Free vibration of anisotropic cylindrical shells with variable parameters

Authors

  • Георгий Георгиевич Влайков Technical Center of NAS of Ukraine, 13 Pokrovskaya str., Kyiv 70, 04 070., Ukraine
  • Александр Ярославович Григоренко S.P. Timoshenko Inst. of Mechanics of NAS of Ukraine, 3 P.Nesterov Street Kyiv 57 03057, Ukraine
  • Людмила Витальевна Соколова Kyiv national university of construction and architecture, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.14870

Keywords:

cylindrical shells, orthotropic material, variable thickness, refined formulation, refined theory, spline-collocation method, discrete orthogonalization method

Abstract

Investigations of the free vibrations of open orthotropic cylindrical shells with circumferentially varying thickness and the different boundary conditions based on the Mindlin shell theory are presented. The approach is based on reduction of two-dimensional boundary-value problem to one-dimensional using the spline-approximation method along one coordinate. The problem is described by the system of partial equations of 10th power with the variable coefficients.The one-dimensional eigenvalues problem is solved by the stable numerical discrete orthogonalization method in combination with the step-by-step search method. The calculations for the various boundary conditions on the end-faces and different variants shapes of cylinder thickness for orthotropic cylindrical shells are presented

Author Biographies

Георгий Георгиевич Влайков, Technical Center of NAS of Ukraine, 13 Pokrovskaya str., Kyiv 70, 04 070.

PhD, Director

Александр Ярославович Григоренко, S.P. Timoshenko Inst. of Mechanics of NAS of Ukraine, 3 P.Nesterov Street Kyiv 57 03057

Head Department of Numerical Methods Department

Людмила Витальевна Соколова, Kyiv national university of construction and architecture

PhD, associate professor, department of higher mathematics

References

  1. Qatu, M. S. Recent research advances in the dynamic behavior of shells: 1989-2000, Part 2: Homogeneous shells [Текст] / M. S. Qatu // Appl. Mech. Rev. – 2002. – Vol. 55. – P. 415-434.
  2. Sividas, K.R. Free vibration of circular cylindrical shells with axially varying thickness [Текст] / K.R. Sividas, N. Ganesan // J. Sound Vib. – 1991. – Vol. 147, № 1. – P. 73-85.
  3. Zhang, L. Exact solution for vibration of stepped circular cylindrical shells [Текст] / L. Zhang, V. Xiang // J. Sound Vib. – 2007. – Vol. 299. – P. 948-964.
  4. Suzuki, K. Exact solution for the free vibration of open cylindrical shells with circumferentially varying curvature and thickness [Текст] / K. Suzuki, A.W. Leissa // J. Sound Vib. – 1986. – Vol. 107(1). – P. 1-15.
  5. Григоренко, А. Я. Об одном подходе к исследованию свободных колебаний цилиндрических оболочек переменой в круговом направлении толщины в уточненной постановке [Текст] / А.Я. Григоренко, Т.Л. Ефимова, Л.В. Соколова // Мат. методи та фіз.-мех. поля. – 2009. – T. 52, № 3. – С. 103–115.
  6. Grigorenko A. Ya. Application of Spline-Approximation for Solving the Problems on Natural Vibration of Rectangular Plates of Variable Thickness / A.Ya. Grigorenko, T.L. Efimova // Int. Appl. Mech. – 2005. – Vol. 41. – P. 1161-1169.
  7. Григоренко Я.М. Методы расчета оболочек в 5 т. Т.4. Теория оболочек переменной жесткости./ Я.М. Григоренко, А.Т. Василенко. – К.: Наук. думка, 1981. – 543 с
  8. Григоренко Я.М. Численно-аналитическое решение задач механики оболочек на основе различных моделей / Я.М. Григоренко, Г.Г. Влайков, А.Я. Григоренко.-К.: Академпериодика, 2006. – 472 с.
  9. Ашкенази Е.К. Анизотропия конструктивних материалов / Е.К. Ашкенази, Э.В. Ганов. Справочник. 2-е изд., пере раб. и доп. – Л.: Машиностроение. Ленингр. Отд-ние, 1980. – 247с
  10. Qatu, M. S. (2002). Recent research advances in the dynamic behavior of shells: 1989-2000, Part 2: Homogeneous shells. Appl. Mech. Rev,Vol. 55, 415-434.
  11. Sividas, K. R., Ganesan, N. (1991). Free vibration of circular cylindrical shells with axially varying thickness, Vol. 147, № 1, 73-85.
  12. Zhang, L., Xiang, V. (2007). Exact solution for vibration of stepped circular cylindrical shells. J. Sound Vib, Vol. 299, 948-964.
  13. Suzuki, K., Leissa, A.W. (1986). Exact solution for the free vibration of open cylindrical shells with circumferentially varying curvature and thickness. J. Sound Vib, Vol. 107(1), 1-15.
  14. Grigorenko, A. Ya., Efimova, T.L., Sokolova, L.V. (2009). Ob odnom podxode k issledovaniyu svobodnyx kolebanij cilindricheskix obolochek peremenoj v krugovom napravlenii tolshhiny v utochnennoj postanovke. Mat. metodi ta fіz.-mex. Polya, T. 52, № 3, 103–115.
  15. Grigorenko, A. Ya., Efimova, T.L. (2005). Application of Spline-Approximation for Solving the Problems on Natural Vibration of Rectangular Plates of Variable Thickness. Int. Appl. Mech., Vol. 41, 1161-1169.
  16. Grigorenko, Ya.M., Vasilenko, A.T. (1981). Metody rascheta obolochek v 5 t. T.4. Teoriya obolochek peremennoj zhestkosti. Nauk. dumka, 543
  17. Grigorenko, Ya.M., Vlajkov, G.G., Grigorenko, A.Ya. (2006) Chislenno-analiticheskoe reshenie zadach mexaniki obolochek na osnove razlichnyx modelej. Akademperiodika, 472.
  18. Ashkenazi, E.K., Ganov, E.V. (1980). Anizotropiya konstruktivnix materialov. Spravochnik. 2-e izd., pere rab. i dop, Mashinostroenie. Leningr. Otd-nie, 247.

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Published

2013-06-19

How to Cite

Влайков, Г. Г., Григоренко, А. Я., & Соколова, Л. В. (2013). Free vibration of anisotropic cylindrical shells with variable parameters. Eastern-European Journal of Enterprise Technologies, 3(12(63), 13–16. https://doi.org/10.15587/1729-4061.2013.14870

Issue

Vol. 3 No. 12(63) (2013): MODERN TECHNOLOGIES IN THE GAS-TURBINE

Section

Modern technologies in the gas-turbine

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Copyright (c) 2014 Георгий Георгиевич Влайков, Александр Ярославович Григоренко, Людмила Витальевна Соколова

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