Calculating acoustic modes for complex room shapes

[lasseo]

After a quick poll amongst a handful of my colleagues working on noise and vibration, and others on structural modelling, I've been twisting their arm to help me build a finite element model of my lounge in order to figure out the acoustic room modes.

So far, I've taken the dimensions of the room and modelled the geometry in 3-D. Here's how it looks like in CAD:

[ATTACH=CONFIG]37573[/ATTACH]

This is going to be the base for generating the FE mesh.

Overkill, you say? Well, several room mode calculators can be found on the web, either as an online tool or spreadsheets available for download. So far, all I have come across are limited to simple rectangular shape. Unfortunately, as you can see the lounge does not really resemble a rectangle, so these simple tools will give rough estimates at best.

Here's the sketch of the living room, some updates compared to the arrangement shown elsewhere in this forum. Loudspeakers in green, main listening position is the red dot with thick edge, guest seat shown in red with dashed edge:

[ATTACH=CONFIG]37571[/ATTACH]

[b.d]

I'm really interested to hear if what you measure in the listening position correlates to what's predicted, keep us posted.

[Guest Peter the Greek]

I understand a lot of very, very smart people have tried this and failed. I'll be rather impressed if this works. I mean everyone gets kinda close and then tweaks treatments and eq post.

I am far too uniformed about this, but everyone always points to too many variables to accurately do this.

Easier to just take measurements in room and apply treatments to suit - quicker and cheaper then having a room full of physicists and CIA style computers to work out

[Aslan]

This is the only way to do it properly:

http://www.cara.de/ENU/index.html

Not exactly cheap, but exceptionally accurate.

[JA]

Yes there are lots of variables to consider - modelling the room shape is only one part of the issue, there is also selection of appropriate boundary conditions, determing their frequency dependence or any other non-linearities and then other simplifying assumptions. If it is an existing room, you can use measurements to determine what the room is adding/subtracting.

Best

JA

Edited November 5, 2011 by JA

[Paul Spencer]

Why try to calculate something that you have already measured? Unless you just want to do it for fun?

[lasseo]

Paul's suspicion is correct, part of me wants to do this simply to see whether I can. Should I be able to pull this off, Elill will think I am a really smart person - thanks for the pep talk guys

Seriously though, lack of detailed test data will often prove to be the sticking point for developing any good model, assuming one has sufficient access to necessary tools and CPU power. As JA pointed out, a lot of simplifying assumptions will have to be taken, and whether these can be accepted or uncertainty tolerated will depend on what one is hoping to achieve. Comparing to in-room measurements will be the sanity check for ensuring the model is not producing complete rubbish.

Anyway, that's quite enough of philosophical silliness for one thread, let's get to it. I am not trying to calculate a full spectrum in-room point-to-point forced response for a given sound source. I don't have detailed information about the frequency response or directivity of my main loudspeakers to begin with. Instead, I am aiming for the lowest-hanging fruit, the acoustic eigenmodes of the air cavity itself, completely disregarding any exotic boundary conditions or acoustic damping other than the air itself. Or furniture, for that matter. I can then check the resonant frequencies against actual in-room measurements, but more importantly, the analysis will also give me the mode shapes for each modal frequency. Even if the frequencies are slightly off, I think I can still use the mode shapes to determine the high/low pressure and velocity points in the room. I would then try and avoid placing speakers at high pressure points, and use them for resonant bass traps. High velocity points should theoretically be good for resistive traps.

The software I'll be using is called Sysnoise, now apparently obsolete and originally developed by this mob, not from Germany but Belgium:

http://www.lmsintl.com/

Good enough for car companies, good enough for me. I am guessing the advantage of the software Aslan refers to will be access to an extensive library of pre-defined surfaces and treatments.

Here's the finite element mesh of the acoustic cavity:

[ATTACH=CONFIG]37704[/ATTACH]

There should be at least six elements along the shortest wavelength to be analysed. For a 100 mm element size the model should be good up to 340/0.6 = 566 Hz. Uncle Schroeder suggests a transition frequency of 2000*sqrt(RT60/V), which for 0.6 s and 90 m^3 translates to 163 Hz. Or 327 Hz if one were to use 4000 as the multiplier. We shall try and calculate modes up to 300 Hz then. The model has around 150k nodes, so this should easily - perhaps in a day or two - analyse on a modern desktop computer. No CIA levels of crunching power required.

[lasseo]

OK, the computation took some two days to finish, and found 324 acoustic modes up to 300 Hz. The first few are:

21.36 Hz

33.11 Hz

46.45 Hz

54.86 Hz

57.81 Hz

59.34 Hz

61.95 Hz

64.24 Hz

73.18 Hz

74.49 Hz

75.26 Hz

77.93 Hz

81.47 Hz

83.17 Hz

88.83 Hz

93.05 Hz

93.31 Hz

The first conclusion is that the rectangular room approximators found on the web miss the lowest mode at 21 Hz, and that the predicted frequencies are different. This is not surprising, with a room geometry that's far from a rectangle.

Here's how the predicted room modes line up with actual in-room response - red with a subwoofer, blue without, acoustic modes predicted by the model indicated with yellow(ish) bars:

[ATTACH=CONFIG]38614[/ATTACH]

I wasn't able to export animation directly. Instead, I had to save them frame by frame (which the software thankfully does automatically), and combine them to an animated gif afterwards. I'm not sure whether the gif animation will work on the post, but here goes. The first three modes, colour mapping indicates pressure magnitude:

[ATTACH=CONFIG]38615[/ATTACH] [ATTACH=CONFIG]38616[/ATTACH] [ATTACH=CONFIG]38617[/ATTACH]

Needless to say, I am pretty pleased with myself right now.

[ylio]

11 years late

https://github.com/Ylio7/room_eigenmodes_simulator

At the moment, the application does not consider materials, only rigid surfaces, but it is a very useful tool to evaluate the eigenmodes in irregular rooms. It is recommended to make the models in sketchup (they can be done for free with sketchup online), export in .stl format and import them in the simulator. Read how to construct models in the attached manual!

It allows calculating the Schroeder frequency (manually entering the Tmid) and there is an excel spreadsheet to evaluate the modal distribution according to Bonello's criterion.

[acg]

@yliogiving it a crack now Agus...looks like a tremendous amount of work you've put into this project.

[ylio]

On 21/11/2022 at 9:42 PM, acg said:

@yliogiving it a crack now Agus...looks like a tremendous amount of work you've put into this project.

Yeah, it really took me a while to put the app together to be as user-friendly as possible. I hope you find it useful!