Enclosure Bracing Simulations, some Help needed

[3eepoint]

Hello everyone,

I know enclosure bracing is a topic that has been discussed quite often but I wanted to take my own tour of the topic by simulating different Bracing types to compare them to each other. Sadly I ran in to some problems which requier experience that I am lacking and, as here are many people that can be considered experts, decided to discuss them further before publishng them in a single post.

This is where I currently stand...


...I have made several Models with the same external dimensions and implemented different Bracing strategies, like single ring Braces:

Simple diagonal Braces:

And even full out B&W Matrix Bracing:

Over all there are 15 differnet Bracing strategies implemented and compared using a Matlab script. Sadly, the results seem to be counter intuitive:

The First plot is a comparison of the maximum wall Flexing at 1 Hz to compare the overall stiffness of the different Enclosure types. The 10 to 25 mm "Braces" are just thicker Walls. And here the confusion starts. I Expected a thicker wall to be more resistent to flexing but this does not seem to be the case, which I highly doubt. And the Matrix enclosure seems to be one of the worst in the field....
The second plot is the displacement above 100 Hz vs Frequency to show the modal region of the different braces. There is not much damping going on but that may be subjective due to the presentation. Does annyone know of a method to "Rate" such modes which would make it more subjective to compare? My first Idea would be to calculate the derivative of the excursion and the sum it up as less modes mean less change in the derivative and would therefore be better, leaving psychoacoustics out of the picture for now.

Also, some comparison between real worls data and my simulations show differences as well.... just not some I would expect.... Juul[1] did some simulations and measurements, here are his results:

and here are mine:

While the Frequencys of the resonances seem to be in the same area, the amplitude is way of( be aware of the 2 dB Scale!). This is schown with the driver radiating in to the same space as the enclosure. For this Plot I replicated his Model and used his material Values. I tried to contact him but I have not recived an answer in over a month.

As for my Simulations. The bottom of the cabinet is assumed to be fixed. The Material Values for the wood parts are:

Youngs Modulus: 4 GPa
Piossons Ratio: 0.18
Density: 700 kg/m³
Bulk Modulus: 1e10 N/m²
Shear Modulus: 5.8e10 N/m²

Material damping is modeled via Rayleigh Damping with alpha = 0.251 1/s and beta = 6.35e-6 s

The driver is assumed to exert 10 N Driving Force on a 0.1 kg Membrane and is modeled as a lumped system and coupled to the enclosure via a prescribed acceleration at the mounting ring of the chassis basket. The Front of the driver radiates in to an acoustically sound hard chamber while the enclosure can radiate sound in to a free air enviroment.

Has annyone an Idea if these Values can be correct? Are there similar studys out ther which I did not find? My intuition says I have done something wrong but my expertise is limited and I would like to hear some opinions.

Have a nice weekend and I am looking forward to what I can learn.

PS: I hope I did post this right in the DIY section.



[1]https://www.google.com/url?sa=i&url...2ahUKEwiD8obgoPHvAhULahoKHeihCXAQr4kDegQIARBo

 

[NTK]

...
As for my Simulations. The bottom of the cabinet is assumed to be fixed. The Material Values for the wood parts are:

Youngs Modulus: 4 GPa
Piossons Ratio: 0.18
Density: 700 kg/m³
Bulk Modulus: 1e10 N/m²
Shear Modulus: 5.8e10 N/m²
...

Just a very quick look. Your material parameters don't seem to be correct. See link below for some example mechanical properties of plywood:
http://edge.rit.edu/edge/P08003/public/materials.xls

Also, see Wikipedia conversion formulae:
Both bulk modulus K and shear modulus G should be less than Young's modulus E. Poisson's ratio ν also seems too low. Another serious complication is that plywood is anisotropic (transversely isotropic), which will make an accurate simulation much more difficult. You need to know the complete detailed material properties in the directions perpendicular and parallel to the boards.
https://en.wikipedia.org/wiki/Elastic_modulus

 

[thewas]

With what a Matlab script did you do those calculations? I would have thought that complex structures like the Matrix could be only numerically approximated and simulated with methods like FE.

 

[3eepoint]

Thanks for the replys!
@NTK
Thanks for the formulae and Values! I assumed the enclosure to be made from MDF(its mitteldichte Faserplatte in German), I dont know the exact translation. I know that layer direction plays a mayor part and therefore decided to evaluate a material without it. I will try these values annyways, at least they make some sense.

@thewas
The Matlab Script only does the presentation, the calculations are done in Comsol

 

[NTK]

I read the DTU speaker enclosure paper in the post #1 link.

The goal of their study was to weight reduce a bass guitar amp cabinet. The commercially available reference cabinet weight was 7.7 kg (cabinet only, no driver and electronics) and was made from 18 mm (~3/4 inch) plywood. The "optimized" cabinet's final weight was 3.6 kg and was made from 6 mm (~1/4 inch) MDF (medium density fiberboard).

