II. How To Use ATILA

6.3 Tonpilz Sonar (2)
BOUNDARY CONDITIONS


PROBLEM - Tonpilz Transducer under Water, Axisymmetry, PZT8, Steel and Aluminum


BOUNDARY CONDITIONS

The boundary conditions needed for the problem are: electrical conditions on the piezoelectric ceramics, definition of the polarization direction of the ceramics, and the mechanical symmetry conditions.

Potential

Data -> Conditions -> Lines -> Potential 0.0 (or Ground in ATILA 5.2.4 or higher version) -> Assign the side surfaces of the PZT -> Forced Potential 1.0 -> Assign the center surface

To apply the electrical boundary conditions on the ceramics, select the Lines tab, and then Electric Potential in the drop-down list. First, apply the Forced condition on the hot electrodes. The Amplitude and Phase of the harmonic signal are 1V and 0º, respectively.

By using a 1V excitation, the results we will obtain (displacement, stress, and pressure) will be per volt. Note that the results computed by ATILA are proportional to the magnitude of the input signal because a linear formulation is used. This means that an input of 100V generates displacements, for instance, 100 times larger than with 1V.

Next, assign a Ground (reference) potential on the cold electrode.

Line Contraints

The axisymmetrical nature of the model requires that the displacement of nodes on the axis of axisymmetry (the X axis) be constrained to that axis (nodes on the axis cannot move away from the axis). To assign this condition select Line-Constraints in the drop-down list. Select the Clamped option for the Y component of the constraint. Apply this condition to the lines of the solid parts that are on the X axis.

Polarization

The piezoelectric ceramics are poled along their thickness direction such that the transduction occurs in the d33 mode. Because the poling of piezoelectric elements such as the rings used in Tonpilz transducers can be assumed to be uniform, we will use a so-called Cartesian polarization for each one of the transducing elements. To define Cartesian polarizations, Local Axes are used. The direction of the polarization is given by the z axis of the local axes.

First, select the Surface tab of the conditions window; then Polarization from the drop-down list. Select Local-Axes | Define to create new local axes. Enter P1 for the name of the local axis.

Select the 3 Points XZ definition mode, for instance. Here, it is convenient to use geometry points to define the center and directions of the local axes. Remember that it is also possible to enter point coordinates in the command line.

To use the mouse cursor to select the points, click once on the lower left corner of the PZT region. GiD should prompt you to use the existing point. Click Join. Repeat for the top left and lower right points to define the local axes.

Continue in a similar way for the second polarization, P2.

Once this is done, make sure Geometry Polarization is set to Cartesian. This will impose a uniform polarization in the selected surfaces. Also make sure that Local-Axes is set to P1. Then assign the condition to one of the piezoelectric surfaces.

Select P2 and repeat for the second piezoelectric surface.

Finally, you may verify that all conditions have been applied by selecting Draw | All Conditions | Exclude Local Axes from the conditions window.

Radiation Boundary

The only additional boundary condition that is needed is the definition of the radiating boundary. From the Boundary Conditions window, select the Lines tab, then the Radiating Boundary condition. Applying this condition to the arc will cause the pressure flux to be absorbed (and not reflected), thus allowing the acoustic energy to radiate in an infinite medium. Further, the elements of that boundary will perform the computation of the far-field pressure. Rules to position the radiating boundary are complex and vary depending on the problem.

Finally, you may verify that all conditions have been applied by selecting Draw | All Conditions | Exclude Local Axes from the conditions window. The Zigzag Arrow indicates the location of the radiating boundary.