Algorithm for forming a reduced system of frequency equations of the FEM in the form of a classical mixed method using interpolation of the main variables

This article discusses the problems that arise when using the finite element method for dynamic calculation of buildings and structures. The main directions of research on this problem are considered. The main part describes the developed algorithm for reducing the system of FEM frequency equations in the form of a classical mixed method using interpolation of basic unknowns and its practical application in the problem of dynamic calculation of a square plate. In the course of the study, its dynamic calculation was carried out using the initial and reduced system of frequency equations. The results of the reduced spectrum of natural frequencies of plate vibrations obtained using the proposed algorithm are analyzed, and the results of numerical calculation with an analytical solution are verified