Open AccessDevelopment of analytical calculation method for axisymmetric oscillations of circular and annular plates on variable Winkler elastic foundation
Author(s) -
Yurii Krutii,
Mykola Surianinov,
Vladimir Osadchiy,
В.Г. Коломійчук
Publication year - 2021
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1164/1/012056
Subject(s) - discretization , rotational symmetry , oscillation (cell signaling) , variable (mathematics) , exact solutions in general relativity , mathematics , mathematical analysis , differential equation , vibration , partial differential equation , physics , geometry , genetics , quantum mechanics , biology
An analytical method for calculating axisymmetric vibrations of circular and annular plates on a variable elastic Winkler base is presented. The proposed calculation method is based on the exact solution of the oscillation equation with the subsequent development of a method for its numerical implementation. To construct an exact solution, the direct integration method is used, which was previously developed by one of the authors for differential equations with continuous variable coefficients. The proposed method does not require the discretization of the considered structure and it is a real alternative to the application of approximate methods during solving this types of problems. Based on the exact solution of the differential equation, this method will allow to obtain better picture of oscillations in comparison with approximate methods. In fact, the exact solution has qualitative information and forms the most complete picture of the physical phenomenon that is researched.