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Flexural vibration of a square plate clamped along its contour

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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.

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Authors and Affiliations

  1. Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia

    S. V. Nesterov

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  1. S. V. Nesterov
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Correspondence to S. V. Nesterov.

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Original Russian Text © S.V. Nesterov, 2011, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2011, No. 6, pp. 159–165.

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Nesterov, S.V. Flexural vibration of a square plate clamped along its contour. Mech. Solids 46, 946–951 (2011). https://doi.org/10.3103/S0025654411060148

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  • DOI: https://doi.org/10.3103/S0025654411060148

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