This is a remix of JoePKrcma's "Hollow Helmholtz Sound Brick". His youtube video lists "And here is the free file if you want to download it and print on your home machine (good luck with the overhangs and support):" The thingiverse model "Enjoy trying to print this nightmare!" Sounded like a challenge. There isn't a flat outside edge and unless the cone is vertical there's the cylinder overhang to deal with.
The engineer in me saw there is a symmetry right down the middle. For the model to be more printable I broke the brick into three pieces that I was able to print without supports. To assemble I used hot glue along the seams, filled it with water and added more hot glue where it still leaked. If you want to go the step further, drain the water and blow in, the bubbles tell where to add more glue which was more than the seams. This version is scaled by 0.306 and smaller than the original.
In addition to breaking it into three pieces I cleaned up the inside area where it would bridge and made the area around the cone be thicker to print separately.
The paper calculated the cavity at "270 Hz", "Testing will be done to find out how accurate the final bricks are in absorbing certain frequencies. " I don't know if the uploaded model matches the molds that were 12% larger to account for shrinking or if it was to match the final ceramic size. I had calculated the original cavity at 253 Hz, I wanted to target a frequency of my 3D printer fan and scaled the model by 0.306 which I had calculated a frequency of 837Hz.
Unfortunately playing a continuous frequency change from 240 to 1600 Hz from the computer I was not able to hear or see a spectrum difference with or without the Helmholtz resonator. I only printed the one brick. From his paper there is a graph showing sound absorption where foam absorbed the most sound at a wide range of frequencies and would be more appropriate for indoor general sound dampening. Helmholtz resonator for specific frequencies, I've not seen how wide or narrow of a range they will absorb.
I've completed the challenge, I don't plan to take this design any further. It was optimized for making ceramic bricks not 3D printing. There are other designs that are more optimized for 3D printing.
The author remixed this model.
Broken into three pieces for FDM 3D printing. Other internal geometry changes for bridges and support the now separately printed cone.