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In article, the exact solution of sinusoidal loaded simply supported elastictransversally inextensible rectangular plate is given. The expressions fordisplacement and stress components are derived and asymptotic expansion withrespect to plate thickness are present. The frequency factors for platethickness to width ratio 0.01, 0.1, 0.2 and 0.4 and various ratios of platelength to width are given.

Analytical solution for free vibrations of simply supported transversally inextensible homogeneous rectangular plate