Now that i think i understand the physics of operation of concertina reeds (thanks to the back-and-forth with Lukasz) i have a proposal for a reed assembly that i believe will sound on either the pull or push cycle. If i have not overlooked something (which i'm sure you'll let me know), it should sound pretty much like a usual concertina reed in either case, though it probably won't sound quite like a traditional reed.
Moreover, as you will see, it would be more difficult to precisely tune with filing/scraping, so may well not be practical. I'll let someone with reed making/tuning experience address that issue.
So on to the description. Take a usual (though it may need to be thicker or thinner in practice) reed frame and file part of the inside end down at an angle, as shown in the cross section of Fig 1 in the picture below. Repeat with a second frame in such a way that it is a mirror image of the first. Now sandwich a flat reed tongue between the two frames as shown in Fig 2. The left end of the reed is clamped between the two frames, and the other end is free to oscillate. Note that when the reed is in its equilibrium position (as shown in Fig 2) there is an air passage between the top and bottom at the free end of the reed tongue. The setting of the free end of the reed is such that it comes very close to the top and bottom frames at the end of the sideways V so that it will effectively cut any air flow occurring from top to bottom or vice versa. (In actuality, the V might need to be shaped like and arc.)
This reed, when placed in the appropriate position in the reed pan, should operate pretty much the way a standard reed does. Imagine the bellows is above the reed in the following description. As it is squeezed with the appropriate button pushed, the pressure inside the bellows is increased above the ambient air pressure outside the concertina. This pressure difference is not enough to cause the reed to move significantly, but it is enough to cause air to flow from the top to the bottom. As this flow of air passes along the bottom of the reed it causes a partial vacuum on the lower side of the reed tongue, so that the pressure difference between the top and bottom of the reed is substantially increased, causing the tongue to move downward. It will continue to move downward until the air flow is effectively cut off as the reed end comes very close to the inside end of the lower frame. (Assuming that the frames are such that this cutoff occurs before the spring force gets too large.) When the air stops flowing, the partial vacuum is no longer maintained and the force due to air pressure is greatly reduced. The internal (spring) force of the reed tongue will eventually bring the motion to a stop, and then push the reed back toward equilibrium. As it does, the air passage is re-opened and the pressure difference will increase substantially again. At some point above the equilibrium plane the force due to pressure and the restoring spring force will bring the reed to a stop and cause it to move back toward equilibrium. The reed will continue to cycle as long as the button is pushed and the bellows is squeezed.
Note that there is an asymmetry in the operation. When the tongue is below its equilibrium position, the spring force is acting upward and that due to air pressure downward (with the latter decreasing as the air flow slows). That is, they act in opposite directions. When the tongue is above the equilibrium position, the two forces act in the same direction (downward).
If the bellows is drawn (pulled), the process is pretty much the same except the greater pressure will be below the reed and the initial air flow will be from bottom to top, causing the partial vacuum on the upper side of the tongue.
Note that if you want the air flow to be cut twice per cycle you need to adjust the thickness of the frames and the V-shaped cutout so that the reed end passes very close to the frames at both ends of the oscillation. In this case, though, the frequency would be twice what it would be if the cut is made only on the low pressure side.
Edited by rlgph, 04 February 2015 - 05:36 PM.