I have recently been doing some FEA calculations an though some might be interested in the results.

Maybe barrel vibration shapes are not important to barrel accuracy. It could be that the distortions in a barrel caused by the gas pressure are more important in determining where the muzzle is pointing when the bullet exits the muzzle.

WHERE THE MUZZLE IS POINTING.... The interesting aspect of this modeling is the direction the muzzle is pointing when the bullet exits. All of the movies have the deformations amplified by 500X so the motion may be more clearly seen.




IMPROVED ACTION AND STOCK.... A 6PPC barrel with an action and a kluged stock to bring the total mass up to about 11.72 pounds. The deformations are amplified by 500X. Maybe looking at barrel vibrations is the wrong route to take. This looks like the pressure induced displacements are much more important than natural vibration modes. The CG of a rifle is typically below the bore axis and since the action is attached to the stock, there is a turning moment induced during firing. I have not included the scope and I suspect that will change the motions but the CG of the rifle will still be below the bore axis.




ADDED TUNER.... Here is the same model with a tuner added to the muzzle. It appears to reduce the up turning of the muzzle. The tuner mass is 1.39 pounds. In each movie the bullet exits the muzzle at the last view.


AT THE TARGET.... After all the calculations, here is pictorial summary and what happens at the 100 yard virtual target. The top "groups" show where the muzzle is pointing when the bullet exits. The bottom "groups" includes the bullet drop and shows where the bullet would hit the target. The vertical plane of symmetry in the model does not allow for horizontal dispersion. The highest and lowest velocity shots increase the group size, but have less of an effect with the tuner. The bullet impact points are shown with small colored dots that are not to scale. The actual size of the bullet holes would have obscured where each bullet would have hit.

There is more information on the analysis here:
http://www.varmintal.com/apres.htm