ANALYTICAL CALCULATIONS OF THE VIBRATIONS OF VERTICAL STRUCTURES CONSIDERING THEIR DEAD WEIGHT (Advances in Civil and Architectural Engineering, 2021)
This paper presents the results of studies on the analytical dependence between the value of a longitudinal distributed load and the frequency of free vibrations in a uniform rod. Based on the exact solution of the corresponding differential equation, a method for calculating vibrations in rod structures, while considering their dead weight, is implemented. The method algorithm is shown using the example of a rod with both ends clamped. This article contains graphs and analytical formulas for displaying dependencies. A table is provided that contains all the necessary coefficients to perform similar calculations for other boundary conditions. These results allow the physical and mechanical characteristics of a system to be used to determine the natural frequency of rod structures without using approximate methods.