Copper rings are there due to my crazy hypothesis that more clarity and lower distortion can be realized by adding rigid mass that absorbs low frequencies, and because the contact points are very small due to the circular cross section, the rings are very good at absorbing low frequencies.
This isn't the same as making an aluminum enclosure (a la LCD-X), because vibrations can transmit all throughout the whole enclosure when there is more contact.
Think tube dampeners/rings but for a rigid headphone baffle.
Now, I reckon copper spheres/balls will be even better, but I haven't found a place that sells small dense copper balls yet, plus placing and securing them inside the enclosure would be a nightmare.