These Matlab scripts calculate the natural frequencies and normal modes of a flat rectangular plate via the finite element method: rectangular_plate_fea.zip
rectangular_plate_fea.m is the main script.
The remaining scripts are supporting function.
Rectangular elements are used for the numerical model, but the plotting elements are triangular.
Here is a reference paper: FEA_plate_bending.pdf
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See also: plate bending frequency
This other page has a Matlab GUI script for calculating the fundamental frequency of a plate using formulas from classical methods.
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– Tom Irvine