Calculation of free vibrations frequencies of towers using Faddeev's and Krylov's methods

The paper considers the issue of dynamic calculation of free vibration frequencies for tower-type structures. The authors propose to use a scheme in the form of a discrete model with the replacement of distributed masses by concentrated masses when calculating a real continuum system. Spreadsheets were used to solve the problem of calculating natural vibration frequencies. The theoretical basis of the calculation includes a description of numerical methods for solving the determinant of the secular equation. The paper shows algorithms of computational operations for calculating free vibrations of systems with a finite number of freedom degrees using the method by D.K. Faddeev and the method by A.N. Krylov. The approaches to finding the roots of the n-degree characteristic equation are analysed. The paper contains calculation examples of natural vibrations of tower-type structures with five and six degrees of freedom.