II. How To Use ATILA

4.1 Rosen Type Transformer (2)
BOUNDARY CONDITIONS


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


BOUNDARY CONDITIONS

The boundary conditions needed for the problem are the electrical conditions on the piezoelectric ceramics and the definition of the polarization direction of the ceramics. There are no mechanical conditions, as the system is considered to vibrate freely in space.

Potential

Data -> Conditions -> Surfaces -> Potential 0.0 (or Ground in ATILA 5.2.4 or higher version) -> Assign the top surface of the PZT -> Forced Potential 1.0 -> Assign the bottom surface

To apply the electrical boundary conditions on the ceramics, select the Surfaces tab, and then Electric Potential in the drop-down list. First, apply the excitation signal by selecting the Forced potential option. Define an excitation signal of amplitude 1V and zero phase, and apply it to one of the input electrodes.


Define the reference electrode by selecting the Ground potential condition and applying it to the other input electrode.


The condition on the output electrode is a little special, and is called Floating. This condition indicates that the surface must display the same potential value at all nodes. However, this value is not imposed. It is computed.


You can verify that all potentials are correctly applied by selecting Draw | Colors.


In this last picture, it is easy to see where the ground, floating, and forced potentials are applied. The other values displayed here have no importance, except for the two immediately following the word "Forced." These values, 1.0 and 0.0, represent the amplitude and phase of the excitation signal.

Polarization/Local Axes

The next step consists in defining the required polarizations. Here, we will consider that the polarization is uniform in each section of the transformer. Therefore, we will apply the polarization named Cartesian.
The polarization in the input section is oriented in the thickness direction, while that of the output section is oriented along the length of the transformer, such that each section of the transformer operates in the so-called d33 mode.
The definition of polarizations is done by using local coordinate systems, also called Local Axes. To understand how the polarization is defined with respect to local axes, please read the help files about the ATILA-GiD interface (under the ATILA | Help menu).
Select the Volume tab of the conditions window, then Polarization from the drop-down list. Select Local-Axes | Define in order to create a polarization.

Enter P_input for the name of the local axes, and select, for instance, the 3 Points XZ definition mode.


 

Here, it is convenient to select three points of the geometry in order to define the local coordinate system, but remember that point coordinates can also be typed in the command line.

Next, define the polarization for the output section, P_output by following the same procedure.


Next, assign the polarizations that you have just created. Select the Local Axes name and then Assign to the appropriate volume. For the P_input polarization, first:


and the P_output polarization:

To review the polarizations, select Draw | This Polarization | Exclude Local Axes.


Finally, it is always a good idea to verify all the boundary conditions. Select Draw | All Conditions | Exclude Local Axes.


In this last drawing, the V indicates that an electrical potential condition is applied. The arrows show the polarizations.