Today we will have a look at an acoustic design that I have been wanting to do for a long time; the Acoustic Demultiplexor.
The acoustic Demultiplexor is a device that can split an input into several outputs based on the frequency content of the input signal. Here, it has three different geometrical outputs, and each output is assigned a certain frequency for which the output intensity is to be maximized. This way, we achieve an "acoustic crossover" of sorts, as opposed to the more common electrical crossover. I first saw this years ago in one of Ole Sigmund's presentations , and still, as then, I find it extremely fascinating. Below I have replicated a very similar setup: A 2D square of 1x1 meters, with an input and three outputs, a plane wave wave input of 1 Pa at the input, and plane wave radiation conditions at three outputs.
The gray domain is where the topology optimization can take place with a certain area ratio (solid to total area), e.g. 20 % of the total area can be solid, the rest has to be air. Three different frequencies are input, 800 Hz, 960 Hz, and 1,120 Hz. I want the the 800 Hz input to go to output 1, the 960 Hz to go to output 2, and the 1,120 Hz output to go to output 3. Try and imagine which topology could possible achieve that... Not that easy, right? But with topology optimization, we can get an answer to this posed problem. One such answer looks like this:
Black indicates solid domains, and white indicates air domains. Now, to be sure that the optimization scheme actually came up with a result that makes sense, you have to create a geometry with a single air domain (white in above figure), with hard walls on the solid domains (black domains in above figure). The result you get is shown below:
The animation on the left is for 800 Hz, and we see that the input pressure wave goes in the direction of output 1, as desired. The black arrows indicate the logarithm of the intensity. In the middle, we have the result for 960 Hz, where the intensity is maximized at output 2, and finally on the right, we have the result for 1,120 Hz. So we can actually split the frequency content in a spatial manner, with quite a simple geometry, which intuiton alone could probably not have achieved.
If you want to have the geometry to see for yourself that it actually works, please leave a comment below. Btw., note that the optimization was done entirely in COMSOL Multiphysics GUI, i.e. no external software was needed.
 I could not find the pdf online, but I do have it on my harddrive. Anyway, check out this link for TopOpt publications.