 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 46, Issue 6 / 2011 | Next article >> |
| S.V. Nesterov, "Flexural Vibration of a Square Plate Clamped along Its Contour," Mech. Solids. 46 (6), 946-951 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
6 |
Pages |
946-951 |
| DOI |
10.3103/S0025654411060148 |
| Title |
Flexural Vibration of a Square Plate Clamped along Its Contour |
| Author(s) |
S.V. Nesterov (Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526 Russia, kumak@ipmnet.ru) |
| Abstract |
Analytical expressions are constructed for calculating the natural frequencies and mode shapes of flexural vibrations of a square homogeneous plate clamped along its contour. An error estimate is given by comparing predicted results with those of known high-precision calculations. Also the results of analytical calculations are compared with experimental data obtained by the author using the resonance method. The analytical and corresponding numerical results coincide with the experimental data to within less than 1%.
High-precision evaluation of natural frequencies is required to design modern precision electromechanical transformers and to analyze the quality of their operation. The proposed investigation techniques and computational algorithm can be used to study flexural vibration of plates
with other types of boundary conditions. |
| Keywords |
square plate, natural frequencies, mode shapes, modified Rayleigh method, experiment |
| References |
| 1. | S. H. Gould,
Variational Methods for Eigenvalue Problems
(Oxford Univ. Press, London, 1970; Mir, Moscow, 1970). |
| 2. | S. G. Mikhlin,
Variational Methods in Mathematical Physics
(Pergamon, New York, 1964; Nauka, Moscow, 1970). |
| 3. | G. Fichera,
Linear Elliptic Differential Systems and Eigenvalue Problems
(Springer, Berlin, 1965). |
| 4. | G. Fichera,
"Approximations and Estimates for Eigenvalues,"
Vortrag der 3en Tagung über Problemen und Methoden der Matheamtischem Physik
Technische Hochschule Karl-Marx-Stadt H.I. (1966), pp. 60-98. |
| 5. | I. A. Birger and Ya. G. Panovko (Editors),
Strength. Stability. Vibrations, Vol. 3
(Mashinostroenie, Moscow, 1968)
[in Russian]. |
| 6. | L. D. Akulenko and S. V. Nesterov,
"Vibration of a Nonhomogeneous Membrane,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 134-145 (1999)
[Mech. Solids (Engl. Transl.)
34 (6), 112-121 (1999)]. |
| 7. | L. D. Akulenko and S. V. Nesterov,
"Experimental Identification of Poisson's Ratio by the Resonance Method,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 6, 49-57 (2000)
[Mech. Solids (Engl. Transl.)
35 (6), 38-45 (2000)]. |
|
| Received |
17 February 2010 |
| Link to Fulltext |
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