Computing the 6mm Piezoelectric Matrix

One or more PRAP analysed resonance files can be added to a PRAP compound file (of extension '.PZC'). By combining the analysis results of the Basic Analysis Package 6mm length, thickness, radial extensional, and thickness shear resonance modes measured in the same material, 9 of the 10 independent properties in the [s^E, d, e^T] matrix of the reduced piezoelectric matrix for 6mm (C_¥) materials are available. The use of the length-thickness extensional mode is optional. The undetermined property is s^E₁₃, and can be found from the following equation;

sE13

where

Due to over parameterisation, frequency dispersion in material properties, and experimental errors, the analysis results from the thickness mode will not be identical to the [s^E, d, e^T] matrix transformed to the [c^E, e, e^S] matrix. The value for s^E₁₃ can be improved by transforming the completed matrix to the [c^E, e, e^S] matrix representation, comparing the corresponding c^E₃₃ to the value of c^E₃₃ determined directly from the resonance modes included in the compound file, and adjusting s^E₁₃ by the discrepancy. This procedure can then be repeated until results converge.

PRAP automates the above considerations in the 6mm Piezoelectric Matrix dialogue box. To construct the complete piezoelectric matrix;

Open a new compound file with the 'New Compound File' command of the File menu.
Using the 'Add PZF File' command of the File menu, add the spectra you wish to study.
Ensure that each spectrum has been analysed, and that samples from the 4 above-mentioned modes are included. You can ensure the spectra are analysed by displaying each included resonance scan with the 'Display Resonance Scan' menu command from the Window menu.
Select the 'Piezoelectric Matrix' command from the Tools menu.
Refinement options and the matrix representation displayed are adjustable from within the Piezoelectric Matrix dialogue box.
The completed matrix can be printed on the current PRAP printer using the 'Print' button.

Using the Rotated TE mode

Use of the LE mode is the usual way of computing the complete piezoelectric matrix. Because of the length of samples needed to induce the LE mode, they are difficult ot pole and difficult to measure. In addition, properties determined from the LE mode are generally of a significantly lower frequency then the properties determined by the other three modes.

PRAP introduces an additional TE mode where the direction of poling has been rotated 45° about the x or y axis. Use of this mode in the PRAP compound document permits the computation of the complete 6mm piezoelectric matrix of a material without use of the LE mode.

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