Home / Examples / Coupled Analysis / Piezoelectric-Acoustic Analysis [Rayleigh/Mach] / Example 1: Harmonic Analysis

Example 1: Harmonic Analysis

General

• The model is a piezoelectric disc. The AC voltage applied across the top and bottom faces generates the vibration,
  resulting in the emission of sound waves into the air.
   

• This is a piezoelectric-acoustic coupled analysis.
   

• Unless specified in the list below, the default conditions will be applied.

 

• Please set the body attributes to solvers properly. Follow the settings on Body Attributes and Material below.
  
   

• 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	m

 

Analysis Conditions

The solvers are Rayleigh and Mach.

Item	Settings
Solver	Piezoelectric Analysis [Rayleigh] Acoustic analysis [Mach]
Analysis Type	Harmonic Analysis
Options	N/A

 

The harmonics analysis tab is set up as follows.

The sound waves propagate outside the analysis region. Therefore the "open boundary" condition below is applied initially.

The default conditions will be applied.

Tab	Setting Item	Settings
Harmonic analysis	Frequency	Minimum: 2000 [Hz] Maximum: 2000 [Hz]
	Sweep Type: Linear Step by Division Number	Number of Divisions: 0
Open Boundary Tab	Type	Absorbing Boundary
	Order of Absorbing Boundary	1st-order
	Coordinates of Origin	x = y = z = 0

 

Model

A piezoelectric disc (Unit) is placed on an aluminium disc (Plate). The hemispheric body (Air) covers the upper area.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
0/Solid	Air	000_Air *
1/Solid	Unit	000_P-4 *
2/Solid	Plate	001_Al *

* Available from the material DB

 

Unit and Plate are for the piezoelectric analysis only, whereas Air is for the acoustic analysis only.

 

Body Attribute Name	Analysis Domain (Solver)
Unit	Piezoelectric Analysis (Rayleigh)
Plate	Piezoelectric Analysis (Rayleigh)
Air	Acoustic Analysis (Mach)

 

Cautions:

In this analysis, it is required to specify the analysis domain.

That is to specify either piezoelectric analysis or acoustic analysis on the analysis domain tab.

Boundary Conditions

The side periphery of the model is fixed in the Z direction.

Electric wall is set on the top and bottom faces of the piezoelectric disc.

The open boundary is set on the hemispheric surface.

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Settings
V0/Face	Electric	Electric Wall	Electric Potential Specified: Electric Potential 0 [V]
V1/Face	Electric	Electric Wall	Electric Potential Specified: Electric Potential 10 [V]
Fix/Face	Mechanical	Displacement	Select UZ and set UZ=0
Open	Acoustic	Open Boundary

 

Results

The magnitude of displacement is shown below.

The largest displacement is indicated in the center area.

 

The contour of the sound pressure on the XZ section is shown below.

The sound waves are propagating from the top of the device.