The vibrations are frictionless. If left alone, they would be eternal -- but they interact with each other and change form. The origin of the vibrations might be something left over from the Big Bang, or, as noted in the essay, may be a fossil of the previous universe before the Big Bang.
The vibrations of different aethers can resonate with each other to form a self-sustaining set of stationary waves that constitute an elementary "particle". The amplitudes and relative phase shifts of these waves define the charge, spin, and other fundamental properties of the particle. The waves are stationary in the particle's own reference frame.
In one form of Common-Plinth theories, the pythagorean sum of the motions of all the dimensions is the speed of light exactly, and the local "energy" at that point is dependent on the aggregate amplitude of the motion. In another form, the pythagorean sum of the motions is less than or equal to the speed of light, and the local energy is dependent on this sum of motions.
If the wave set is in motion in the first aether (ordinary space), according to some other reference frame, then this is a moving particle. If the sum of motions must be equal to the speed of light, then the motion through ordinary space requires the internal vibrations to slow down, causing time dilation. Of course, the time dilation is identical to that described by the "Minkowski blackboard". A photon has a fixed wave pattern moving at the speed of light, with no movement of the wave components relative to each other, because time does not exist for a photon -- in its own "inertial frame", it is created and absorbed in the same moment in the same place. I'm not sure how this would work if the sum of motions could be less than the speed of light.
These vibrations also generate fields that propagate, as waves, throughout space. These fields can only interact with "particles" at discrete energies, but the fields' strengths can have any value. This is because the "particles" are wave sets with discrete vibrational modes.
As noted in the essay, these resonant motions create a contraction of the hypervolume in the second and/or third aethers, causing a dilation of volume in the first aether (ordinary space), causing Einsteinian gravitation.