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Розв’язок в рядах задачі про вільні коливання циліндричної оболонки з довільними граничними умовами
| Назва | Розв’язок в рядах задачі про вільні коливання циліндричної оболонки з довільними граничними умовами |
| Назва англійською | An exact series solution for free vibration of cylindrical shell with arbitrary boundary conditions |
| Автори | Дубик, Ярослав Романович Ориняк, Ігор Володимирович Іщенко, Олексій Антонович Dubyk, Yaroslav Orynyak, Igor Ishchenko, Oleksii |
| Принадлежність | ТОВ «ІПП-Центр», Київ, Україна
Інститут проблем міцності ім. Г. С. Писаренко НАН України, Київ, Україна
Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського», Київ, Україна
“IPP-Centre” Ltd, Kyiv, Ukraine
G.S. Pisarenko Institute for Problems of Strength, National Academy of Sciences of Ukraine, Kyiv, Ukraine
National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine |
| Бібліографічний опис | Dubyk Y. An exact series solution for free vibration of cylindrical shell with arbitrary boundary conditions / Yaroslav Dubyk, Igor Orynyak, Oleksii Ishchenko // Scientific Journal of TNTU. — Tern. : TNTU, 2018. — Vol 89. — No 1. — P. 79–88. — (Mechanics and materials science). |
| Bibliographic description: | Dubyk Y., Orynyak I., Ishchenko O. (2018) An exact series solution for free vibration of cylindrical shell with arbitrary boundary conditions. Scientific Journal of TNTU (Tern.), vol. 89, no 1, pp. 79-88. |
| DOI: | https://doi.org/10.33108/visnyk_tntu2018.01.079 |
| УДК |
534.12 |
| Ключові слова |
циліндрична оболонка
розв’язок у рядах
власні частоти коливань
cylindrical shell
domain decomposition method
natural frequencies
free vibration |
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У вигляді методу початкових параметрів записано точні формули для пошуку власних частот коливань циліндричної оболонки з довільними граничними умовами на основі теорії Донела-Муштарі. Також дано вирази з урахуванням деформаційної складової, показано що її вплив дуже незначний і ним можливо знехтувати. Наведено порівняння з літературними даними й показано, що отримані залежності добре описують експериментальні результати.
Simple accurate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using series expansion for axial coordinate and Fourier series for the circumferential direction, a simple explicit solution is obtained. Also, the influence of deformation component is investigated, it is shown that it can be neglected. Good agreement with experimental data and FEM is shown. The advantage of a current approach over the existing formulas is simplicity in programming. |
| Перелік літератури |
1. Xing Y., Liu B., Xu T. Exact solutions for free vibration of circular cylindrical shells with classical boundary conditions International Journal of Mechanical Sciences, 2013, Vol. 75, 178 – 188 p.
2. Lee H., Kwak M.K. Free vibration analysis of a circular cylindrical shell using the rayleigh-ritz method and comparison of different shell theories, Journal of Sound and Vibration, 2015, Vol. 353, 344 – 377 p.
3. Yu Y.Y. Free vibrations of thin cylindrical shells having finite lengths with freely supported and clamped edges, Journal of Applied Mechanics, 1955, Vol. 22, 547 – 552 p.
4. Soedel W. A new frequency formula for closed circular cylindrical shells for a large variety of boundary conditions, Journal of Sound and Vibration, 1980, Vol. 70, No 3, 309 – 317 p.
5. Qu Y., Hua H., Meng G. A domain decomposition approach for vibration analysis of isotropic and composite cylindrical shells with arbitrary boundaries, Composite Structures, 2013, Vol. 95, 307 – 321 p.
6. Xuebin L. Study on free vibration analysis of circular cylindrical shells using wave propagation, Journal of Sound and Vibration, 2008, Vol. 311, No 3 – 5, 667 – 682 p.
7. Dubyk I., Orynyak I. Analysis of water hammer due to sudden rupture of reactor coolant system, Vancouver, Pressure Vessels and Piping Division Conference PVP, 2016, Vol. 4, 10 p.
8. Кан, С.Н. Строительная механика оболочек, [Текст] / С.Н. Кан. Москва, "Машиностроение", 1966. – 508 с.
9. El-Mously M. Fundamental natural frequencies of thin cylindrical shells: a comparative study, Journal of Sound and Vibration, 2003, Vol. 264, No 5, 1167 – 1186 p.
