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.