MATEC Web Conf.
Volume 116, 20176th International Scientific Conference “Reliability and Durability of Railway Transport Engineering Structures and Buildings” (Transbud-2017)
|Number of page(s)||12|
|Section||Structures, Buildings and Facilities|
|Published online||10 July 2017|
Exact solution of the differential equation of transverse oscillations of the rod taking into account own weight
Odessa State Academy of Civil Engineering and Architecture, Structural Mechanics, Department Didrikson str., 4, Odessa, 65029, Ukraine
* Corresponding author: email@example.com
The free transverse oscillations of the rod of uniform cross section taking into account its own weight are considered in this work. The appropriate partial differential equation of transverse oscillations of a rod was reduced to two ordinary differential equations for the time function and the amplitude function of deflections. Concurrent with the differential equations for the amplitude state, the equivalent system of differential equation is considered. In total, the exact solution of the initial partial differential equation of transverse oscillations of a rod, expressed in nondimensional fundamental functions and initial parameters is attained. The method of power series was used for the construction of fundamental functions. Due to the exact solution, the formulas in an explicit form for dynamic variables of the state of a rode – deflections, angular displacement, bending moment and transverse force – were defined. The analytical form for equation of free oscillation frequency is defined. That has limited the finding of frequency to definition the unknown non-dimensional parameter through the frequency equation. As a result, the presence of derivative exact solutions provides the possibility to investigate the free oscillations of rod with various types of boundary conditions.
© The Authors, published by EDP Sciences, 2017
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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