Singular integral equations for free vibration problem of a fluid-filled shell of revolution
Keywords:
fluid-structure interaction; finite and boundary element methods; systems of singular integral equations; the logarithmic singularity
Abstract
The problem to analyze dynamics of shells of revolution partially filled with an ideal incompressible liquid was reduced to solving the system of singular integral equations. The direct formulation of boundary integral equation method was in use. The singularities in kernels of integral operators obtained were analyzed. The method of numerical simulation was proposed, the comparison of numerical and analytical solutions of singular integral equations was accomplished. The free vibration problem for hemisphere was solved with usage of proposed method.
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References
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Вандышев К.В., Еселева Е.В., Стрельникова Е.А. Собственные формы сингулярных и гиперсингулярных операторов на круге/ Труды XIV Международного симпозиума «Методы дискретных особенностей в задачах математической физики», Харьков-Херсон, 2009, ч.1, С.34-37.
S.M. Hasheminejad, M. Aghabeigi, Liquid sloshing in half-full horizontal elliptical tanks, J. Sound Vib. 324, pp. 332–349, 2009.
L. Xu, Fluid Dynamics in Horizontal Cylindrical Containers and Liquid Cargo Vehicle Dynamics, Ph.D. Thesis, University of Regina, Saskatchewan, 2005.
Celebi, M.S., Kim, M.H., Beck, R.F. Fully Non-linear 3-D Numerical Wave Tank Simulation. J. of Ship Research, Vol.42, No.1, pp 33-45. 1998
K. Modaressi-Tehrani, S. Rakheja, I. Stiharu, Three-dimensional analysis of transient slosh within a partly-filled tank equipped with baffles, Veh. Syst.Dyn. 45, pp. 525–548, 2007.
L. Xu, Fluid Dynamics in Horizontal Cylindrical Containers and Liquid Cargo Vehicle Dynamics, Ph.D. Thesis, University of Regina, Saskatchewan, 2005.
Brebbia, C.A., Telles, J.C.F. & Wrobel, L.C. Boundary Element Techniques, Springer-Verlag: Berlin and New York, 1984
Градштейн И.С., Рыжик И.М. Таблицы интегралов, сумм, рядов и произведений – М.: Физматгиз, 1963. – 1100 с.
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Published
2014-04-28
How to Cite
Огородник, У. Е., Стрельникова, Е. А., & Шувалова, Ю. С. (2014). Singular integral equations for free vibration problem of a fluid-filled shell of revolution. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 24(1105), 129-135. Retrieved from https://periodicals.karazin.ua/mia/article/view/14256
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