The structural material properties used in this problem (taken from Yan [1]) are as follows:
| Material | Elastic Modulus (Pa) | Poisson's Ratio | Density (Kg/m3) |
|---|---|---|---|
| Alumina | 3e11 | .2 | 3720 |
| Aluminum | 7e10 | .3 | 2700 |
| PZT | 9.2e10 | .33 | 7700 |
| Steel | 2.1e11 | .3 | 7800 |
| Titanium | 1.1e11 | .32 | 4430 |
Piezoelectric materials typically have orthotropic material properties, although isotropic materials are assumed in this example, as they are defined in that manner in the reference.
The piezoelectric materials properties (taken from Berlincourt [3]) are as follows:
|
Relative permittivity in x, y |
762 |
|
Relative permittivity in z |
663 |
|
Piezoelectric constant e13 |
-5.2028 |
|
Piezoelectric constant e23 |
-5.2028 |
|
Piezoelectric constant e33 |
15.0804 |
|
Piezoelectric constant e52 |
12.7179 |
|
Piezoelectric constant e61 |
12.7179 |
A system damping ratio of 0.1 percent is assumed for the model, as the ultrasonic transducer has very little damping.