Non-stationary longitudinal vibrations of an electromagnetoelastic rod
UDC
593.3DOI:
https://doi.org/10.31429/vestnik-17-2-57-65Abstract
The coupled non-stationary longitudinal vibrations of electromagnetoelastic rods are investigated. It is assumed that the material of the rod is a homogeneous isotropic conductor. The equations used take into account the initial electromagnetic field, the Lorentz force, Maxwell's equations and the generalized Ohm's law. They are obtained as a special case of the corresponding relations for thin electromagnetoelastic shells under the assumption that the desired functions depend only on the longitudinal coordinate.
Two variants of the rods are considered: the infinite rod under the condition that the desired functions are limited and the finite rod with fixed and isolated end cross sections. In the initial electromagnetic field, only the magnetic field strength differs from zero. The solution is presented in integral form with kernels in the form of Green functions. To determine the kernels, the Laplace transform in time and the Fourier transform or trigonometric series in the longitudinal coordinate are used. Explicit forms of solutions are obtained when the transverse compression is ignored and under the conditions of a quasi-static perturbed electromagnetic field. Examples of calculations are provided.
Keywords:
coupled non-stationary electromagnetoelasticity, rod, longitudinal vibrations, Green functions, Laplace transforms, Fourier transforms, trigonometric seriesReferences
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Dates
Submitted
May 17, 2020
Accepted
May 26, 2020
Published
June 27, 2020
How to Cite
[1]
Pham, T.D., Tarlakovskii, D.V., Non-stationary longitudinal vibrations of an electromagnetoelastic rod. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2020, т. 17, № 2, pp. 57–65. DOI: 10.31429/vestnik-17-2-57-65
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