Speaker Resonator Interaction

Numerical methods and mathematical models of Elmer
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Gary R
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Speaker Resonator Interaction

Post by Gary R »

Hi all,
Operating System: Debian GNU/Linux 11
KDE Plasma Version: 5.20.5
KDE Frameworks Version: 5.78.0
Qt Version: 5.15.2
Kernel Version: 5.10.0-16-amd64
OS Type: 64-bit
Processors: 4 × AMD FX(tm)-4350 Quad-Core Processor
Memory: 15.6 GiB of RAM
Graphics Processor: AMD CAICOS

I have been trying to model a speaker coupled to a helmholtz resonator (bass reflex system). I wish to apply a constant amplitude sinusoidal force to the speaker (plate) and obtain the speaker deflection vs frequency. Because of some things that I plan to do to modify the system, I can't use the usual off the shelf design software that is available.

Since the plate and resonator interact, I need a coupled system. This is my first attempt to use coupled solvers and I am at a total loss. Attached is a tar file that contains the whole project as far a I have gotten. The device is modeled in FreeCAD, Exported as a .brep file that is meshed with gmsh (latest). The .msh file is run through ElmerGrid (ElmerGrid 14 2 ArcTest2.msh -autoclean -merge 0.25). I set up the plate as a spring mass system whose parameters are conversions of the Thiel parameters of the speaker. Could anyone fill in the blanks for me?

Screenshot_20220830_143529.png
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Gary R.
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Testjig3.tar.gz
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kevinarden
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Re: Speaker Resonator Interaction

Post by kevinarden »

The first error I received was unrecognized keyword Spring changed it to
Spring = Real 1.471E+03
Second error was the helmholtz solver could not find frequency added frequency to solver 1
Frequency = 5000.0
Third error was it could not find youngs modulus, poisson ration, thickness for the plate solver added to material 2
Youngs Modulus = 1.E8
Poisson Ratio = .3
Thickness = 1

It then provided a solution
deflection.png
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case.sif
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raback
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Re: Speaker Resonator Interaction

Post by raback »

Hi

So this is the key point here: "Since the plate and resonator interact, I need a coupled system."

This is not an easy task. There is one consistency test case for this "ShoeboxFsiHarmonicPlate". It basically creates a 2x2 block matrix for the coupled problem and solves it using block preconditioning techniques and GCR at the outer level. I fear you may need the ShellSolver if you have more than one flexible wall in your system.

-Peter
Gary R
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Joined: 12 Apr 2012, 07:23
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Location: Long Beach CA, USA

Re: Speaker Resonator Interaction

Post by Gary R »

Hi all,
To simplify the problem, I created a project of just the speaker cone alone. The whole project is contained in the attached tar file. I set everything up as best that I could but got result that are unrealistic. What I expected was that the plate would move normal to the face. The results seems to show motion along the thin section. The displacement was expected to move the plate like a piston. If I can get this to work I will be able to check the parameters of the problem. Any help will be appreciated.

Gary R
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SpeakerCone.tar.gz
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kevinarden
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Re: Speaker Resonator Interaction

Post by kevinarden »

Many things to discuss on elastic deformations. The SMITC solver is for 2D elements not solid elements. If model with plate elements (2D elements with thickness defined for out of plane deflection) then the shell solver is more suited. 3D elements would require elasticsolver 3D elements. Attached is an example of a shell element model. Later I will proved an example of a 3D element model.

elastic is sensitive to element type and mesh density. Tetrahedron elements are the least effect, linear triangles are bad. Both of these types of elements require quadratic formulation or higher order integration. Quads and Hex Elements are better.

Attached is the shell solver solution for quad plate elements. I will work on the solid element solution next.
plate.tar.gz
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kevinarden
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Re: Speaker Resonator Interaction

Post by kevinarden »

This is the solid element case
solid.tar.gz
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