High-precision analytic solution of the problem on bending vibrations of a clamped square plate |
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Authors: | S V Nesterov |
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Institution: | 1.Ishlinsky Institute for Problems in Mechanics,Russian Academy of Sciences,Moscow,Russia |
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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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