Richardson,
Art's right about the binding point. That's also the starting point of the accelerating mass.
The barrel volume is a resonant cavity. The volume of that cavity increases as the center of the projectile (ejectile) mass moves down the barrel. You begin to see the complexity. It is an infinite series of shock-impact nodes. We didn't have access to Finite Element Analysis tools for our project in '70-71.
The freqency is extremely broad band, as you can guess by the expanding resonant cavity dimensions and the model of a series of impact-shock nodes.
In an earlier life as an instrumentation techician for the US Gov't, I measured and recorded the behavior of internal ballistics energy on the outside of the barrel of the GAU-7 (caseless ammo, 25 mm gatling gun). It was abandoned due to the mechanical synchronization problem between feeder, loader and rotating chambers at high speeds. I believe the GAU-8 30 mm succeeded it and went on the A-10. The caseless ammo didn't like being skinned up during transport to the chamber. We started a fire once right in the middle of a 200 round burst.
The first thing we discovered was that we were unintentionally filtering the vibration frequencies with our instrumentation package. Remember the rule: you affect the behavior of a system by observing it? Well, we at least were affecting the data collected. Regroup. Reinstrument. Try again. Wow! Where did all that "stuff" come from?
The random vibrations damped out quickly, but the sine signals just went on and on ... 300 - 400 msec? 'Don't really remember. As the harmonics died out, the full barrel internal cavity's resonant frequency became most predominant. Each gun will be different. The broad banded vibration pulse packages would travel down the barrel chasing the moving mass (projectile) then run back up and and then down the barrel again until the energy was expended. I think the separation of pulses was due to the density of the barrel mass and the lateral dimensions of it, i.e., barrel thickness and center of the circumference mass center in the material cross-section. Also, the changing lateral dimensions as you move from breech to muzzle were a factor on the pulse train patterns, as I recall.
'Been a long time. All this was done on single shot barrels supplied for ammo testing. Yeah, the US Gov't was testing the guns, feeder/loaders AND the ammo at the same time. How smart is that?
Quite a show! I became quite impressed with the ability of barrel steel to temporarily lose it's mind, so to speak, then return to shape. The primary vibration (tail wagging) mode, as well as barrel mass (momentum), was a factor in the damping of the secondaries.
Knowing where to be in the primary vibration node at muzzle exit is the key to the B.O.S.S system of Browning.
Let me know how it goes. Try
Varmint Al and click on the "Engineering" link on his site for some interesting reading. He may save you some time. He's a retired ME, I think, from Livermore Labs. Cool guy. I need to visit his site more often. Tell him I said, Hi!
[This message has been edited by sensop (edited March 30, 2000).]