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Electrostatic Spring Softening in Frequency Domain

Posted Nov 15, 2021, 10:46 a.m. EST Electromagnetics, Structural & Acoustics, MEMS & Piezoelectric Devices Version 5.6 3 Replies

Anosh Daruwalla
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Hi,

I am simulating a capacitive MEMS device (similar to an in-plane flexural beam) with an electrode on either side of the beam for actuation and sensing respectively, with air gaps between them properly defined. I am using the electromechanical physics with the frequency domain prestressed study. The device is biased using a DC voltage and an AC voltage is applied to the electrode via harmonic perturbation. These are my boundary conditions: Terminal 1 with Harmonic perturbation - One electrode (AC voltage) Terminal 2 - Output electrode on the other side Terminal 3 - Device itself biased with DC voltage

In the results, I am looking at the resonance peak of the device in a graph showing frequency range vs output current at terminal 2.

This is similar to the "biased resonator" example that COMSOL provides - and works well for displacement in the linear range of the gap (ie for small AC and DC voltages), however when I increase the AC voltage, it continues to show a linear peak in the frequency response even at large displacements. Clearly, the simulation isn't taking the electrostatic nonlinearity into consideration. Is there any way to simulate the nonlinear resonance peak from large displacement in the frequency domain?

3 Replies Last Post Nov 19, 2021, 3:07 a.m. EST
Henrik Sönnerlind COMSOL Employee

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Posted: 3 years ago Nov 16, 2021, 3:45 a.m. EST

Frequency domain analysis has the fundamental assumption that all quantities, excitation as well as response, are harmonic. This is not the case in a nonlinear system.

The only way to study a nonlinear system is in time domain. You can, however, use a linear frequency domain analysis to set up reasonable initial values for the time domain analysis. In that way, it takes less time to converge to a cyclic solution in time domain. You can still, however, expect to have to run the analysis for many cycles, in particular if the damping is low.

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Henrik Sönnerlind
COMSOL
Frequency domain analysis has the fundamental assumption that all quantities, excitation as well as response, are harmonic. This is not the case in a nonlinear system. The only way to study a nonlinear system is in time domain. You can, however, use a linear frequency domain analysis to set up reasonable initial values for the time domain analysis. In that way, it takes less time to converge to a cyclic solution in time domain. You can still, however, expect to have to run the analysis for many cycles, in particular if the damping is low.
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Posted: 3 years ago Nov 16, 2021, 9:53 a.m. EST

Thanks Henrik for your timely response. Are there any examples you'd recommend me to look at with regard to this?

Thanks Henrik for your timely response. Are there any examples you'd recommend me to look at with regard to this?
Henrik Sönnerlind COMSOL Employee

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Posted: 3 years ago Nov 19, 2021, 3:07 a.m. EST

I am not aware of such a model, but in principle you do the following:

  1. Two study steps, the first is Frequency Domain and the second is Time Dependent.
  2. Add a suitable load to be used in the frequency domain study. Typically, this is the same load as you would use later in the time domain study, but without the sin(omega*t) factor.
  3. Add the same load with the sin(omega*t) factor.
  4. In the Initial Values node, write displacement as imag(u) etc., and velocity as omega*real(u)
  5. In the studies, disable the non-used load for each study.
  6. Make sure that for the frequency domain study, the Stationary Solver has Linearity set to Linear.

Note: The exact use of real() and imag() and the signs in front of the operators depend on how you consider your time depence. In frequency domain, a quantity having no explicit phase is assumed have an implicit cos(omega*t)

Providing an example of this approach seems like a good idea. I have added such a suggestion.

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Henrik Sönnerlind
COMSOL
I am not aware of such a model, but in principle you do the following: 1. Two study steps, the first is Frequency Domain and the second is Time Dependent. 2. Add a suitable load to be used in the frequency domain study. Typically, this is the same load as you would use later in the time domain study, but without the sin(omega\*t) factor. 3. Add the same load with the sin(omega\*t) factor. 4. In the Initial Values node, write displacement as imag(u) etc., and velocity as omega\*real(u) 5. In the studies, disable the non-used load for each study. 6. Make sure that for the frequency domain study, the Stationary Solver has Linearity set to Linear. Note: The exact use of real() and imag() and the signs in front of the operators depend on how you consider your time depence. In frequency domain, a quantity having no explicit phase is assumed have an implicit cos(omega\*t) Providing an example of this approach seems like a good idea. I have added such a suggestion.

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