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Time Dependent Simulations With Piezoelectric Devices

Posted Sep 9, 2024, 4:37 a.m. EDT 10 Replies

Sergey Filimonov
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Hi. I have a problem with the Time-Dependent solver when working with the piezoelectrics module. I am modeling a piezoelectric ring that is fixed by Roller on the inner hole. First I do the modeling in Static analysis, then in Eigeinfrequency for natural frequencies (I chose the frequency 46380 Hz. Everything works well), then to check the identity of the shape of oscillations at 46380 Hz I check in Frequency Response mode (the results of oscillations coincide with Eigeinfrequency). But in Time-Dependent mode the oscillation shape does not match. How I adjusted Time-Dependent: I created an analytical function V0 = 100*sin(2*pi*46380*t). Then substituted V0(t) into Terminal. I set the range depending on the applied frequency (frequency 46380 Hz corresponds to a period of approximately 22 µs) range(1.0e-6,1.0e-6,2.0e-5 [s]) . But the result always shows as in Static mode. It feels like it doesn't see the frequency. How to get a match with Frequency Response mode?

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10 Replies Last Post Sep 15, 2024, 3:31 p.m. EDT
Edgar J. Kaiser Certified Consultant
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Posted: 2 months ago Sep 9, 2024, 11:02 a.m. EDT

Hi Sergej,

you may need to run the time dependent solver with manual time stepping instead of the default setting. Make sure the manual time steps resolve the waveform with sufficient precision.

Cheers Edgar

-------------------
Edgar J. Kaiser
emPhys Physical Technology
www.emphys.com
Hi Sergej, you may need to run the time dependent solver with manual time stepping instead of the default setting. Make sure the manual time steps resolve the waveform with sufficient precision. Cheers Edgar
Henrik Sönnerlind COMSOL Employee

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Posted: 2 months ago Sep 10, 2024, 3:42 a.m. EDT

Note also that you in general need to run many cycles (maybe 10-100) to reach the steady state corresponding to a frequency domain analysis. The amount of damping in the structure, and the quality of the initial conditions determine how many cycles you need.

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Henrik Sönnerlind
COMSOL
Note also that you in general need to run many cycles (maybe 10-100) to reach the steady state corresponding to a frequency domain analysis. The amount of damping in the structure, and the quality of the initial conditions determine how many cycles you need.
Sergey Filimonov
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Posted: 2 months ago Sep 11, 2024, 11:21 a.m. EDT
Updated: 2 months ago Sep 11, 2024, 11:45 a.m. EDT

Thank you for the recommendations. I tried to implement them. I slightly changed the boundary condition - changed the Roller mounts to Fixed. Accordingly, the frequency has changed (I use 38270 Hz). The shape of oscillations in the Eigeinfrequency mode corresponds to the Frequency Response mode (Screenshot_3 + Screenshot_4). The shape of oscillations looks like a traveling wave in several points. The analytical formula became 100sin(pi38270*t).

In the Time Dependent: range(0,1.0e-6,3.0e-5 [s]); Tolerance - user controlled; Relative tolerance - 0.0001.

In the section Direct: Solver - SPOOLES; Preordering algorithm - Nested dissection; Pivot threshold - 0.1.

In the section Time-Dependent Solver: Solver tipe - Implicit; Method - Generalized Alpha; Step taken by solver - Manual; Time step - 1.0e-6; Absolute tolerance - 0.0001.

In the section Fully Coupled: Maximum number of iterations - 100.

But unfortunately the result for Time-Dependent mode has not changed (Screenshot_2). The shape of oscillations remains the same as in static mode, compressing and uncompressing along the thickness. By the way, if you plot the Point Graph, you can see that the oscillation frequency corresponds to approximately 1 Hz, i.e. the specified frequency is not applied in the calculation (Screenshot_5). Maybe I have set something wrong? What else can be done?

Thank you for the recommendations. I tried to implement them. I slightly changed the boundary condition - changed the Roller mounts to Fixed. Accordingly, the frequency has changed (I use 38270 Hz). The shape of oscillations in the Eigeinfrequency mode corresponds to the Frequency Response mode (Screenshot_3 + Screenshot_4). The shape of oscillations looks like a traveling wave in several points. The analytical formula became 100*sin(pi*38270*t). *In the Time Dependent:* range(0,1.0e-6,3.0e-5 [s]); Tolerance - user controlled; Relative tolerance - 0.0001. *In the section Direct:* Solver - SPOOLES; Preordering algorithm - Nested dissection; Pivot threshold - 0.1. *In the section Time-Dependent Solver:* Solver tipe - Implicit; Method - Generalized Alpha; Step taken by solver - Manual; Time step - 1.0e-6; Absolute tolerance - 0.0001. *In the section Fully Coupled:* Maximum number of iterations - 100. But unfortunately the result for Time-Dependent mode has not changed (Screenshot_2). The shape of oscillations remains the same as in static mode, compressing and uncompressing along the thickness. By the way, if you plot the Point Graph, you can see that the oscillation frequency corresponds to approximately 1 Hz, i.e. the specified frequency is not applied in the calculation (Screenshot_5). Maybe I have set something wrong? What else can be done?
Edgar J. Kaiser Certified Consultant
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Posted: 2 months ago Sep 11, 2024, 2:38 p.m. EDT

As Henrik commented, the mode won't build up after just one period. It also depends on the way you apply the exciting load. It may or may not couple well into the specific mode.

