Home / Examples / Acoustic Analysis [Mach] / Example 1: Radiation Impedance of Disc

Example 1: Radiation Impedance of Disc

General

• A vibrating disc is placed in the air. The sound waves generated by it are analyzed.
   

• The sound power, the radiation impedance and the sound pressure distribution for each frequency 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	m

 

Analysis Conditions

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

 

The harmonic 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: 200[Hz] Maximum: 3000[Hz]
	Sweep Type	Select Linear Step by Division Number. Division: 20
	Frequency Sweep	Discrete Sweep
Open Boundary Tab	Type	Absorbing boundary
	Order of Absorbing Boundary	1st order
	Coordinates of Origin	x = y = z = 0

Model

The air hemisphere is created from a solid body.

The open boundary is set on the surface of the hemisphere. A circular sheet body is defined for imprinting.
The velocity boundary condition is applied.

Body Attributes and Materials

The hemispheric solid body is created. The material is air.

The "speed" boundary condition is set on the circular face topology, which is created by segmenting the circular sheet body.

Body Number/Type	Body Attribute Name	Material Name
0/Solid	Air	000_Air(*)

* Available from the material DB

Boundary Conditions

The [speed] boundary condition is set on the face of the imprinting body.

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Settings
Open/Face	Acoustic	Open boundary
V0/Face	Acoustic	Speed	1[m/s]

Results

To see the calculated characteristics, go to the [Results] tab,

 

 

 and click [Show Numerical Summary Table].

 

As an example, radiation impedance is shown below. The graph can be displayed as well, by pressing the [Graph] button at the bottom of the table.

Other characteristics can be seen on other tabs.

 

 

The results and the theoretical values match. The theoretical values are calculated and plotted by Excel.

 

The theoretical values are calculated by the equations below. (*)

R: real part of the radiation impedance, X: imaginary part of the radiation impedance,

a: radius of the driving source, ρ: air density, c: sound speed, k: wavenumber (=2π/wavelength),

J1(z): 1st-order Bessel function

S(z): Struve function

 

 

 

The gradation contour of the sound pressure at the driving frequency of 200[Hz]

 

The gradation contour of the sound pressure at the driving frequency of 900[Hz]

 

The gradation contour of the sound pressure at the driving frequency of 2020[Hz]

 

The gradation contour of the sound pressure at the driving frequency of 3000[Hz]

 

The sound pressure varies as the driving frequency changes.

 

Note * Rayleigh's theoretical formula