Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
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IssuesArchive of Issues2016-6pp.672-676

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Total articles in the database: 9179
In Russian (. . ): 6485
In English (Mech. Solids): 2694

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S.V. Nesterov, "High-Precision Analytic Solution of the Problem on Bending Vibrations of a Clamped Square Plate," Mech. Solids. 51 (6), 672-676 (2016)
Year 2016 Volume 51 Number 6 Pages 672-676
DOI 10.3103/S0025654416060066
Title High-Precision Analytic Solution of the Problem on Bending Vibrations of a Clamped Square Plate
Author(s) S.V. Nesterov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, kumak@ipmnet.ru)
Abstract An original iteration algorithm is used to construct new analytic expressions for computing approximate natural frequencies and shape modes of bending vibrations of a square homogeneous plate clamped along its contour. The errors are estimated by comparing with the results of well-known numerical high-precision computations. The results of analytic computations are also compared with experimental data obtained by the author by the resonance method. The proposed research technique and the obtained high-precision expressions for the natural shape modes can be used in the case of rectangular plates and for other types of boundary conditions.

A numerical-analytical method is used to show that the small isoperimetric theorem holds.
Keywords square plate, natural frequency, natural shape mode, modified Rayleigh method, small isoperimetric theorem
References
1.  S. V. Nesterov, "Flexural Vibration of a Square Plate Clamped along Its Contour," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 159-165 (2011) [Mech. Solids (Engl. Transl.) 46 (6), 946-951 (2011)].
2.  G. Fichera, Linear Elliptic Differential Systems and Eigenvalue Problems (Springer, Berlin, 1965).
3.  G. Fichera, "Approximations and Estimates for Eigenvalues," Vortrag der 3en Tagung über Problemen and Methoden der Mathematischen Physik Technische Hochschule Karl-Marx-Stadt H.I. (1966), pp. 60-98.
4.  I. A. Birger and Ya. G. Panovko (Editors), Strength. Stability. Vibrations, Vol. 3 (Mashinostroenie, Moscow, 1968).
5.  S. H. Gould, Variational Methods for Eigenvalue Problems (Oxford Univ. Press, London, 1970; Mir, Moscow, 1970).
Received 16 September 2014
Link to Fulltext http://link.springer.com/article/10.3103/S0025654416060066
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