I found interesting that they lined the barrels with Stellite and coated that with a ceramic coating.
That would be a expensive barrel.
It (Stellite liners and special coatings) was common for bigger weapons even before they tried it for these barrels.
The report makes a few mentions of the work on heavier weapons where they borrow some technology and try to apply it here.
Since the overall program focus was a combination of weight reduction and the material science applications, they really don't publish anything all that informative about the modal analysis, other than to compare a few parameters of their proposed changes to the existing baselines.
If you noticed, their predictions and the actual dispersion results were vastly off, but in reality, their analysis here never was intended to predict the target. It was just to compare some stiffness/stress parameters based on the section changes.
It takes a lot more complex modeling to close loop on ballistic accuracy, velocity, heat, and wear, than what is shown in this report. Those types of report are not public.
If there is a real takeaway point to the report, it is that stress, dynamics, and thermal models of weapon systems were highly dependent on experimental anchoring before the analytic models became useful.
My definition of useful here being the use of the model to avoid more costly prototype and physical lab work, and to drive designs that met performance.
The damping, wear, thermal, and dynamics presented in the report, didn't do a very good job at all. However, the point of the project wasn't to perfect the analysis models.
The use of stress, dynamics, and harmonic analysis for guns and cannons pre-dates the use of FEM or NASTRAN models. I was shocked at how old some of the work that predates the design of Mauser barrels was when I was a student. Those papers were from the 1800's in German.
Do barrel sections affect vibrations and does that matter? Of course, the answer is yes, it matters very much. YMMV