To the decision of task about the vibrations of circular plate with a thickness decreasing from a center on a protuberant parabola

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

“…1. A general analytical solution to the IV-order differential equation has been derived for a problem on the free axisymmetric oscillations of a plate whose thickness h=H 0 (1-µρ) 2 . This solution makes it possible to consider a series of problems about oscillations of parabolic platessolid and circular ones, with different types of contour fastening, including a point support in the center.…”

“…за параболiчним законом h=H 0 (1-μρ) 2 . При побудовi розв'язку використовувався синтез методу факторизацiї з методом симетрiй.…”

“…-to derive, based on the synthesis of symmetry and factorization methods, a general analytical solution to the differential equation for a problem on the free axisymmetric oscillations of a plate whose thickness h=H 0 (1-µρ) 2 ; -to transform the general solution to the form that meets the conditions on the support;…”

“…For a plate whose thickness h=H 0 (1-µρ) 2 , work [3] gives a differential equation for the shapes of natural axisymmetric bending oscillations, which can be represented in the following form…”

“…A series of problems on the natural oscillations of circular plates of various thicknesses have been considered in studies [1][2][3]. They also outline issues that reveal the importance and essence of the problem, review the ways to solve it with appropriate literary references.…”