MATEC Web Conf.
Volume 230, 20187th International Scientific Conference “Reliability and Durability of Railway Transport Engineering Structures and Buildings” (Transbud-2018)
|Number of page(s)||10|
|Section||Structures, Buildings and Facilities|
|Published online||16 November 2018|
Analytic formulas for the natural frequencies of hinged structures with taking into account the dead weight
Odessa State Academy of Civil Engineering and Architecture, Didrikson str., 4, Odessa, 65029, Ukraine
* Corresponding author: firstname.lastname@example.org
Free bending vibrations of hinged vertical uniform rod with taking into account the dead weight are investigated. The research is based on the exact solution of the partial differential vibration equation with variable coefficients. This approach allows to get more reliable picture of rod’s vibration because only the exact solution carries information of a qualitative nature and forms the most complete picture of the physical phenomenon under consideration. The frequencies equation of problem was written in dimensionless form and the way of its root finding is shown. It has been shown that the problem of determination the nature frequencies of structures is reduced to finding corresponding dimensionless vibration coefficients from equation. The formulas for the first three vibration frequencies of structures were obtained in analytical form. An analytic relationship between the frequencies with and without taking into account the dead weight of the structures was established. The nature of the dependence of frequencies on the value of the longitudinal load was revealed. The presence of conclusive analytical formulas for determining the vibration frequencies of hinged vertical structures with taking into account the dead weight is a real alternative for using the approximate methods for solving this class of problems of solid mechanics.
© The Authors, published by EDP Sciences, 2018
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