# Discussion Forum

## loss factor

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Liu Jun

May 5, 2012 8:29am UTC

loss factor

Hi,

Is the loss factor in COMSOl the same with the viscosity factor?
I got the viscosity factor of silicon( as in the attachment) . And i want to use thest datas to calculate the Q factor of a MEMS resonator.

How can I do it? Can I directly consider the datas as loss factor in comsol?
Thanks!

Jun

Ivar Kjelberg

May 5, 2012 9:38am UTC in response to Liu Jun

Re: loss factor

Hi

first of all I'm not sure you are really allowed to "publish" such a nice article here on the forum (copyright issues), I would strongly advise you to extract just the image of the formula and use that here.

For the loss factor Q factor etc, there are many books and even wiki pages describing this nicely
And in all generality, in such cases I make myself up a small model and test it, to see how well
eta fits to 1/2/Q and how it relates to c/sqrt(k*m) i.e. for structural physics

note that dampoing is often changing slightly its definition for different physics (in the sens the constant are sometiems different, a factor 2, or 2 pi or ...
--
Good luck
Ivar

Liu Jun

May 7, 2012 9:03am UTC in response to Ivar Kjelberg

Re: loss factor

Hi

first of all I'm not sure you are really allowed to "publish" such a nice article here on the forum (copyright issues), I would strongly advise you to extract just the image of the formula and use that here.

For the loss factor Q factor etc, there are many books and even wiki pages describing this nicely
And in all generality, in such cases I make myself up a small model and test it, to see how well
eta fits to 1/2/Q and how it relates to c/sqrt(k*m) i.e. for structural physics

note that dampoing is often changing slightly its definition for different physics (in the sens the constant are sometiems different, a factor 2, or 2 pi or ...
--
Good luck
Ivar

Ivar

There is another question:
As i know, there are two methods for calculating the Q factor of a resonator: frequency response analysis and the damp eigenfrequency analysis. The calculation time of the former method is much longer than that of the later one.
Thus , i want to use the damp eigenfrequency analysis module to calculate the Q factor(Q=abs(imag(lambda)/2/real(lambda))).
The relation between the viscosity factor(eta_vis) of the silicon i got and the loss factor( eta) is :
eta=omega*eta_vis;
so I substitued omega*eta_vis into the loss factor option in the software.

Results show that the real part of the eigenvalue calculated is zero.

Must i use the frequency response analysis module for calculation the Q factor?

Thanks

Jun Liu

Ivar Kjelberg

May 7, 2012 7:34pm UTC in response to Liu Jun

Re: loss factor

Hi

wich mode gives "0" eigenfrequency ? If your device is "free to float around" theen indeed you should expect up to 6x "0" Hz eigenfrequencies fr the 6 DoF body modes, the 7th will be the "first" eigenfrequency to look at the realand imaginary part (if you have defined a damping, else you will have only real eigenfrequencies),and yo might get a different Q factor for the different > "0"= Hz modes too

The frequency domain scan is also a nice way to check, but its only worth to scan directly around the mode, you you need an eigenfrequency anaysis to get the first mode todefine your frequency scan range

--
Good luck
Ivar

Liu Jun

May 8, 2012 9:11am UTC in response to Ivar Kjelberg

Re: loss factor

Ivar

Thank you very much for your suggestions.
what i described may be not accurate.

the eigenfrequency is not zero.

In the damp eigenvalue analysis module, the eigenvalue is complex ,
but the real component of the eigenvalue is zero when the loss factor (eta=omega*eta_vis)is added as shown above, why?

thank you very much!

Jun Liu

Ivar Kjelberg

May 8, 2012 12:08pm UTC in response to Liu Jun

Re: loss factor

Hi
That the eigenfrequrency becomes complex, whn you add damping, is normal, it expresses the amplitude phase relation, but normally the real part should be >0 except if it's one of the fundamental Rigid Body modes, in which case the physics is not fully set up, or you should only consider the first >0Hz mode

--
Good luck
Ivar

Nagi Elabbasi
Certified Consultant
Veryst Engineering

May 8, 2012 2:59pm UTC in response to Ivar Kjelberg

Re: loss factor

Hi Liu, Ivar,

I had a similar problem in the past where I made the material loss factor eta a function of omega and COMSOL assumed omega=0 and resulted in no damping. I never pursued it further to see if it was an input error from my part, a theoretical issue or a COMSOL issue. It could be a theoretical issue because the eigenvalue solver may not be suitable for cases where damping is a function of the eigenvalue itself (which is part of the solution).

There is a workaround however, where you first solve without damping then put damping based on the current value of omega, solve again, update the damping and iterate. For mildly damped systems it should not take more than a couple of iterations.

Nagi Elabbasi
Veryst Engineering

Ivar Kjelberg

May 8, 2012 4:16pm UTC in response to Nagi Elabbasi

Re: loss factor

Hi Nagi

Thanks for pointing out the omega dependence, it's right that I mostly use a constant damping factor

--
Good luck
Ivar

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