10. Koval L.R., Cranch E. T. On the free vibrations of thin cylindrical shells subjected to an initial static torque, Proceedings of the 4th U.S. National Congress on Applied Mechanics, 1962, 107 – 117 p.
11. Smith B.L., Haftf E.E. Natural frequencies of clamped cylindrical shells, AIAA Journal, 1966, Vol. 6, No 4, 720 – 721 p.
12.Cammalleri M., Costanza A. A closed-form solution for natural frequencies of thin-walled cylinders with clamped edges, International Journal of Mechanical Sciences, 2016, Vol. 110, 116 – 126 p.
13.John E. C.N., Sewall L. An experimental and analytical vibration study of thin cylindrical shells with and without longitudinal stiffeners, NASA technical note, Vol. NASA P. 56 p.
14. Wang C., Lai J. C. S. Prediction of natural frequencies of finite length circular cylindrical shells, Applied acoustics, 2000, Vol. 59, No 4, 385 – 400 p.
15. Dai L., Yang T., Du J., Li. W., Brennan M. An exact series solution for the vibration analysis of cylindrical shells with arbitrary boundary conditions, Applied Acoustics, 2013, Vol 74, 440 – 449 p. |
| References: |
1. Xing Y., Liu B., Xu T. Exact solutions for free vibration of circular cylindrical shells with classical boundary conditions International Journal of Mechanical Sciences, 2013, Vol. 75, 178 – 188 p.
2. Lee H., Kwak M.K. Free vibration analysis of a circular cylindrical shell using the rayleigh-ritz method and comparison of different shell theories, Journal of Sound and Vibration, 2015, Vol. 353, 344 – 377 p.
3. Yu Y.Y. Free vibrations of thin cylindrical shells having finite lengths with freely supported and clamped edges, Journal of Applied Mechanics, 1955, Vol. 22, 547 – 552 p.
4. Soedel W. A new frequency formula for closed circular cylindrical shells for a large variety of boundary conditions, Journal of Sound and Vibration, 1980, Vol. 70, No 3, 309 –3 17 p.
5. Qu Y., Hua H., Meng G. A domain decomposition approach for vibration analysis of isotropic and composite cylindrical shells with arbitrary boundaries, Composite Structures, 2013, Vol. 95, 307 – 321 p.
6. Xuebin L. Study on free vibration analysis of circular cylindrical shells using wave propagation, Journal of Sound and Vibration, 2008, Vol. 311, No 3 – 5, 667 – 682 p.
7. Dubyk I., Orynyak I. Analysis of water hammer due to sudden rupture of reactor coolant system, Vancouver, Pressure Vessels and Piping Division Conference PVP, 2016, Vol. 4, 10 p.
8. Kan S.N. Stroitelnaya mehanica obolochek, Moskva, "Mashinistroenie" 1966, 508 p. [In Russian].
9. El-Mously M. Fundamental natural frequencies of thin cylindrical shells: a comparative study, Journal of Sound and Vibration, 2003, Vol. 264, No 5, 1167 – 1186 p.
10. Koval L.R., Cranch E.T. On the free vibrations of thin cylindrical shells subjected to an initial static torque, Proceedings of the 4th U.S. National Congress on Applied Mechanics, 1962, 107 – 117 p.
11. Smith B.L., Haftf E.E. Natural frequencies of clamped cylindrical shells, AIAA Journal, 1966, Vol. 6, No 4, 720 – 721 p.
12.Cammalleri M., Costanza A. A closed-form solution for natural frequencies of thin-walled cylinders with clamped edges, International Journal of Mechanical Sciences, 2016, Vol. 110, 116 – 126 p.
13.John E. C.N., Sewall L. An experimental and analytical vibration study of thin cylindrical shells with and without longitudinal stiffeners, NASA technical note, Vol. NASA P. 56 p.
14. Wang C., Lai J. C. S. Prediction of natural frequencies of finite length circular cylindrical shells, Applied acoustics, 2000, Vol. 59, No 4, 385 – 400 p.
15. Dai L., Yang T., Du J., Li. W., Brennan M. An exact series solution for the vibration analysis of cylindrical shells with arbitrary boundary conditions, Applied Acoustics, 2013, Vol 74, 440 – 449 p
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