Example9 Thickness Shear Mode

General

The thickness-shear mode vibration of AT-cut quartz is analyzed.
The frequency characteristics of electrode’s impedance and the displacement vectors are solved.
Unless specified in the list below, the default conditions will be applied.

The analysis type is resonant analysis.

Item	Settings
Solvers	Piezoelectric Analysis [Rayleigh]
Analysis Type	Harmonic analysis
Options	N/A

The harmonic analysis tab is set up as follows.

Tab

Setting Item

Settings

Harmonic analysis

Frequency

Minimum: 18.0×10^6[Hz]

Maximum: 18.6×10^6[Hz]

Step

Select “Linear step by division number”.

Division number: 50

Circular electrodes are placed on the top and bottom faces of the AT-cut quartz.

The quartz is divided into 3 layers in order to have properly sized meshes.
The thickness of each triple layer is approximately 1/6 wavelength of the analysis frequency, which would yield the reasonable mesh size.

* Available from the Material DB

The cutting angle is set by Euler angle.

Body Attribute Name

Tab

Quartz

Direction

Specified by: Euler angle

Euler angle: Z=0, X=125.25, Z=0

Electrode

Thickness/Width

Thickness of Sheet Body: 0.2×10^-3

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Settings
earth/Face	Electric	Electric wall	Voltage specified: Voltage 0[V]
hot/Face	Electric	Electric wall	Voltage specified: Voltage 1[V]

The frequency plot of this antenna’s impedance is shown below.

The resonant frequency is around 18.32[MHz]. The anti-resonant frequency is around 18.36[MHz].

The thickness shear mode at 18.3[MHz] is calculated.

The displacement vectors for it are shown below.