# Discussion Forum

## Piezo shunts and eigenfrequency analysis

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Jacopo Marconi

June 18, 2017 8:03am UTC

Piezo shunts and eigenfrequency analysis

Hi all,
I'm modelling a beam with a piezo attached on the top, and an electrical circuit attached to the patch: to do so I used the solid mechanics (solid), electrostatic (es) and circuit (cir) modules. I used successfully this model in both frequency domain and time domain analysis, but now that I want to perform the eigenvalue analysis (I want to extract the dispersion using my model as a periodic cell...) it doesn't work and it says that one equation is missing ("Singular matrix. - Detail: There are 1 void equations (empty rows in matrix) for the variable comp1.es.term1.Q0_ode. at coordinates: (0,0), ... "). The implementation is ok I think, in fact removing terminals and circuit it works... any idea?
Jacopo

Some more details:
The piezo-shunt is implemented as follows: the bottom face of the piezoelectric patch (attached to the beam) is grounded (es.ground), the upper one is connected to a circuit terminal (es.terminal 1 - type circuit), then a capacitor (in cir) is connected from node 0 (ground) to node 1 which is in turn connected to the terminal (in es) through a "External I - Terminal" connection (selecting terminal 1 for the electric potential). This layout always worked for me, I don't know what is going wrong this time...

Magnus Olsson
COMSOL Employee
Sweden

June 19, 2017 7:38am UTC in response to Jacopo Marconi

Re: Piezo shunts and eigenfrequency analysis

Hi Jacopo,

This is because the electrical circuit interface does not explicitly support the eigenfrequency study. There is a simple workaround:

* In the Model Builder, select the Electrical Circuit node.
* In the Settings window, expand the Equation section.
* Set the Equation form to Frequency domain.
* Set the Frequency to User defined and type freq in the f field.

Now, the Electrical Circuit will have the right equation form and variables to perform eigenfrequency analysis.

N.B. Do not forget to switch back to Study controlled before running a stationary or time dependent study.

Best regards,
--
Magnus

Jacopo Marconi

June 22, 2017 2:12pm UTC in response to Magnus Olsson

Re: Piezo shunts and eigenfrequency analysis

Hi Magnus,

thank you very much for your answer. I did what you suggested, but unfortunately it didn't work. Here the error:

"Error in sweep. The following feature has encountered a problem:
Singular matrix.
- Detail: There are 1 void equations (empty rows in matrix) for the variable comp1.es.term1.Q0_ode.
at coordinates: (0,0), ...
There are 1 void equations (empty rows in matrix) for the variable comp1.es.term2.Q0_ode.
at coordinates: (0,0), ...
- Feature: Eigenvalue Solver 1 (sol1/e1)"

I even tried change the settings in the electrostatic node as I did in the electric circuit node, but without success. Could it be due to the sweep analysis? I'll keep trying, thank you for the help!

Jacopo

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