4mm Symmetry Module

The 4mm Symmetry module provides six standard 1-dimensional unloaded resonator modes of the 4mm (C_4v) 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

k_t, c^D₃₃, c^E₃₃, e₃₃, h₃₃, e^S₃₃

Length Extensional

k₃₃, s^D₃₃, s^E₃₃, d₃₃, g₃₃, e^T₃₃, e^S₃₃

Length-Thickness Extensional

k₁₃, s^E₁₁, d₁₃, g₁₃, e^T₃₃

Rotated (45°) Length-Thickness Extensional

k₁₃^45:Z, s₁₁^E45:Z, d₁₃, g₁₃, e₃₃^T

Thickness Shear

k₁₅, c^D₅₅, c^E₅₅, s^D₅₅, s^E₅₅, e₁₅, h₁₅, d₁₅, g₁₅, e^S₁₁, e^T₁₁

Breathing

k, s, e, N_s, rN²_s

Reduced 4mm Piezoelectric Matrix

Also included with the 4mm symmetry module is the piezoelectric matrix tool used to construct the complete reduced piezoelectric matrix for 4mm 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, LTE, rotated LTE, and breathing modes.

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 4mm (C_4v) material using the PRAP Compound document.

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