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Frequency response of displacement at a point -- maximum amplitude varies with frequency resolution
Posted 13.11.2014, 20:45 GMT-5 Structural Mechanics Version 4.4 4 Replies
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I am studying an example in the Model Libraries, the 'shear bender' under 'Structral Mechanics Module\Piezoelectric Effects'.
The example has only Stationary study.
I added a Eigenfrequency study, and found one of the resonant frequencies to be 19057.945Hz.
I then added a Frequency Domain study to see the ampliftude of displacement around 19057Hz.
I chose a point on the tip of the shear band to generate a 1-D plot of the displacement at that point.
I started with a frequency resolution of 50Hz, the plots looks fine, I can see the displacement peaks around the resonant frequency.
The problem is when I increase the freqeucny resolution from 50Hz, to 10Hz, 5Hz, 1Hz, the maximum value keeps increasing. This may be fine, if the system has high Q. At better resolution, I expect to see the peak increase to some extent. However, when I change frequency resolution from 0.1Hz to 0.5Hz, the amplitude jumped from 0.35mm to 4.5mm, more than 10 times! (I have attached a pdf file with the plots.)
The shear bender is used as example here. I noticed this issue in one of my own projects, in which a metal plate is being studied. At finer resolution, the maximum displacement also jumps like discribed above. Eventually the value obtained becomes unrealistic given the thickness of the metal plate. We are trying to compare the displacements at several resonant frequencies, but now it seems those results are questionable.
Can anyone share some thoughts on this? Thanks.
The example has only Stationary study.
I added a Eigenfrequency study, and found one of the resonant frequencies to be 19057.945Hz.
I then added a Frequency Domain study to see the ampliftude of displacement around 19057Hz.
I chose a point on the tip of the shear band to generate a 1-D plot of the displacement at that point.
I started with a frequency resolution of 50Hz, the plots looks fine, I can see the displacement peaks around the resonant frequency.
The problem is when I increase the freqeucny resolution from 50Hz, to 10Hz, 5Hz, 1Hz, the maximum value keeps increasing. This may be fine, if the system has high Q. At better resolution, I expect to see the peak increase to some extent. However, when I change frequency resolution from 0.1Hz to 0.5Hz, the amplitude jumped from 0.35mm to 4.5mm, more than 10 times! (I have attached a pdf file with the plots.)
The shear bender is used as example here. I noticed this issue in one of my own projects, in which a metal plate is being studied. At finer resolution, the maximum displacement also jumps like discribed above. Eventually the value obtained becomes unrealistic given the thickness of the metal plate. We are trying to compare the displacements at several resonant frequencies, but now it seems those results are questionable.
Can anyone share some thoughts on this? Thanks.
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4 Replies Last Post 13.01.2015, 08:32 GMT-5
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Posted:
10 years ago
Hei!
I think the problem is, that your system is undamped, leading to an infinite gain at resonance. As your frequency variable is discrete, you cannot see the singularity, as long as you don't evaluate your function directly at resonance frequency. But as you increase the resolution, the resulting values close to resonance are growing to absurd numbers.
Try to add some kind of damping to your model (as I am pretty new to Comsol myself, I cannot come up with a suggestion myself unfortunately).
I think the problem is, that your system is undamped, leading to an infinite gain at resonance. As your frequency variable is discrete, you cannot see the singularity, as long as you don't evaluate your function directly at resonance frequency. But as you increase the resolution, the resulting values close to resonance are growing to absurd numbers.
Try to add some kind of damping to your model (as I am pretty new to Comsol myself, I cannot come up with a suggestion myself unfortunately).
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Posted:
10 years ago
Hi, Daniel,
Your are quite right about the cause. Once I added damping, I no longer see the singularities.
The issue now becomes how to model the damping effect. The Comsol documentation suggestes a few ways to introduce damping. For example, one way is to specify a lossing factor, but the Comsol built-in material doesn't supply such values. In one of their examples, they specify a loss factor of 0.02 for steel. I'm experimenting other materials, and there are no information about loss factor.
There are other ways you can take some measurement of the Q around resonance and deduce the damping ratio. But I'm still evaluting the system I want to build, there is no measuremnt data.
Your are quite right about the cause. Once I added damping, I no longer see the singularities.
The issue now becomes how to model the damping effect. The Comsol documentation suggestes a few ways to introduce damping. For example, one way is to specify a lossing factor, but the Comsol built-in material doesn't supply such values. In one of their examples, they specify a loss factor of 0.02 for steel. I'm experimenting other materials, and there are no information about loss factor.
There are other ways you can take some measurement of the Q around resonance and deduce the damping ratio. But I'm still evaluting the system I want to build, there is no measuremnt data.
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Posted:
10 years ago
Hi,
as I am facing the same problem in one of my models, I did some research and as far as I know, there is no way to deduce the damping properties just from material parameters without measurement data. In my case, I am modelling a silicon cantilever, fixed at one end and operating in high vacuum. My workaround so far is, to estimate the quality factor separately using analytical approaches (there is literature available to estimate loss through thermoelastic damping, clamping, etc ...) and then introducing a loss factor to my simulation.
Has anyone an idea for a better approaches to study the structuryl behavior close to resonance frequency?
as I am facing the same problem in one of my models, I did some research and as far as I know, there is no way to deduce the damping properties just from material parameters without measurement data. In my case, I am modelling a silicon cantilever, fixed at one end and operating in high vacuum. My workaround so far is, to estimate the quality factor separately using analytical approaches (there is literature available to estimate loss through thermoelastic damping, clamping, etc ...) and then introducing a loss factor to my simulation.
Has anyone an idea for a better approaches to study the structuryl behavior close to resonance frequency?
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Posted:
10 years ago
Hi Daniel,
Material damping in general cannot be calculated, it has to be measured. There are exceptions like thermoelastic damping which can be calculated, and also damping from a surrounding fluid which you don’t have in your case. In some small scale applications (common in MEMS) thermoelastic damping may be the main source of damping and you can neglect other forms of material damping. To predict thermoelastic damping from FEA analysis or analytical equations you need reliable thermal properties however.
Nagi Elabbasi
Veryst Engineering
Material damping in general cannot be calculated, it has to be measured. There are exceptions like thermoelastic damping which can be calculated, and also damping from a surrounding fluid which you don’t have in your case. In some small scale applications (common in MEMS) thermoelastic damping may be the main source of damping and you can neglect other forms of material damping. To predict thermoelastic damping from FEA analysis or analytical equations you need reliable thermal properties however.
Nagi Elabbasi
Veryst Engineering