On the problem of nonlinear dynamics of shell systems influenced by the internal pressure local impulse

Authors

  • О.О. Азюковський Національний технічний університет «Дніпровська політехніка», Дніпро, Україна Author
  • В.З. Грищак Національний технічний університет «Дніпровська політехніка», Дніпро, Україна Author
  • К.А. Зіборов Національний технічний університет «Дніпровська політехніка», Дніпро, Україна Author
  • С.О. Федоряченко Національний технічний університет «Дніпровська політехніка», Дніпро, Україна Author
  • Т.А. Кравчук ДП НВО «Павлоградський хімічний завод», Павлоград, Україна Author

DOI:

https://doi.org/10.33271/crpnmu/71.179

Keywords:

shell systems, local momentum, nonlinear

Abstract

Purpose. Critical infrastructure facilities, including pipelines and tanks, are an integral part of ensuring the functioning of industrial and civil life support facilities. External factors that may affect their functioning can be both the cause of force majeure and targeted actions by third parties. Therefore, the purpose of this work is to establish a mathematical description of the dynamic behavior of cylindrical shells under the action of a local impulse caused by internal pressure. Methodology. To achieve the goal of the work, the provisions of the nonlinear dynamics of the system of forces are applied, taking into account approximate analytical and asymptotic methods. Results. The results obtained make it possible to describe nonlinear processes caused by local pulses of internal pressure in shell systems, which can be interpolated for use in numerous methods for determining the parameters of the strength and bearing capacity of the corresponding structure, taking into account the physical and mechanical parameters of the materials used and the nature of the force action. Interpolation of the results to similar technical systems will allow scaling the mathematical approach in solving engineering problems. Scientific novelty. The existing dynamic models are mostly represented by simplified calculation models without taking into account the totality of real loads and characteristic design and technological factors. In this paper, it is proposed to take into account the nonlinearity of dynamic processes due to the shape of the impulse action, the power exponent of the nonlinearity of displacements, and the Dirac delta function. This approach is new of scientific and practical significance. Practical significance. The resulting singular inhomogeneous model of interaction in the form of a differential equation with variable coefficients makes it possible to provide numerical simulation of interaction processes with asymptotically approximate results and to establish the parameters of dynamic behavior to impulse action. As a result, it is possible to obtain new technical solutions for shell structures resistant to dynamic impact, which will have improved technical and operational characteristics.

References

1. Mott,N. (1953) Physics in the 1930s . Bristol University.

2. Gurney, R. W., & Condon, E. U. (1929). Quantum Mechanics and Radioactive Disintegration. Physical Review, 33 (2), 127–140. https://doi.org/10.1103/PhysRev.33.127

3. Belytschko, T., Lin, J. I., & Chen-Shyh, T. (1984). Explicit algorithms for the nonlinear dynamics of shells. Computer Methods in Applied Mechanics and Engineering, 42 (2), 225–251. https://doi.org/10.1016/0045-7825(84)90026-4

4. Sieber, J., Hutchinson, J. W., & Thompson, J. M. T. (2019). Nonlinear dynamics of spherical shells buckling under step pressure. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475 (2223), 20180884. https://doi.org/10.1098/rspa.2018.0884

5. Ruggirello, K. P., Thomas, J. D., Love, E., Rider, W. J., & Heinstein, M. (2022). High fidelity coupling methods for blast response of thin shell structures. Finite Elements in Analysis and Design, 212 , 103834. https://doi.org/10.1016/j.finel.2022.103834

6. Чернецький, В.В. (2015). Вплив теплових факторів пожежі на цілісність вертикальних сталевих резервуарів з нафтопродуктами . (Дисертація на здобуття наукового ступеня кандидата технічних наук).

7. Егоров, Е.А. (2004). Комплексный анализ, оценка и управление надежностью стальных резервуаров для хранения нефтепродуктов. Сборник научных трудов ПГАСиА .

8. Gristchak, V. Z., & Ganilova, O. A. (2008). A hybrid WKB–Galerkin method applied to a piezoelectric sandwich plate vibration problem considering shear force effects. Journal of Sound and Vibration, 317(1–2), 366–377. https://doi.org/10.1016/j.jsv.2008.03.043

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Published

2020-01-01

Issue

No. 71 (2022)

Section

Статті

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