natural frequency of a structure when there are infinite natural frequencies.
sir we can find the natural frequencies of a structure in any software ( STAAD or Nastran-patran)how about the excitation in these cases? without any external excitation how can we get natural frequencies?
Hello Vishwas,
Thanks for asking some questions on our blog.
Your questions are rather complex, perhaps you would be better to contact us directly and discuss I think for us to offer any advise we would need to have a lot more information about your structure and the tests you want to perform.
It is possible make a judgement on a natural frequency without excitation, but you have to consider many other issues.
Your better to isolate a structure and test it in isolation with measured excitation. That is the best way to find the natural frequencies.
Dear Ricer,
Very glad to find your blog here. And now i am finding some materials about “resonance point vibration durability test”. I think your blogs may not focus on reliability test, as a quality engineer, i want to learn the result of this resonnance point, how about its effect to our product after long time working.
And the most difficult question for me to define is the resonance point vibration test cycle and its duration time. How to calculate?
Looking forward to your reply, as i am not a English-speaking people, hoping you can understand my question.
Thank you!
Hello Belinda,
Thank you for asking a question on our blog.
For sure resonance will affect the long term reliability of your products.
Generally speaking products are designed so that in normal use the resonant frequency is never excited.
If your product is used at a range of frequencies that include its resonant frequency your testing should replicate the range of frequencies that the product will be exposed to during its working life. If you are trying to accelerate the life testing of a product then you can subject the product to higher levels of the same frequency that it would otherwise be exposed to. The increase in level is proportional to the acceleration and therefore life testing of the product.
Dear James,
Thanks for your reply.