Surface Waves in a Microstructural Couple Stress Half Space under the Extended Mindlin’s Restrained Boundary Conditions

IF 0.6 4区 工程技术 Q4 MECHANICS
Mandeep Kaur, Satish Kumar, Vikas Sharma
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Abstract

Boundary conditions play a crucial role from theoretical and experimental perspectives in comprehending the dynamics of wave propagation in elastic solids. Stress free boundary conditions, are achieved by setting the surface tractions to zero, while for rigid surface boundary conditions displacements, are equated to zero. Despite utility of these two types of boundary conditions, it is crucial to acknowledge that these conditions are the extreme idealizations, and real-world scenarios often fall somewhere between the extremes of stress free and rigid surface boundary conditions. In the current investigation, the elastically restrained boundary conditions (ERBC) are proposed to examine the propagation of plane waves at the surface of semi-infinite elastic media. The elastically restrained boundary conditions act as an intermediate link between traction-free and rigid surface conditions. In the study, a microstructural couple stress half-space is considered to comprehend the propagation of surface waves. The impacts of boundary conditions are depicted through three parameters called as normal stiffness \(\left( {{{k}_{n}}} \right)\), shear stiffness \(\left( {{{k}_{t}}} \right)\), and rotational stiffness \(\left( {{{k}_{r}}} \right)\). The characteristic length scale parameter (l) within the couple stress model represents the influence of microstructural effects. Dispersion relations have been derived analytically and the classical cases of stress-free (Rayleigh type wave), rigid surface boundary conditions are obtained as the special cases. Mathematical results have been illustrated graphically.

Abstract Image

Abstract Image

扩展明德林约束边界条件下微结构耦合应力半空间中的表面波
摘要 从理论和实验的角度来看,边界条件在理解弹性固体中波传播动力学方面起着至关重要的作用。无应力边界条件是通过将表面牵引力设为零来实现的,而对于刚性表面边界条件,位移等于零。尽管这两种边界条件都很有用,但必须承认的是,这些条件都是极端理想化的,而现实世界中的情况往往介于无应力边界条件和刚性表面边界条件这两个极端之间。在当前的研究中,提出了弹性约束边界条件(ERBC)来研究平面波在半无限弹性介质表面的传播。弹性约束边界条件是无牵引和刚性表面条件之间的中间环节。在研究中,考虑了微结构耦合应力半空间来理解表面波的传播。边界条件的影响通过三个参数来描述,分别是法向刚度(left( {{{k}_{n}}} \right)\)、剪切刚度(left( {{{k}_{t}}} \right)\)和旋转刚度(left( {{{k}_{r}}} \right)\)。耦合应力模型中的特征长度尺度参数(l)表示微结构效应的影响。通过分析得出了扩散关系,并将无应力(瑞利波)、刚性表面边界条件等经典情况作为特例。数学结果已用图形说明。
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来源期刊
Mechanics of Solids
Mechanics of Solids 医学-力学
CiteScore
1.20
自引率
42.90%
发文量
112
审稿时长
6-12 weeks
期刊介绍: Mechanics of Solids publishes articles in the general areas of dynamics of particles and rigid bodies and the mechanics of deformable solids. The journal has a goal of being a comprehensive record of up-to-the-minute research results. The journal coverage is vibration of discrete and continuous systems; stability and optimization of mechanical systems; automatic control theory; dynamics of multiple body systems; elasticity, viscoelasticity and plasticity; mechanics of composite materials; theory of structures and structural stability; wave propagation and impact of solids; fracture mechanics; micromechanics of solids; mechanics of granular and geological materials; structure-fluid interaction; mechanical behavior of materials; gyroscopes and navigation systems; and nanomechanics. Most of the articles in the journal are theoretical and analytical. They present a blend of basic mechanics theory with analysis of contemporary technological problems.
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