ANALYTICAL CALCULATIONS OF THE VIBRATIONS OF VERTICAL STRUCTURES CONSIDERING THEIR DEAD WEIGHT

• Main Authors: Yurii Krutii, Victor Vandynskyi, Petr Konstantinov
• Format: Article
• Language: English
• Published: Faculty of Civil Engineering Osijek 2021-01-01
• Series: e-GFOS
• Subjects: rod structure; variable longitudinal force; bending vibration; natural frequency
• Online Access: http://e-gfos.gfos.hr/app/storage/protected/23-07-2021-05-56-27-egfos-2021-22-3.pdf

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.