Home / Examples / Piezoelectric Analysis [Rayleigh] / Example 9: Thickness Shear Mode

Example 9: Thickness Shear Mode

General

• 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.
   

• Obtain this session's project file. (Right-click and choose 'Save link as')




• Results will vary depending on Femtet version and the PC environment.

 

Analysis Space

Item	Settings
Analysis Space	3D
Model Unit	mm

 

Analysis Conditions

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]. Number of Divisions: 50

Model

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 Attributes and Materials

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 Conditions

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]

Results

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.