Original scientific paper
https://doi.org/10.13167/2021.22.3
ANALYTICAL CALCULATIONS OF THE VIBRATIONS OF VERTICAL STRUCTURES CONSIDERING THEIR DEAD WEIGHT
Yurii Krutii
orcid.org/0000-0001-7105-3087
; Odessa State Academy of Civil Engineering and Architecture, Department of Information Technology and Applied Mathematics
Victor Vandynskyi
; Odessa State Academy of Civil Engineering and Architecture, Building mechanical Department
Petr Konstantinov
; Odessa State Academy of Civil Engineering and Architecture, Department metal, wooden and plastic structures
Abstract
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.
Keywords
Rod structure; variable longitudinal force; bending vibration; natural frequency
Hrčak ID:
261278
URI
Publication date:
30.7.2021.
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