The models you showed looks like they are made with boards thicker quite a bit than 6 mm. The one with the B&W style bracing looks especially beefy. IMHO, if that much bracing and thick walls are being used, the cabinet will be inert and the FEA is just an academic exercise.

Here are the material properties used in the COMSOL study in the paper. Their simulation assumed isotropic material properties for MDF, and therefore only the Young' modulus and Poisson's ratio are needed. The other properties are derived using the formulae shown in my previous post. They didn't say (and I assume not) if material damping was modeled.

I haven't, but will read the COMSOL examples referenced in the paper. I used COMSOL in my last company, and do not have access to it anymore. Anyway, they didn't have the acoustics module license (they had no use for it).

This multiphysics simulation is very interesting. It started with using the T/S parameters to compute the speaker diaphragm motions, to the acoustic pressures inside and outside the speaker cabinet, to an acoustic-structural interaction to model the cabinet deformation/vibration, and then back to acoustics to simulate the sound radiated from the cabinet. It is a pretty thorough model. Fortunately, and as it was designed, there wasn't much coupling between the different physics and the numerical computations are pretty straight forward. The authors of the study stated that they could complete a sweep of 200 frequencies in about 2 hours (no mentioning of what computer was used, only RAM usage of 3.4 GB). I am sure you will learn a lot from it.

I think the more suitable place to look for help may be the COMSOL forum, or other fora specialized in FEM/multiphysics simulations.

Good luck and have lots of fun with it!

MDF properties:
https://www.researchgate.net/public...F_as_function_of_density_and_moisture_content

 

[3eepoint]

The Models I showd had 15 mm Wall thickness unless stated otherwise. The reference Cabinet from the paper was modeled with 6 mm and the material Proporties mentioned in the Paper, thats why I am so insecure about my findings, the results dont match. Thanks for taking your time reading it!

And as you say, the Matrix one should be basically innert but is not in my findings thats one of the main resonst I made this post as this should not be.

The Multiphysics is insane, somtimes insanely frustrating to set up, especially with matlab. The hours I lost to this Program...

I thought about Posting in the Comsol Forum but thier replys are few and far between. I also wanted a second opinion on the Loudspeaker side first.

Thanks, I will keep you update on my findings!

 

[NTK]

I don't think I am in the position to provide much help beyond offering some generic suggestions on troubleshooting multiphysics simulations.

1. Start simple, add one physics at a time. You can start with only a Pressure Acoustics / Frequency Domain plus Boundary Elements simulation. For example, simulate only the vibrating woofer diaphragm with a closed box (i.e. ignore the pressure inside the cabinet and bass reflex), and see if the frequency response and directivities make sense. Make sure the mesh size is appropriate (elements in the acoustics domains should be smaller than 1/4 wavelength, per COMSOL example).
2. Add the cabinet interior air space and the bass port to the simulation. See if the frequency response, directivities, and interior pressure of the cabinet make sense.
3. Now switch to structural mechanics only. Simulate the vibration modes of the cabinet. Then apply a periodic pressure load to the interior of the cabinet walls at one of the natural (eigen) frequencies, and see if the deflections (shape and displacements) make sense. Test a few other frequencies.
4. Add the Pressure Acoustics, Frequency Domain and Boundary Elements physics to the structural mechanics, and see if the acoustic radiations produced by the flexing cabinet make sense.
5. Once you have these separately resolved, you then proceed to the fully coupled simulation.

If you have gotten the basics to work but still have trouble with the full simulation, I think the COMSOL forum (or COMSOL support if you have access) will probably be the only place to get help. (Their moderators can get a bit obnoxious when they think you are asking a typical support type question.) There aren't that many people in this entire world doing this type or level of acoustics FEA work. (My guess is far fewer than 1 in a million, especially if you limit it to COMSOL )

Good luck and let us know how things go!

 

[3eepoint]

Good luck and let us know how things go!

Thanks for your input, I checked some things again and came to some results that make sense at least.

First of all I made an evaluation error. I calculated the maximum displacement of each wall but did not limit it to a plane. The sidewalls for example move in the y Direction in my simulation but my previus evaluation showed the overall movement of the wall in x,y,z which drowns out the flexing I wanted to see.

Second, I did a seperate Simulation of the acoustic and mechanical load inflicted by the driver:

This is with only acoustic coupling. Here we see the expected results as in that a 25 mm walled enclosure shows less flexing then an 10 mm enclosure. While I still do not take the amplitude at face value due to the discrepancys to the Juul Paper, I think this allows for a good comparison in itself.

Now for the mechanical induced vibrations:

This draws a different Picture. I think what this means is that flexure wise the mechanically introduced forces may outweight the acoustic ones by far and a different approach at bracing these flexures could yield better results in cabinet stiffnes.

No progress on the Mode front tho. Still thinking about a way to evaluate them down to a metric.

 

[René - Acculution.com]

I can review your simulation files if needed.

/René

- About me -
BSEE, MSc (Physics), PhD (Microacoustics), FEM and BEM simulations specialist in/for loudspeaker, hearing aid, and consultancy companies. Own company Acculution, blog at acculution.com/blog