First results of numerical simulation indicates that on a dual membrane drum, the first mode of the membrane is actually more influenced by the shell depth than the tension itself. This is a direct consequence of the heavy coupling occurring in drums : the first membrane mode ((1,0) with one nodal circle being the edge of the membrane for both membranes, in phase) being volume conservative, the volume of air between the two membrane is mass-loading this mode.
The graph below illustrates how the first membrane mode shifts in frequency for standard shells (3,5 to 10″) and a purely simulated 60 inch shell.
The frequency shift follows well the square root of the depth, indicating a mass behaviour. The system is alike one mass between 2 springs representing the stiffness of the membranes.
Then simulation of opening in the shell, corresponding to the standard venting (one single vent hole) and to the patented Repercussion radial venting system have been conducted.
The mechanical mobility – or admittance- has been computed : this quantity is the ratio of the velocity of the head for 1N applied (at its center). The greatest this quantity, the « easier » it is for the membrane to vibrate, and the more energy is likely to be transmitted to the instrument (and not reflected back into the stick).
One very significant phenomenon occurs as soon as an opening is made in the shell : a resonance « Helmhotz-like » with maximum velocities in the vent appears around 50Hz.
in practice, this phenomenon is very likely not to be heard nor felt, because of the poor radiation efficiency (small surface) of the vent and because of the very heavy damping that will be caused by air flow & turbulence.
Picture of the 1st « mode » maxima (the two heads are one phase opposition)
The second effect of venting is the slight raise (10%) from low frequency of the mobility : the air can now flow outside of the drum and compression added stiffness disappears.
The third major effect is, in the case of the patented Repercussion radial venting system only, the increase of the mobility at a lower frequency (the pitch drops down to the one of a 25″ shell – 4x the physical depth of the shell) and a 25% increase on the max mobility.
What does it mean for the player ?
- A more evenly distributed sound around the shell (radial venting) with a very strong low end giving « in your chest » punch.
- A way more present sound for the audience and musician around (the sound « flows » out of the drum very efficiently
- A drum easier to play : more motion for the force injected : More sound, less force, less chances for injuries.