Plate vibrations with periodically changing parameters
DOI:
https://doi.org/10.21638/spbu01.2021.412Abstract
Vibrations of square plate with periodically changing parameters are considered. The averaged fourth-order partial differential equation for the plate deflection w is offered. Solution of the problem is obtained by using the approximate theory. The approximate results are presented by analytical formulas. Asymptotic averaging (realized in Wolfram Mathematica) and Finite Elements Method (ANSYS) are used to get the values of vibrations frequencies. The comparison of numerical and asymptotic results is performed.Keywords:
plate, reinforced plate, heterogeneous plate, vibrations of plates, deformations of plates
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References
Литература
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References
1. Madenci E., Guven I. The Finite Element Method and Applications in Engineering Using ANSYS. New York, Springer (2006).
2. Oliveira Neto L., de Paiva J.B. A special BEM for elastostatic analysis of building floor slabs on columns. Computers and Structures 81 (6), 359–372 (2003). https://doi.org/10.1016/S0045- 7949(02)00449-2
3. Sanches L.C.F., Mesquita E., Pavanello R., Palermo L. Dynamic Stationary Response of Reinforced Plates by the Boundary Element Method. Mathematical Problem in Engineering 2007, 62157 (2007). https://doi.org/10.1155/2007/62157
4. Fernandes G.R., Venturini W.S. Stiffened plate bending analysis by the boundary element method. Computational Mechanics 28, iss. 3, 275–281 (2002).
5. Filippov S.B., Naumova N.V. Vibrations and buckling of cylindrical shell made of a general anisotropic elastic material. Proc. of the 10th Shell Structures Theory and Applications Conference 3, 289–292 (2013).
6. Naumova N.V., Ivanov D.N. Vibrations of an inhomogeneous rectangular plate. Technische Mechanik 31 (1), 25–33 (2011).
7. Tovstik P.E., Tovstik T.P., Naumova N.V. Long-wave vibrations and waves inanisotropic beam. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 4 (62), iss. 2, 323–335 (2017). https://doi.org/10.21638/11701/spbu01.2017.216 (In Russian) [Engl. transl.: Vestnik St. Petersb. Univ. Math. 50, 198–207 (2017). https://doi.org/10.3103/S1063454117020121].
8. Nazarov S.A., Slutskij A.S., Sweers G.H. Korn Inequalities for a Reinforced Plate. Journal of Elasticity 106, iss. 1, 43–69 (2012).
9. Naumova N.V., Ivanov D., Voloshinova T. Deformation of a Plate with Periodically Changing Parameters. AIP Conference Proceedings 1959, 070026 (2018). https://doi.org/10.1063/1.5034701
10. Argatov I., Mishuris G. Contact Mechanics of Articular Cartilage Layers. Asymptotic Models. Springer (2015).
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Published
2022-01-04
How to Cite
Naumova, N. V., Ivanov, D. N., & Dorofeev, N. P. (2022). Plate vibrations with periodically changing parameters. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8(4), 661–669. https://doi.org/10.21638/spbu01.2021.412
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Mechanics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
