Home / Examples / Acoustic Analysis [Mach] / Example 11: Interference of Sound Waves (2D Transient Analysis)

Example 11: Interference of Sound Waves (2D Transient Analysis)

General

The interference in Example 3 in the harmonic analysis is reproduced in the transient analysis.
We will confirm that the sound pressure distribution shifts to the steady state over time and the result matches with that of the harmonic analysis.
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	2D
Model Unit	m

Analysis Conditions

Analysis conditions for the transient analysis are listed below.

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

The analysis conditions for the harmonic analysis are mostly the same as Example 3. The difference is that the analysis frequency for comparison is set to 1KHz only.

General mesh size on the Mesh tab is set to 0.02m.

The timestep in the Transient Analysis tab is set up as follows.

By setting the timestep to Automatic, the timestep width will be automatically set so as not to incur the numerical instability.

The time steps of 20000 and the output interval of 100 will output 200 steps of field data.

Tab	Setting Item	Settings
Mesh	General Mesh Size:	0.02 [m]
Transient Analysis	Timestep	Automatic
	Calculation Steps	20000
	Output Interval	100

Model

The model is created in 2D. A semi-circle and two rectangle sheet bodies form the air.
The [speed] boundary condition by the sine wave is set on the sound generating portion. The [open boundary] is set to the perimeter of the semi circle.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
5/Sheet	Air	000_Air(*)

* Available from the material DB

Boundary Conditions

The boundary conditions of open boundary and speed are set for the transient analysis. The pressure boundary in Example 3 for the harmonic analysis is changed to the speed boundary of 0.01 [m/s].

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Settings
Open/Face	Sound Wave	Open Boundary	-
V1/Face	Acoustic	Speed (Sine Wave)	-0.01 [m/s] 1 [kHz]
V2/Face	Acoustic	Speed (Sine Wave)	-0.01 [m/s] 1 [kHz]

Results

The gradation contour diagrams of the particle velocities are shown below. The diagrams show the 10th, 25th, and 40th step of the transient analysis.

For easy viewing, the maximum and minimum values are set to 10 [mm/s] and 0 [mm/s] respectively in the gradient contour diagram setting.

Please note that the time at each step depends on the mesh if the time step is set to automatic.

Below is an approximate time with the general mesh size of 0.02 [m].

10th Step [1.55 ms]

25th Step [3.86 ms]

40th Step [6.18 ms]

It can be observed that the interference pattern is generated by the propagating sound waves over time.

The contour diagrams below are the results of the harmonic analysis with the same analysis conditions as the transient analysis.

170th Step [26.3 ms] Harmonic Analysis [1 kHz, phase 0°]

The transient analysis graph of radiation energy below shows the steady state is almost reached after time=25 ms ( approximately 160th step).

The gradation contour diagram of the particle velocity at the 170th step, which is in the steady state, is almost the same as that of the harmonic analysis.

It is verified that the results of the transient analysis are correct.

(Note: The results of the transient analysis change over time. It is not the case that the results after reaching the steady state match with those of the harmonic analysis at all times.)

The results match with a phase somewhere in the results of the harmonic analysis. In the case above, the result in the phase 0° is the same as that in the 170th step.)