Diaphram displacement on Helmholtz Resonator

Numerical methods and mathematical models of Elmer
raback
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Re: Diaphram displacement on Helmholtz Resonator

Post by raback »

Hi,

This is an interesting case. I looked a few minutes of what you might have to do:

1) Harmonic motion causes pressure waves
- See test cases "HelmholtzStructure*"
- But to my understanding this is not what you need. Your direction of causality is reverse.

2) Pressure waves cause displacements
- 1st solve Helmholtz equation with pressure inlet
- Solve the StressSolver with "Harmonic Analysis = True"
- Add BCs for the structure:
Normal Force = Equals "Pressure Re"
Normal Force Im = Equals "Pressure Im"
(It could be that the Helmholtz solver has names "Pressure 1" and "Pressure 2", don't remember the default...)

3) You need to solve a coupled system of pressure waves & harmonic motion
- This is the ultimate challenge but is solvable.
- Study the test cases "FsiShoebox*" involving Helmholtz equation
- Note that SmitcSolver could well be used for the plate part but then plate needs to be in (x,y) plane.
Thin structures are not ideal for StressSolver, particularly with lowest order elements.

Have fun!
Peter
Rich_B
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Re: Diaphram displacement on Helmholtz Resonator

Post by Rich_B »

Hello All,

Gary originally stated
record the deflection of a diaphragm vs frequency in the side of a Helmholtz Resonator
I can't tell whether his goal was to record the diaphragm movement due to being driven by externally applied pressure waves or that the diaphragm was actually the driver. In the typical bass reflex ported speaker, the diaphragm will be driven by the speaker piston, thereby creating the pressure waves.

Unless Gary says otherwise, it seems to me that assuming the speaker piston is the driving force would be appropriate. Which suggests that the 3 HelmholtzStructure test cases should be directly applicable.

Rich.
Rich_B
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Re: Diaphram displacement on Helmholtz Resonator

Post by Rich_B »

Attached is another gmsh model, this time redesigned to look like a bookshelf style bass reflex speaker, with the port internal to the box. There are two bodies, air and piston, with three boundaries.

Next version, perhaps we'll add some room air in front of the speaker.

Rich.

Edit: removed the gmsh model, speaker3.geo, it will be replaced by speaker4.geo
Last edited by Rich_B on 11 Nov 2022, 19:23, edited 1 time in total.
raback
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Re: Diaphram displacement on Helmholtz Resonator

Post by raback »

Hi Rich,

Ok, I think the HelmholtzStructure3 should then be very close to what is needed. It has harmonic body force + frequency sweep.

-Peter
raback
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Re: Diaphram displacement on Helmholtz Resonator

Post by raback »

Btw, "ben qui" has created really fancy vibroacoustic cases with Elmer. See the videos on youtube:

https://www.youtube.com/playlist?list=P ... k3DAvM2EZw
kevinarden
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Re: Diaphram displacement on Helmholtz Resonator

Post by kevinarden »

" diaphragm movement due to being driven by externally applied pressure waves or that the diaphragm was actually the driver. "

I believe in a speaker the diaphragm is driven, and is not the driver of the motion. It is driven by electrical impulses, that pushes the air waves. I was interested in the acoustic waves driving the structural displacements. The test cases appear to be the opposite, in a speaker the electrical impulses drive the diaphragm which pushes the airwaves, but I did not think that was the intent of this simulation.
Rich_B
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Re: Diaphram displacement on Helmholtz Resonator

Post by Rich_B »

Hello,

Attached is another gmsh model of a bass reflex port speaker. The test case 'HelmholtzStructure' has been adapted to run with the speaker model. This model is closer to a drum than a speaker, where the drum head membrane vibrates at the natural frequency and drives the air.

Rich.
pressure1.png
pressure1.png (72.37 KiB) Viewed 749 times
eigenmode3.png
eigenmode3.png (51.1 KiB) Viewed 749 times
Attachments
my-HelmholtzStructure.zip
(2.64 KiB) Downloaded 41 times
Rich_B
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Re: Diaphram displacement on Helmholtz Resonator

Post by Rich_B »

Hello Peter,

I tried to follow your instructions:
2) Pressure waves cause displacements
- 1st solve Helmholtz equation with pressure inlet
- Solve the StressSolver with "Harmonic Analysis = True"
- Add BCs for the structure:
Normal Force = Equals "Pressure Re"
Normal Force Im = Equals "Pressure Im"
Take a look at the attached, and let me know your thoughts. I took the ElmerGUI tutorial, FsiObstacleGUI, and made some changes, such as removing Navier-Stokes and Elastic Solver and adding Helmholtz and StressSolver.

Thanks, Rich.
pressure_wave_x.png
pressure_wave_x.png (44.7 KiB) Viewed 738 times
displacement_harmonic.png
displacement_harmonic.png (26.52 KiB) Viewed 738 times
Attachments
FsiObstacleGUI.zip
(96.16 KiB) Downloaded 43 times
Rich_B
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Re: Diaphram displacement on Helmholtz Resonator

Post by Rich_B »

Here is another variation, this time creating the geometry for the FsiObstacleGUI case with an elmergrid input file. The archive contains a working ElmerGUI project.

Rich.
Attachments
my-FsiObstacleGUI-grd.zip
(161.71 KiB) Downloaded 41 times
kevinarden
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Re: Diaphram displacement on Helmholtz Resonator

Post by kevinarden »

Looks good, going back to the speaker cabinet
displacement.png
(68.72 KiB) Not downloaded yet
rcase.sif
(3.66 KiB) Downloaded 51 times
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