Geodesic
A one-dimensional mathematical model of barrel vibrations with arbitrary cross-sectional shapes
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 80 (2022), pp. 133-146

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The problem of longitudinal and transverse vibrations of a barrel with arbitrary cross-sectional shapes is considered and solved in the framework of a one-dimensional model. The study shows that the amplitude of transverse vibrations in the vertical plane significantly exceeds that in the horizontal plane. This paper proposes to reduce the amplitude of vibrations by changing the shape of the barrel cross-section, namely by adding stiffeners. The numerical algorithm for solving the problem is developed on the basis of the integro-interpolation method. The verification of the numerical integration method is carried out, and the grid convergence is verified by means of the modeling of barrel vibrations for a 30 mm automatic cannon. The study of the impact of the barrel cross-section shape shows that the use of stiffeners can reduce the initial deflection and the amplitude of muzzle vibrations when firing in bursts. The obtained results demonstrate a narrow spread of projectile departure angles, and, consequently, the improved shooting accuracy of the automatic cannon.
Keywords: mathematical model, numerical methods, barrel vibrations, automatic cannon, stiffening. 
@article{VTGU_2022_80_a11,
     author = {I. G. Rusyak and V. G. Sufiyanov and D. A. Klyukin},
     title = {A one-dimensional mathematical model of barrel vibrations with arbitrary cross-sectional shapes},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {133--146},
     publisher = {mathdoc},
     number = {80},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2022_80_a11/}
}
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I. G. Rusyak; V. G. Sufiyanov; D. A. Klyukin. A one-dimensional mathematical model of barrel vibrations with arbitrary cross-sectional shapes. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 80 (2022), pp. 133-146. http://geodesic.mathdoc.fr/item/VTGU_2022_80_a11/