Analysis of solutions of specified dynamic equations of beam bending on the example of investigation of the transverse forces evolution

Authors

DOI:

https://doi.org/10.15587/1729-4061.2015.37380

Keywords:

asymptotic-group, transverse force, bending wave, bending moment, non-stationary wave

Abstract

The paper deals with investigating the disturbed region of the beam during a suddenly applied load on the border (the problem of suddenly applied bending moment). Structural dynamics is described by the new specified one-dimensional dynamic equations of the beam bending. These equations were derived based on a rigorous mathematical algorithm (so-called non-minimal simplification of three-dimensional dynamic equations of elasticity theory).

The resulting equations have allowed to explore the layer-thickness averaged three-dimensional picture of the disturbance propagation by constructing graphs of respective solutions for the transverse forces. The results are in good agreement with the elasticity theory, in particular, the wave-front velocities coincide with the velocities according to elasticity theory problems. At the same time, all boundary conditions are defined in the same way as in the known problems of strength of materials. 

Author Biography

Лариса Николаевна Егармина, Zaporozhye State Engineering Academy Lenin avenue, 226, Zaporozhye, Ukraine, 69006

Candidate of technical sciences, associate professor

Department of The Higher and Applied Mathematics

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Published

2015-02-25

How to Cite

Егармина, Л. Н. (2015). Analysis of solutions of specified dynamic equations of beam bending on the example of investigation of the transverse forces evolution. Eastern-European Journal of Enterprise Technologies, 1(7(73), 27–31. https://doi.org/10.15587/1729-4061.2015.37380

Issue

Vol. 1 No. 7(73) (2015): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2015 Лариса Николаевна Егармина

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