 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12882 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8071
|
| In English (Mech. Solids): | | 4811 |
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| << Previous article | Volume 51, Issue 6 / 2016 | Next article >> |
| 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 |
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