Non‐stationary bending of a finite electromagnetoelastic rod

Abstract

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.

Spatially localized nonlinear magnetoelastic waves in an electrically conductive micropolar medium

“…The vast majority of the problems of magnetoelasticity are considered in the linear approximation and in one-dimensional or two-dimensional formulation. Among recent publications, we would like to underline [10][11][12].…”

“…In [11] the problem of non‐stationary bending of a finite electromagnetoelastic rod under the assumption that the rod material is a homogeneous isotropic conductor was presented. The statement of the problem considers the initial electromagnetic field, the Lorentz force, Maxwell's equations and the generalized Ohm's law.…”