Cheers Edgar

-------------------
Edgar J. Kaiser
emPhys Physical Technology
www.emphys.com
As Henrik commented, the mode won't build up after just one period. It also depends on the way you apply the exciting load. It may or may not couple well into the specific mode. Cheers Edgar
Sergey Filimonov
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Posted: 2 months ago Sep 12, 2024, 5:06 a.m. EDT

Thank you. Got it.

I needed to increase the measurement time without changing the step. I did so range(0,1.0e-6,300.0e-5), that is, I increased the measurement range by 100 periods. At the first periods it is purely static mode, and then the mode of oscillation of the set frequency, which coincides with the modes Eigeinfrequency and Frequency Response, began to appear.

But still it somehow echoes the static mode. Maybe it is necessary to increase the measurement time?

And I understand that the result analysis should be done on the last periods of the specified range, the initial results should be simply ignored.

Thank you. Got it. I needed to increase the measurement time without changing the step. I did so range(0,1.0e-6,300.0e-5), that is, I increased the measurement range by 100 periods. At the first periods it is purely static mode, and then the mode of oscillation of the set frequency, which coincides with the modes Eigeinfrequency and Frequency Response, began to appear. But still it somehow echoes the static mode. Maybe it is necessary to increase the measurement time? And I understand that the result analysis should be done on the last periods of the specified range, the initial results should be simply ignored.
Dave Greve
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Posted: 2 months ago Sep 12, 2024, 12:29 p.m. EDT

The time required for a transient analysis to reach steady state depends on the amount of damping in the system and can be extremely long if there is little damping. (100 periods is nothing as quality factors can be...tens of thousands in some systems).

It is not clear why it is necessary to do a transient analysis. If really necessary it may be possible to approach the steady-state solution by choosing the "right" initial condition. Alternatively some insight might be gained by increasing the damping, especially if there is additional damping in the actual physical system.

The time required for a transient analysis to reach steady state depends on the amount of damping in the system and can be extremely long if there is little damping. (100 periods is nothing as quality factors can be...tens of thousands in some systems). It is not clear why it is necessary to do a transient analysis. If really necessary it may be possible to approach the steady-state solution by choosing the "right" initial condition. Alternatively some insight might be gained by increasing the damping, especially if there is additional damping in the actual physical system.
Sergey Filimonov
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Posted: 2 months ago Sep 12, 2024, 2:52 p.m. EDT
Updated: 2 months ago Sep 12, 2024, 3:26 p.m. EDT

Thank you for the additional recommendations. The problem is that we don't need a transient process as such. We need to see the shape of the piezoelement oscillations. Yes, it can be seen in Eigeinfrequency and Frequency Response modes, but only at one frequency.

And we need to see the shape of piezoelement oscillations when several frequencies are applied to it simultaneously. That's why we have to use Time Dependent mode. I just thought at first that it would automatically show the shape of oscillations under the desired frequency, but here it is different. Without all your advice everything would have stayed the same. Thanks all.

Thank you for the additional recommendations. The problem is that we don't need a transient process as such. We need to see the shape of the piezoelement oscillations. Yes, it can be seen in Eigeinfrequency and Frequency Response modes, but only at one frequency. And we need to see the shape of piezoelement oscillations when several frequencies are applied to it simultaneously. That's why we have to use Time Dependent mode. I just thought at first that it would automatically show the shape of oscillations under the desired frequency, but here it is different. Without all your advice everything would have stayed the same. Thanks all.
Dave Greve
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Posted: 2 months ago Sep 13, 2024, 2:35 p.m. EDT

If the system is linear you can use superposition to combine the results from multiple frequency dependent simulations. I think this could even be done with Comsol postprocessing, but it would require some of the advanced options.

If the system is linear you can use superposition to combine the results from multiple frequency dependent simulations. I think this could even be done with Comsol postprocessing, but it would require some of the advanced options.
Sergey Filimonov
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Posted: 2 months ago Sep 15, 2024, 1:19 p.m. EDT

This is very interesting. I can't yet imagine how this can be implemented. If possible, could you go deeper into this direction?

This is very interesting. I can't yet imagine how this can be implemented. If possible, could you go deeper into this direction?
Dave Greve
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Posted: 2 months ago Sep 15, 2024, 3:31 p.m. EDT

This is very interesting. I can't yet imagine how this can be implemented. If possible, could you go deeper into this direction?

Suppose you want the time-dependent displacement of a point. Solve the sinusoidal steady state problem for the various frequencies fn. The displacement of the point at frequency fn is xn(t)=real(Xne^j2pifn*t) where Xn is the complex phasor that is the solution at frequency fn. Now add up the xn(t) to get the total displacement.

>This is very interesting. I can't yet imagine how this can be implemented. >If possible, could you go deeper into this direction? Suppose you want the time-dependent displacement of a point. Solve the sinusoidal steady state problem for the various frequencies fn. The displacement of the point at frequency fn is xn(t)=real(Xn*e^j*2*pi*fn*t) where Xn is the complex phasor that is the solution at frequency fn. Now add up the xn(t) to get the total displacement.

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