Omar Kikvidze*

Akaki Tsereteli State University, Georgia

*Corresponding Author: Omar Kikvidze, Akaki Tsereteli State University, Georgia.

Received: August 14, 2021; Published: December 24, 2021

Abstract

The paper dwells on flexural vibrations of an elastic beam, the axial line of which in natural state is a plane curve and after loading remains plane. We made the following assumptions: all the cross-sections of beam remain plane and perpendicular to the longitudinal axis during deformation, the length of longitudinal axis is changing, the temperature field is stationary and nonhomogeneous. The thermoelastic curve for a beam is represented mathematically as functions of beam length and time:, where:  and  are respectively the vertical displacement, horizontal displacement and slope angle. To obtain these functions we have nonlinear differential equations, which contains the change in length of longitudinal axis.

The nonlinear differential equations of motion contain inertia of rotation of the cross-section. In particular, the paper describes the equations of small vibrations of a prismatic beam. To determine the range of natural frequencies of beam, the equations are written using boundary conditions. The impact of axial deformation and a temperature gradient on the frequencies is studied. Numerical calculations are carried out in a mathematical editor Mathcad.

Keywords: Thermoelastic Beam; Dynamics; Differential Equation; Frequency

References

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Citation

Citation: Omar Kikvidze. “Study of Nonlinear Problem of Thermoelastic Beam Dynamics by Numerical Method". Acta Scientific Computer Sciences 3.1 (2022): 54-58.

Copyright

Copyright: © 2022 Omar Kikvidze. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.