Deflections and Free Vibrations of Circular Isotropic Plates of Thickness Varying in Accordance with a Parabola

The paper considers the relationship between the dynamic and static parameters of circular isotropic plates under various boundary conditions. The studies of the plates were carried out under static and dynamic loading, taking into account the variability of the thickness. The authors established the relationship between the maximum deflection and the natural frequencies of the transverse vibrations of the plates, and assessed the matching of the coefficient K obtained by numerical studies with its analytical one. The curves for the frequencies of free vibrations and deflections under the static load and the change in the coefficient K depending on the thickness of the plate and boundary conditions were plotted. Studies showed that the coefficient K complies within 5% of the dependence of Professor V.I. Korobko only when the ratio of the thickness in the center to the thickness on the support t2/t1 = 60/50 < 1.2 for both support schemes. This is due to the fact that formula (16) was derived for isotropic plates with constant thickness and the distribution of mass evenly over the entire area of the plate leads to a significant error already at the stage of a small difference between the thicknesses at the support and in the center. With a thickness ratio t2/t1 = 100/50 = 2, the difference between the K coefficient and the analytical one is about 16%.