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Homogenization of very rough interfaces for the micropolar elasticity theory

机译：微极性弹性理论中非常粗糙界面的均质化

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摘要

In this paper, the homogenization of a very rough two-dimensional interface separating two dissimilar isotropic micropolar elastic solids is investigated. The interface is assumed to oscillate between two parallel straight lines. The main aim is to derive homogenized equations in explicit form. These equations are obtained by the homogenization method along with the matrix formalism of the theory of micropolar elasticity. Since obtained homogenized equations are totally explicit, they are a powerful tool for solving various practical problems. As an example, the reflection and transmission of a longitudinal displacement plane wave at a very rough interface of tooth-comb type is investigated. The closed-form formulas for the reflection and transmission coefficients have been derived. Based on these formulas, some numerical examples are carried out to show the dependence of the reflection and transmission coefficients on the incident angle and the geometry parameter of the interface.
机译：在本文中，研究了分离两个不同的各向同性微极性弹性固体的非常粗糙的二维界面的均质化。假定界面在两条平行的直线之间振荡。主要目的是以显式形式导出均化方程。这些方程式是通过均质化方法以及微极弹性理论的矩阵形式来获得的。由于获得的均化方程是完全明确的，因此它们是解决各种实际问题的有力工具。例如，研究了在齿梳型的非常粗糙的界面处纵向位移平面波的反射和透射。推导了反射系数和透射系数的封闭式公式。基于这些公式，通过一些数值例子说明了反射系数和透射系数对入射角和界面几何参数的依赖性。

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  • 来源
    《Applied Mathematical Modelling》 |2018年第2期|467-482|共16页
  • 作者

    P.C.Vinh; V.T.N. Anh; D.X. Tung; N.T. Kieu;

  • 作者单位

    Faculty of Mathematics, Mechanics and Informatics, Hanoi University of Science, 334, Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam;

    Faculty of Mathematics, Mechanics and Informatics, Hanoi University of Science, 334, Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam;

    Faculty of Civil Engineering. Hanoi Architectural University, Km 10 Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam;

    Faculty of Civil Engineering. Hanoi Architectural University, Km 10 Nguyen Trai Street, Thanh Xuan, Hanoi, Vietnam;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Homogenized equations; Very rough interfaces; Theory of micropolar elasticity; Reflection and transmission of waves;

    机译：均质方程非常粗糙的界面;微极性弹性理论;波的反射和透射;

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