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