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High-precision analytic solution of the problem on bending vibrations of a clamped square plate

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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.

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References

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Authors and Affiliations

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

    S. V. Nesterov

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

Additional information

Original Russian Text © S.V. Nesterov, 2016, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2016, No. 6, pp. 67–74.

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Nesterov, S.V. High-precision analytic solution of the problem on bending vibrations of a clamped square plate. Mech. Solids 51, 672–676 (2016). https://doi.org/10.3103/S0025654416060066

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  • DOI: https://doi.org/10.3103/S0025654416060066

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