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

In article, the exact solution of sinusoidal loaded simply supported elastic transversally inextensible rectangular plate is given. The expressions for displacement and stress components are derived and asymptotic expansion with respect to plate thickness are present. The frequency factors for plate thickness to width ratio 0.01, 0.1, 0.2 and 0.4 and various ratios of plate length to width are given.