The beam modes shown in my previous post are only in the one direction. In a real barrel there are many more types of modes. VarmintAl has produced an animation (see link below) of the first 8 modes with the action held rigid. Using the terms in my previous he has modeled it as Fixed-Free beamhttp://www.varmintal.com/amode.htm
Read this page carefully as he makes some key points that can be missed if you just look at the pictures.
I should point out that the modes animated on this page don’t necessarily occur when the bullet is in the barrel.
A point I should expand on is his comment “a frequency of about 500 Hz will not be able to complete one full cycle before the bullet exits the barrel”. Essentially, the lower the frequency the slower the movement is to a point where the bullet exits the barrel before the movement is great enough to cause a material impact on the bullet.
To illustrate this time aspect further, consider the 1 Hz (wave 1) and 2 Hz (wave 2) standing waves both with an amplitude of 1 below.
At 0 seconds both waves are passing though 0 amplitude.
At 0.01 seconds wave 1 is at 0.06 amplitude and wave 2 is at 0.12 amplitude.
At 0.02 seconds wave 1 is at 0.13 amplitude and wave 2 is at 0.24 amplitude.
Now another aspect...
The sources of waves in a barrel are mostly obvious ie:
- Firing pin hitting the primer
- The combustion of the powder
- Bullet engaging the lands
- Bullet traveling down the barrel getting accelerated, both linearly and radially
However, one source that is not so obvious is the recoil. The physics to gain a deeper understanding of this is moments and forces.
These types of moments are not the ones that occur when the target comes up and you see the marker and think: How the F#(K did that happen? You can search the internet for “moments and forces” for the physics definition.
Essentially, under recoil the rifle will try to rotate about the center of gravity of the rifle which causes the action to start a transverse wave on the barrel. I’ve previously posted more information about this on posts #6 & 9 in the thread below.https://www.ozfclass.com/phpbb/viewtopic.php?f=5&t=8394&p=69816#p69816
The only additional thing I’ll add to those previous posts is some more results from Geoffrey Kolbe’s barrel vibration simulator:
Medium Palma barrel with high rifle center of gravity
Medium Palma barrel with low rifle center of gravity
The only parameters changed between these two simulations is the vertical location of the center of gravity. When looking at these graphs the Y axis is the angle of the muzzle.