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Rayleigh Damping model
Posted Sep 4, 2010, 12:57 p.m. EDT 2 Replies
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Hello everybody,
I'm trying to simulate a silicon cantilever which with a quality factor of 50. To implement the damping I'm using Rayleigh Damping model following the documentation of 3.5a structural smeug.pdf about damping (pages 140++, 199, 372) .
To calculate the parameters alfa and beta, I'm using two methods:
- Fix alfa to zero and compute beta knowing that the damping factor is 1/(2*Q)
- Using two frequencies close to the resonance frequency and computing alfa and beta using the relationship between the damping factor and the quality factor (dampf=1/(2*Q)). I'm using the MATLAB code shown in the 3.5a documentation.
To do the simulation I'm using a point force applied at the free end of the cantilever with a specific value. Doing a frequency domain simulation between two frequencies near the first vertical resonance (which I know because I've done an eigenfrequency simulation). When the simulation finish I plot the displacement of the tip vs the frequency and I compute the quality factor at a half of the resonance amplitude (-3dB) but either in both case it isn't 50.
Any clue about why the frequency response isn't showing the right quality factor?
Anything I'm doing wrong?
Thanks for your help and have fun!
I'm trying to simulate a silicon cantilever which with a quality factor of 50. To implement the damping I'm using Rayleigh Damping model following the documentation of 3.5a structural smeug.pdf about damping (pages 140++, 199, 372) .
To calculate the parameters alfa and beta, I'm using two methods:
- Fix alfa to zero and compute beta knowing that the damping factor is 1/(2*Q)
- Using two frequencies close to the resonance frequency and computing alfa and beta using the relationship between the damping factor and the quality factor (dampf=1/(2*Q)). I'm using the MATLAB code shown in the 3.5a documentation.
To do the simulation I'm using a point force applied at the free end of the cantilever with a specific value. Doing a frequency domain simulation between two frequencies near the first vertical resonance (which I know because I've done an eigenfrequency simulation). When the simulation finish I plot the displacement of the tip vs the frequency and I compute the quality factor at a half of the resonance amplitude (-3dB) but either in both case it isn't 50.
Any clue about why the frequency response isn't showing the right quality factor?
Anything I'm doing wrong?
Thanks for your help and have fun!
2 Replies Last Post Sep 5, 2010, 7:09 a.m. EDT
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Posted:
1 decade ago
Hi Jordi,
I think what's wrong in your procedure is just the definition of Q factor, since -3dB correspond to 1/sqrt(2) of the maximum amplitude and not to half amplitude.
Moreover you should check how fine is the frequency sweep about resonance peaks. You would obtain Q = 50 only if your frequency subdivision is quite "fine", so that the resonance curve is "smooth" enough.
I hope this helps.
Hi!
Alessandro
I think what's wrong in your procedure is just the definition of Q factor, since -3dB correspond to 1/sqrt(2) of the maximum amplitude and not to half amplitude.
Moreover you should check how fine is the frequency sweep about resonance peaks. You would obtain Q = 50 only if your frequency subdivision is quite "fine", so that the resonance curve is "smooth" enough.
I hope this helps.
Hi!
Alessandro
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Posted:
1 decade ago
Thank you very much Alessandro!
As you said, I was doing the calculation of the bandwidth wrong.
As you said, I was doing the calculation of the bandwidth wrong.