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Non‐stationary bending of a finite electromagnetoelastic rod
Author(s) -
Pham Thong D.,
Tarlakovskii Dmitry V.,
Paimushin Vitaliy N.
Publication year - 2021
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.202000316
Subject(s) - mathematics , mathematical analysis , laplace transform , fourier series , euler's formula , electromagnetic field , fourier transform , trigonometric series , bernoulli's principle , classical mechanics , physics , quantum mechanics , thermodynamics
The related problem of non‐stationary bending of a finite electromagnetoelastic rod is considered. It is assumed that the material of the rod is a homogeneous isotropic conductor. The problem statement takes into account the initial electromagnetic field, the Lorentz force, Maxwell's equations and the generalized Ohm's law. The unknown functions are assumed to be bounded, and the initial conditions are assumed to be zero. It has noted that it is difficult to construct a solution analytically for a general model. Therefore, a transition is made to simplified equations corresponding to the Bernoulli‐Euler rod and the electromagnetic field is considered quasi‐stationary. For a rod with hinged ends, trigonometric series expansions and the Laplace transform in time are used. The solution of the problem is constructed in integral form with kernels in the form of influence functions. Images of kernels are found in the space of transformations and Fourier in the spatial coordinate. Their original functions are found explicitly. The present study presents examples of calculations for a concentrated load.