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A series of problems on the natural oscillations of circular plates of various thicknesses have been considered in studies [1–3]. They also outline issues that reveal the importance and essence of the problem, review the ways to solve it with appropriate literary references. In practice, there are cases when a circular plate in engineering structures is fixed inside the inner contour whose diameter is much smaller than that of the outer one. This situation necessitates considering a problem on the oscillations of a solid plate with a point support. The transition from natural conditions inside the internal contour to the conditions of point fastening is predetermined by the desire to simplify the plate estimation model without a significant loss of accuracy. For a plate of constant thickness with a support in the center, the results of solving the problem are reported in [4–7]. There is a basic issue related to a variable-thickness plate ‒ the search for a general analytical solution based on the original differential equation of free oscillations. If it is solved, it is possible to consider a series of applied problems on the oscillations of solid or circular, free, or fixed-in-different ways plates, including those with a point support. The relevance of the issue of calculating the oscillations of a plate of variable thickness with a point support is due to the need to improve the efficiency of estimation models, which is inextricably linked to their simplification, as is noted for the case of point fastening.

Analysis of free oscillations of round thin plates of variable thickness with a point support