Abstract:

A new method for calculating bending oscillations of vertical cantilever structures with allowance for their own weight is proposed. The method is based on the exact solution of the corresponding partial differential oscillation equation with variable coefficients. In the analytical form with the help of dimensionless fundamental functions, formulas for dynamic parameters – motion, angle of rotation, bending moment and shear force, which completely characterize the state of the rod, are written out. In general, the frequency equation is written out and the method for finding its roots is determined. It is shown that the problem of determining natural frequencies can be reduced to finding the corresponding dimensionless coefficients from the frequency equations. The formulas for determining mode shapes are found. The algorithm that allows determining natural frequencies and mode shapes of cantilever structures with any given accuracy is described. The algorithm is implemented on the example of a through lattice tower. It is found that the numerical values obtained by the author’s method coincide with the results obtained with the help of the software system that implements the finite element method. In comparison with approximate methods, this method allows obtaining a more reliable picture of oscillations of cantilever structures, since it is the exact solution that carries information of a qualitative nature and forms the most complete picture of the physical phenomenon under consideration. Using explicit analytical formulas, the accuracy of calculation of bending oscillation is increased. The proposed method does not require the discretization of the structure and is a real alternative to the use of approximate methods when solving this class of problems of solid mechanics. Author Biographies Yurii Krutii, Odessa State Academy of Civil Engineering and Architecture Didrihsona str., 4, Odessa, Ukraine, 65029 Doctor of Technical Sciences, associate professor Vice-rector in the Research and Educational Work

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