6mm Symmetry Module

The 6mm Symmetry module is part of the Basic PRAP Analysis Package that is part of all releases of PRAP. This package includes the seven 1-dimensional unloaded resonator modes of the 6mm (C_¥) symmetry. Each mode is generated by a different sample geometry, and different material properties are determined from each mode. See links in the following table to view specific technical information about each mode.

Mode	Properties	Geometries
Thickness Extensional	kt, cD33, cE33, e33, h33, eS33
Length Extensional	k33, sD33, sE33, d33, g33, eT33
Length-Thickness Extensional	k13, sE13, d13, g13, eT33
Thickness Shear	k15, cD55, cE55, sD55, sE55, e15, h15, d15, g15, eS11, eT11
Length Shear	k15, cD55, cE55, sD55, sE55, e15, h15, d15, g15, eS11, eT11
Radial Extensional	sE11, sE12, d13, eT33, kP, kp, eP33, s, cP11, eP13, sE66
Rotated (45°) Thickness Extensional	kt45:X,Y, c33D45:X,Y, h3345:X,Y, b33S45:X,Y

Reduced 6mm Piezoelectric Matrix

Also included with the 6mm symmetry module is the piezoelectric matrix tool used to construct the complete reduced piezoelectric matrix for 6mm materials. This is done by combining several analysed resonance spectra of the above modes in the PRAP Compound file. The minimum modes required are the TE, LE, TS, and radial modes.

Because of the required length to width aspect ratio required for the LE mode, is is generally difficult to obtain good measurements with the LE mode. The rotated TE mode has been added as a substitute to the LE mode.

Circuit Models

Each of the above modes also generates an equivelent circuit model. For details, please see the following link;

Circuit Models

Features

Some additional features of the modes of the Basic Analysis Package are as follows;

• Determine complex circuit components

• Determine Van Dyke's circuit components

• Report real elastic and coupling properties determined from the equations of the IEEE Standard on Piezoelectricity

• Determine the complete complex reduced piezoelectric matrix for a 6mm (C_¥) material using the PRAP Compound document.

Tutorials

The following tutorials should assist you in performing some typical analysis procedures with PRAP Basic Analysis Package. Note that there is also extensive on-line information in the PRAP help system.

• Analysing the TE mode 

• Analysing the LE mode 

• Analysing the TS mode 

• Analysing the LS mode 

• Analysing the LTE mode 

• Analysing the Radial mode 

• Determining the reduced 6mm piezoelectric matrix 

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