A comparative analysis of axisymmetric vibrations of conical and cylindrical fluid-filled elastic shells
Keywords:
vibrations; ideal incompressible liquid; sloshing; cylindrical and conical shells; singular integral equations; boundary and finite element methods
Abstract
This paper presents the comparison of low- frequency vibrations in liquid-filled cylindrical and truncated conical elastic shells. The liquid is supposed to be an ideal and incompressible one and its flow is irrotational. To evaluate a velocity potential the system of singular boundary integral equations has been obtained. The boundary element method is used for their numerical simulation. The vibration modes of the shells with liquids are determined as linear combinations of their natural vibration modes without liquids. Sloshing frequencies and modes of fluid-filled cylindrical and truncated conical shells are estimated. The solution of the hydro-elasticity problem is obtained using a combination of boundary and finite element methods. Shells with both rigid and elastic bottoms are considered. The illustrative examples are provided to demonstrate the accuracy and efficiency of the method.
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References
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Аврамов К.В., Стрельникова Е.А. Хаотические колебания пластинок при их двустороннем взаимодействии с потоком движущейся жидкости/ К.В.Аврамов, Е.А. Стрельникова // Прикладная механика. 2014. т. 50, №3. С. 86-93.
Gnitko V, Marchenko U, Naumenko V, Strelnikova E., “Forced vibrations of tanks partially filled with the liquid under seismic load,” in Proc. of XXXIII Conference “Boundary elements and other mesh reduction methods” WITPress, Transaction on Modeling and Simulation International Journal of Modern Physics and Applications, vol. 52, pp. 285-296, 2011.
K.M. Liew, T.Y. Ng, X. Zhao, “Free vibration analysis of conical shells via the element-free in Ritz method, ” J. Sound Vib., vol. 281, pp. 627-645, 2005.
T.C. Ramesh, N. Ganesan, “A finite element based on a discrete layer theory for the free vibration analysis of conical shells,”J. Sound Vib., vol.166, no. 3, pp. 531-538, 1993.
Shu C., “An efficient approach for free vibration analysis of conical shells,” Int. J. Mech. Sci., vol. 38, no. 8-9, pp. 935-949, 1996.
Y.Kerboua, A.A. Lakis, M.Hmila, “Vibration analysis of truncated conical shells subjected to flowing fluid,”Applied Mathematical Modelling, vol. 34, no. 3, pp.791-809, 2010.
J. Ravnik, E. Strelnikova, V. Gnitko, K. Degtyarev, U. Ogorodnyk, “BEM and FEM analysis of fluid-structure interaction in a double tank “ Engineering Analysis with Boundary Elements, vol. 67, pp.13-25, 2016,
K.V. Avramov, E.A. Strel’nikova, C. Pierre, “Resonant many–mode periodic and chaotic self–sustained aeroelastic vibrations of cantilever plates with geometrical nonlinearities in ncompressible flow,” Nonlinear Dynamics, vol. 70, pp. 1335 - 1354, 2012.
V. Gnitko, K. Degtyariov, V. Naumenko, E. Strelnikova, “BEM and FEM analysis of the fluid-structure Interaction in tanks with baffles,” Int. Journal of Computational Methods and Experimental Measurements, vol.5, no.3, pp. 317-328, 2017.
Еселева Е.В., Гнитько В.И., Стрельникова Е.А. Собственные колебания сосудов высокого давления при взаимодействии с жидкостью / Е.В. Еселева, В.И. Гнитько, Е.А. Стрельникова // Пробл. машиностроения. 2006. №1, С.105 - 118.
C.A.Brebbia, J.C.F. Telles&L.C. Wrobel, Boundary Element Techniques, Springer-Verlag: Berlin and New York, 1984.
V.V. Naumenko, H.A. Strelnikova, “Singular integral accuracy of calculations in two-dimensional problems using boundary element methods,” Engineering analysis with boundary elements, vol. 26, pp. 95-98, 2002.
K. Degtyarev, V. Gnitko, V. Naumenko, E. Strelnikova, “Reduced Boundary Element Method for Liquid Sloshing Analysis of Cylindrical and Conical Tanks with Baffles,” Int. Journal of Electronic Engineering and Computer Sciences ,vol.1, no. 1, pp.14-27, 2016.
Published
2018-04-24
How to Cite
Degtyarev, K., Gnitko, V., Naumenko, Y., & StrelnіkovaЕ. (2018). A comparative analysis of axisymmetric vibrations of conical and cylindrical fluid-filled elastic shells. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 38(2), 33-41. Retrieved from https://periodicals.karazin.ua/mia/article/view/11461
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