Product: ABAQUS/Standard
The frequency extraction analysis capability for materials that include piezoelectric coupling is illustrated.
The model is the cylinder described in “Static analysis for piezoelectric materials,” Section 3.5.1. Three analyses are performed using two different models. One model uses sixteen CAX4E elements, and the other uses four CAX8E elements. In addition, a single test that extracts the eigenvalues of an unconstrained CPE4E element using temperature- and field-variable-dependent piezoelectric and dielectric properties is included.
The first 10 modes are extracted. The lowest frequency for the CAX4E element model is 41.8 kHz. The lowest frequency for the CAX8E element model is 44.6 kHz. These mode shapes will be used in the following sections for the linear dynamics options. The restart capability will be used for this purpose. For the CAX8E element model the *SECTION FILE option is used to output the total force on the edge lying on the 
-axis.
For the unconstrained eigenvalue extraction test, the results match the corresponding results for an equivalent model where the piezoelectric and dielectric properties are independent of temperature and field variables.
Frequency extraction with CAX4E elements and *PIEZOELECTRIC, TYPE=S.
Frequency extraction with CAX4E elements and *PIEZOELECTRIC, TYPE=E.
Frequency extraction with CAX8E elements.
Restart of frequency extraction with CAX4E elements.
Frequency extraction for an unconstrained CPE4E element using temperature- and field-variable-dependent piezoelectric and dielectric properties.