II. How To Use ATILA

4.1 Rosen Type Transformer (4)
PROBLEM TYPE VIEW RESULTS


PROBLEM - Rosen Transformer 25 mm x 8 mm x 2.2 mm t


PROBLEM TYPE - Modal Analysis

Data -> Problem data -> 3D, Modal Resantires

We wish to perform a modal analysis of the transformer in order to identify its resonance frequency. With the boundary conditions that we have defined, the resonance mode will correspond to a low-signal excitation at the input side of the transformer, and open-circuit conditions at the output side.

You can use any Printing value. This will not affect the results, but only the amount of information printed in the LST file generated by ATILA. The Geometry should clearly be set to 3D. The Analysis that we wish to perform here is a Modal Resantires, because this particular type of modal analysis takes into account the piezoelectric properties of the material. In particular, it computes the resonance modes, as well as the antiresonance modes, of the structure. Finally, the Number of Modes is set arbitrarily. However, here, because the model consists in a 3D structure that is free of mechanical conditions, the first 6 modes computed by the modal analysis will correspond to the 6 rigid-body modes of the structure. It is therefore recommended to use a number greater than 6. Here, we pick 20.

Note that the mesh density limits the number of modes that can be accurately computed. With the mesh we have defined, we cannot expect to accurately compute modes that display more thanhalf a wavelength in the thickness direction, or more than one wavelength in the width direction, or more than three wavelengths in the length direction.
Note also that computation time increases geometrically with mesh density and with the number of modes.

Finally, make sure the Mesh Units are set to millimeters.

Do not forget to validate your changes by clicking on Accept Data. Then File | Save the problem.

CALCULATION - Modal Analysis

Calculate -> Calculate window -> Start

You can use the Calculate Window, as well as View Process Info commands in order to monitor the progression of the computation.

Note: Because we have set Printing = 0 in this tutorial (Problem Data section), very little information will be displayed in the View Process Info window. To obtain more details about the progression of the computation, set Printing to 1.

POST PROCESS/VIEW RESULTS - Modal Analysis

Click for Opening the Post Calculation (Flavia) Domain

Once the computation is completed, go to the postprocessing environment in GiD.
To see the list of frequencies, click on:

The list of frequencies for the resonance and antiresonance modes, as well as electromechanical coupling factors, is shown below.

Note that the first 6 modes clearly correspond to rigid body modes. Then, in the above figure, we have highlighted one mode (at 71.15kHz) which displays a high electromechanical coupling co-efficient (22.3%). This mode is most likely the λ/2 longitudinal mode.

Note that the frequency list is available in a comma separated value (CSV) format in the problem directory (use ATILA | Open Shell to directly access it).

This is easy to verify by displaying the deformation. For instance, from the GiD Deformation and View Results windows, select the resonance mode at 71.15kHz and display the mode shape.

 

Note that the values obtained for the displacement are only relative values. They do not represent absolute displacement values. To obtain displacement values at a specific frequency, it is necessary to perform a harmonic computation.

PROBLEM TYPE - Harmonic Analysis

Data -> Problem data -> 3D, Harmonic, Click "Include Losses"

We now want to compute the deformation and voltage gain at resonance.
Return to the preprocessing environment and save the problem under a new name, using File | Save_As. Change the Problem Dataso that the Analysis is now Harmonic. Make sure Losses is checked, so that losses are taken into account for this computation. Select Accept Data to validate your changes.

Click on to define the frequency intervals for the harmonic computation.
Here, we will use only one interval centered on the resonance frequency that was previously computed at about 71kHz. Therefore, we will define a frequency sweep between 70 and 72kHz, with increments of 40Hz.

Click Accept Data to validate your changes.

CALCULATION - Harmonic Analysis

In this problem, we are not changing any of the boundary conditions. We are still applying a 1V amplitude signal to the input section, and letting the output in open-circuit conditions. Therefore, we do not need to regenerate the mesh.
Make sure to save your problem (File | Save), and start the computation (Calculate | Calculate).

POST PROCESS/VIEW RESULTS

Click for Opening the Post Calculation (Flavia) Domain
Click Admittance/Impedance Result
 

Then, because we have used an excitation of amplitude 1V, displaying the electrical potential shows directly the transformation gain.

 

Note that we have displayed the magnitude of the potential on the drawing of the real part of the structure deformation.

View Animation - Vibration Mode at a Particular Frequency

View results -> Default Analysis/Step -> Harmonic-Magnitude -> Set a Frequency
(Peak Point : 71160 Hz for Resonance Mode)
Double Click Loading frequency: 71160 Hz Harmonic Case -> Click OK (Single Click and Wait for a while!)
Set Deformation -> Displacement
View results -> Deformation -> Displacement

Other parameter than Displacement

Set Results View -> View results -> Contour Fill -> Electric Potential
After setting both “Results view” and “Deformation” -> Click to see the Animation