Home / Examples / Piezoelectric Analysis [Rayleigh] / Example 13: Tensile Force and Resonant Frequency

Example 13: Tensile Force and Resonant Frequency

General

The model is a bar with two reversely polarized piezoelectric plates stuck together.
It is subjected to the tensile force, and the resonant frequency changes.
[Analysis with the initial stress taken into account] is applied. See Analysis with initial stress taken into account for the details.
The device's displacement and the resonant frequencies 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.

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	Resonant Analysis
Options	Analysis with initial stress taken into account Select Take into account Select Specify static load for boundary condition.

The resonant analysis tab is set up as follows.

Tab	Setting Item	Settings
Resonant analysis	Number of Modes	3
Resonant analysis	Approximated Frequency	0 [Hz]

Model

Two reversely polarized piezoelectric plates are stuck together. The end faces are set with the boundary condition of pressure.
The top and bottom faces are set with the boundary condition of specified electric potential.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
0/Solid	upper	000_P-4 *
1/Solid	lower	000_P-4 *

* Available from the material DB

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 10 [V]
f_left/Face	Mechanical	Pressure	-1X109 [Pa]
f_right/Face	Mechanical	Pressure	-1X1099 [Pa]

Results

The displacement diagram of Mode[0] is shown below.

The fundamental resonant frequency is 4.481E+4 [Hz].

On the [Results] tab

and click [Table] .

The table below shows the resonant frequencies.

Other characteristics can be seen on other tabs.

The table below is the results with the tensile force set to 0.

The tensile force affects the resonance.