Non-stationary bending of a finite electromagnetoelastic rod,ZAMM - Journal of Applied Mathematics and Mechanics

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Non-stationary bending of a finite electromagnetoelastic rod
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2021-03-15 , DOI: 10.1002/zamm.202000316
Thong D. Pham ₁ , Dmitry V. Tarlakovskii _{1,

2} , Vitaliy N. Paimushin _{3,

4}

Affiliation

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.

中文翻译：

有限电磁弹性杆的非平稳弯曲

考虑了有限电磁弹性杆非平稳弯曲的相关问题。假定杆的材料是均匀的各向同性导体。问题陈述考虑了初始电磁场、洛伦兹力、麦克斯韦方程和广义欧姆定律。假定未知函数是有界的，并且假定初始条件为零。它已经注意到，很难为一般模型构建一个解析解。因此，过渡到对应于伯努利-欧拉杆的简化方程，并且电磁场被认为是准平稳的。对于带铰链端的杆，使用三角级数展开和拉普拉斯时间变换。问题的解决方案是用影响函数形式的内核以积分形式构造的。核的图像位于变换空间中，傅立叶位于空间坐标中。显式地找到了它们的原始功能。本研究提供了集中荷载计算的示例。

更新日期：2021-03-15

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