General
Home / Examples / Piezoelectric Analysis [Rayleigh] / Example 9: Thickness Shear Mode
The thickness-shear mode vibration of AT-cut quartz crystal is analyzed.
The frequency response of electrode's impedance and the displacement vectors are solved.
Unless specified in the list below, the default conditions will be applied.
Results will vary depending on Femtet version and the PC environment.
Item |
Settings |
Analysis Space |
3D |
Model Unit |
mm |
The analysis type is resonant analysis.
Item |
Settings |
Solver |
Piezoelectric Analysis [Rayleigh] |
Analysis Type |
Harmonic Analysis |
Options |
N/A |
Output Setting |
Select [Impedance] |
The harmonic analysis tab is set up as follows.
Tab |
Setting Item |
Settings |
Mesh |
Meshing Setup | Set the general mesh size automatically: Deselect General Mesh Size: 0.06 [mm]
|
Harmonic Analysis |
Frequency |
Minimum: 18.0×106 [Hz] Maximum: 18.6x106 [Hz] |
Sweep Type |
Select [Linear Step by Division Number]. Division: 50 |
Circular electrodes are placed on the top and bottom faces of the AT-cut quartz crystal. Electric potential is applied to the electrodes.
The quartz crystal is divided equally into 3 layers. This makes the division size in the thickness
direction less than 1/6 of the wavelength regardless of the setting mesh size.
Note: If the vibration is thickness-shear mode, the thickness is half of the wavelength.
Body Number/Type |
Body Attribute Name |
Material Name |
0/Solid |
Quartz |
301_Quartz * |
3/Solid |
Quartz |
301_Quartz * |
4/Solid |
Quartz |
301_Quartz |
5/Sheet |
Electrode |
003_Ag * |
6/Sheet |
Electrode |
003_Ag * |
* Available from the material DB
The cutting angle is set by Euler angle.
Body Attribute Name |
Tab |
Tab |
Quartz |
Direction |
Euler Angle Specified: Euler Angle: Z=0, X=125.25, Z=0 |
Electrode |
Thickness/Width |
Thickness of Sheet Body: 0.2x10-3 |
Boundary Condition Name/Topology |
Tab |
Boundary Condition Type |
Settings |
earth/Face |
Electric |
Electric Wall |
Electric Potential Specified: Electric Potential 0 [V] |
hot/Face |
Electric |
Electric Wall |
Electric Potential Specified: Electric Potential 1 [V] |
The calculated frequency response of the impedance across the electrodes from an S(Y) parameters graph is shown below.
To change the range of X axis, set the range in the Graph Properties.
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 are shown below.
The displacement is specific to the thickness shear mode.