Development of analytical calculation method for axisymmetric oscillations of circular and annular plates on variable Winkler elastic foundation

Abstract

Abstract 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.