We study natural vibrations of a thin isotropic elliptic shell of constant thickness by the finite-element method realized with the use of the high-performance FEMAR software developed for the engineering analyses. The comparative analysis of the numerical results and experimental data is carried out.
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A. Ya. Grigorenko, Yu. G. Zolotoi, A. P. Prigoda, I. Yu. Zhuk, V. V. Khorishko, and A. V. Ovcharenko, “Experimental investigation of natural vibrations of a thick-walled cylindrical shell by the method of holographic interferometry,” Mat. Metody Fiz.-Mekh. Polya, 55, No. 3, 93–98 (2012); English translation: J. Math. Sci., 194, No. 3, 239–244 (2013).
A. Ya. Grigorenko, S. V. Puzyrev, and E. A. Volchek, “Investigation of free vibrations of noncircular cylindrical shells by the spline-collocation method,” Mat. Metody Fiz.-Mekh. Polya, 54, No. 3, 60–69 (2011); English translation: J. Math. Sci., 185, No. 6, 824–836 (2012).
Ya. M. Grigorenko, E. I. Bespalova, A. B. Kitaigorodskii, and A. I. Shinkar’, Natural Vibrations of Elements of the Shell Structures [in Russian], Naukova Dumka, Kiev (1986).
Ya. M. Grigorenko and A. T. Vasilenko, Theory of Shells with Variable Stiffness, in: Methods for Numerical Analyses of the Shells [in Russian], Vol. 4, Naukova Dumka, Kiev (1981).
Ya. M. Grigorenko and A. P. Mukoed, Solving of Nonlinear Problems of the Theory of Shells on Computers [in Russian], Vyshcha Shkola, Kiev (1983).
Ya. M. Grigorenko and N. D. Pankratova, Computational Methods in the Problems of Applied Mathematics [in Ukrainian], Lybid’, Kiev (1995).
R. Kh. Makaeva, A. M. Tsareva, and A. Kh. Karimov, ”Determination of the vibrational characteristics of disks with constant thickness by the experimental-numerical method with the use of holographic interferometry,” in: Holography in Russia and Abroad. Science and Practice. Proc. of the Fourth Internat. Sci.-Pract. Conf. [in Russian], Moscow (2007), pp. 116–118.
K. N. Rudakov, FEMAP 10.2.0. Geometric and Finite-Element Modeling of Structures [in Russian], “KPI” National Technical University, Kiev (2011).
I. H. Sabih and E. J. Boisvert, “Vibration of elliptic cylindrical shells: higher order shell theory,” J. Acoust. Soc. Amer., 128, No. 3, 1063–1072 (2010).
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 57, No. 1, pp. 145–152, January–April, 2014.
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Budak, V.D., Grigorenko, A.Y., Borisenko, M.Y. et al. Determination of the Natural Frequencies of an Elliptic Shell of Constant Thickness by the Finite-Element Method. J Math Sci 212, 182–192 (2016). https://doi.org/10.1007/s10958-015-2658-0
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DOI: https://doi.org/10.1007/s10958-015-2658-0