Home / Examples / Acoustic Analysis [Mach] / Example 5: Resonance in Cavity

Example 5: Resonance in Cavity

General

 

• The resonance of sound waves excited in a cavity is analyzed.
   

• The sound waves radiated from the cavity are peaked when the excitation frequency matches the cavity's resonant frequency.
   

• 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.

The project contains an axially-symmetric model (AxialSymModel) and a 3D model (3dModel). The axially-symmetric model only is explained here.
For the 3D model, a quarter of calculation is applied to the model utilizing the symmetry. For easy calculation, the mesh size and the analysis frequency are different from the axially-symmetric model.
That is for comparing with the axially-symmetric model.

 

Analysis Space

Item	Settings
Analysis Space	Axisymmetric
Model Unit	mm

 

Analysis Conditions

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

 

The tab setting is listed below.

Tab	Setting Item	Settings
Harmonic analysis	Frequency: Sweep Values	Minimum:  1 [kHz] Maximum: 20 [kHz] Frequency Step: 0.1 [kHz]
	Frequency: Sweep Type	Linear Step by Frequency
	Frequency Sweep	Discrete Sweep
Open Boundary	Coordinates of Origin	x = 0 z = 0

Model

It is axisymmetric, so just right half of the section is created with a sheet body and defined as air. The open boundary is set on the perimeter of the quadrant circle representing the surface of the cavity.

The speed is set as the boundary condition on the bottom of the cavity.

 

 

 

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
8/Sheet	AIR	000_Air(*)

* Available from the material DB

 

 

Boundary Conditions

The [speed] boundary condition is set on the bottom of the cavity and the [open boundary] condition is set on the perimeter.

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

 

 

Results

The Figure below is the frequency plot of the sound pressure level [dB] at x=0, z=10.

The peak is at 8.8 [kHz].

 

 

The Helmholtz resonance equation below gives an approximated resonant frequency of 8.69 [kHz].

The value almost coincides with the calculated value.

 

C: Sound speed, V: Volume of cavity

 

 

 

The gradation contour of the sound pressure level at the driving frequency of 8.8 [kHz] is shown below.

 

 

 

The sound pressure is quite high in the cavity.