Piezoelectric coupled with a shunt circuit for vibration damping

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Rocksmida

Rocksmida

September 12, 2012 8:42pm UTC

Piezoelectric coupled with a shunt circuit for vibration damping

Hi, everyone! I am simulating the effect of a shunt circuit on the vibration of a piezoelectric device. Theoretically, with a shunt circuit connected (a resistor and a inductor in parallel with the pzt), the vibration of the device will be further damped. This is because the mechanical energy generated by the vibration of the pzt will be converted to electric energy and further consumed by the shunt circuit in the form of Joule heating. However, when I connect a shunt circuit to the two electrodes of the pzt, the vibration amplitude is unchanged. I bet the circuit and the pzt is not coupled well and the circuit does not back-affect the pzt module.

To make the problem clearer, I list the main boundary setup of my model:

For the PZD module: 1. one end of the pzt beam is fixed and a harmonic loading is applied on the other end;
2. the lower face of the beam is grounded; the upper face is set as floating potential; the other faces are set as zero charge;

For the electric circuit module:
1. ground node is 0;
2. a resistor node is added between 1 and 0;
3. a inductor is added between 1 and 0;
4 "External I vs.U" is added between 1 and 0 and is connected the PZD module and the voltage is the floating potential on the upper face of the pzt beam.


So the question is: 1. will the "electric circuit " module response back to the pzd module?
2. will the "electric circuit" module consider the conservation of energy and thus can consume the mechanical energy in the form of joule heating?
3. any comment on this model and any suggestions?

Thank you in advance for any comment and help!!

Rock

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Ivar Kjelberg

Ivar Kjelberg

September 19, 2012 7:06am UTC in response to Rocksmida

Re: Piezoelectric coupled with a shunt circuit for vibration damping

Hi

indeed V4.3 has changed something, I believe it was different in 4.2, this needs some more testing ;)

--
Good luck
Ivar

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Damiano Milani

Damiano Milani

September 19, 2012 3:03pm UTC in response to Ivar Kjelberg

Re: Piezoelectric coupled with a shunt circuit for vibration damping

Hello,

I have the same problem (version 4.2), as I described here www.comsol.com/community/forums/general/thread/12098/

The pzt beam behaves like a voltage generator: changing the impedance of the circuit, only the current changes.

Indeed the piezo beam should be affected by the electric load and vice versa.

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Ivar Kjelberg

Ivar Kjelberg

September 21, 2012 11:43am UTC in response to Ivar Kjelberg

Re: Piezoelectric coupled with a shunt circuit for vibration damping

Hello again,

How many elements do you have in the thickness of your PZT ? to see any effect on the damping versus CIR impedance you need at least 5 if possible far more in the THICKNESS (between the electrodes ;)

Or is it all "just" a mesh density effect, I would like to see the "k" factor come out

By the way CIR does not seem to be set up form eigenfrequency mode analysis (?)

--
Good luck
Ivar

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Damiano Milani

Damiano Milani

September 23, 2012 9:21am UTC in response to Ivar Kjelberg

Re: Piezoelectric coupled with a shunt circuit for vibration damping

Hello Ivar,

I have attached my model. I have 6 elements between the electrodes, but I still can not see any dependence of the electrical impedance in the CIR.

I would expect that the output power is dependent on the electrical load, but varying the resistance there is no change in the mechanical or electrical behavior of the beam.

Maybe I have set wrong conditions (the "terminated" Terminal could help?), or maybe wrong analysis (indeed you cannot use eigenfreq analysis with CIR physics).

Thanks in advance

Attachments:   2d_piezobeam_dynamics.mph  

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Ivar Kjelberg

Ivar Kjelberg

September 24, 2012 5:48am UTC in response to Damiano Milani

Re: Piezoelectric coupled with a shunt circuit for vibration damping

Hi

Indeed something seems to have changed over the last versions.

First of all with CIR I do not get any differences either, even if I see a difference in the induced voltage along the thickness of the beam (when you have more than 3 elements in the thickness ;)
So there are two comments / warnings for CIR "External I Terminal", as well as the one I usually use "External I vs U Terminal" about back coupling the current source, this might need something more.
But anyhow in stationary, at time t= INF the current is = 0

So I believe one need transient or harmonic /frequency sweep cases.

Anyhow, you can also use the terminal node alone without CIR physics, by adapting power input and changing manually the impedance from 1 to 1E6 ohm

So try to add a frequency domain solver at 20 Hz, remove (delete fully) the CIR physics, first disable the floating terminal, then set the terminal 1 to Terminated, 0 mW and User defined impedance 1 Ohm, then derived variables average line 8, dump the values of u2 and v2 into a table. Change the impedance to 1E6 ohm and run again, check the average u2, v2, then enable floating terminal and run again, you will see the displacement amplitudes at 50 Hz are slightly different, with a damping (imaginary part) when you change R, but no damping with the Floating terminal

Now you can try to change the mesh density and see the effects

And CIR seems not to accept eigenfrequency PZD solutions, again looks like some (back)coupling is missing that we have to set up manually, this needs more thoughts, even Multiphysics require that we fully understands what is behind it all ...

--
Good luck
Ivar

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Damiano Milani

Damiano Milani

October 8, 2012 11:10pm UTC in response to Ivar Kjelberg

Re: Piezoelectric coupled with a shunt circuit for vibration damping

Hi Ivar,
Thank you very much for your help.

I tried to follow your suggestions, but I have noticed 2 things:

- during the eigenfrequency analysis, changing the resistance value, the natural frequency has a very small variation; instead if I use a frequency domain analysis, the resistance is very effective on the natural frequency.

- using this frequency domain analysis on the resistance I get a complex voltage value. I suppose that it is a phasor, whose phase refers to the applied load. But the current, although there is a resistive load, does not have the same phase.

Another thing: what is the difference between eigenfrequency and eigenvalue analysis? does the eigenfrequency consider the damping matrix?

Thanks

Damiano

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