Abstract:
Unsymmetrical buckling of nonuniform circular plates with elastically restrained edge and subjected to normal pressure is studied in this paper. The asymmetric part of the solution is sought in terms of multiples of the harmonics of the angular coordinate. A numerical method is employed to obtain the lowest load value at which waves in the circumferential direction can appear. The effect of material heterogeneity and boundary on the buckling load is examined. For a plate with elastically restrained edge, the buckling pressure and mode number increase with a rise of spring stiffness. Increasing of the elasticity modulus to the plate edge leads to increasing of the buckling pressure, but the mode number does not change. If the translational flexibility coefficient is small, decreasing of the elasticity modulus to the shell (plate) edge leads to sufficient lowering of the buckling pressure.
The work was carried out with the support of the Russian Foundation for Basic Research (grant no. 19-01-00208) and using the equipment of the resource center of the St. Petersburg State University Scientific Park “Observatory of Environmental Safety”
Citation:
S. M. Bauer, E. B. Voronkova, “On non-axisymmetric buckling modes of inhomogeneous circular plates”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8:2 (2021), 204–211; Vestn. St. Petersbg. Univ., Math., 8:3 (2021), 113–118
\Bibitem{BauVor21}
\by S.~M.~Bauer, E.~B.~Voronkova
\paper On non-axisymmetric buckling modes of inhomogeneous circular plates
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2021
\vol 8
\issue 2
\pages 204--211
\mathnet{http://mi.mathnet.ru/vspua108}
\crossref{https://doi.org/10.21638/spbu01.2021.201}
\transl
\jour Vestn. St. Petersbg. Univ., Math.
\yr 2021
\vol 8
\issue 3
\pages 113--118
\crossref{https://doi.org/10.1134/S1063454121020023}
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https://www.mathnet.ru/eng/vspua108
https://www.mathnet.ru/eng/vspua/v8/i2/p204
This publication is cited in the following 4 articles:
Desheng Li, Baowang Huang, Jiangtao Yu, “Fundamental mathematical model on nonlinear non-symmetric free vibration of thin circular plate carrying concentrated masses”, Thin-Walled Structures, 2025, 113208
N. F. Morozov, A. V. Lukin, I. A. Popov, “Symmetry Breaking and Multistability of Electrostatically Actuated Annular Microplates”, Mech. Solids, 59:1 (2024), 32
N. F. Morozov, A. V. Lukin, I. A. Popov, “Symmetry Breaking and Multistability of Electrostatically Actuated Annular Microplates”, Izvestiâ Rossijskoj akademii nauk. Mehanika tverdogo tela, 2024, no. 1, 110
S. M. Bauer, L. A. Venatovskaya, E. B. Voronkova, “Models of Solid Mechanics in the Problems of Ophthalmology”, Vestnik St.Petersb. Univ.Math., 56:4 (2023), 493
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