The method for solving the problem of determining the shapes and frequencies of natural oscillations in elastic systems

In the dynamic calculation of various engineering structures, resonant modes of vibrations are considered (with frequencies which very close to the own frequencies of elastic vibrations). Therefore, it is often necessary to pay great attention precisely to the accuracy of calculating the frequencies and especially the modes of own vibrations of these structures. From this point of view, the best method for calculating the dynamic characteristics is undoubtedly the Kochy method in combination with the method of differential sweep, which allows to obtain the modes and frequencies of oscillations with any accuracy. In this paper, we propose a modified version of the differential sweep method for solving an one-dimensional spectral problem. The numerical implementation of the algorithm of the proposed method for solving the one-dimensional and axisymmetric spectral problem of free vibrations of structural elements of both constant and variable thickness is considered.