On the existence of Rayleigh waves with full impedance boundary condition

Author:

Giang Pham Thi Ha1,Vinh Pham Chi2ORCID

Affiliation:

1. Faculty of Civil Engineering, Hanoi Architectural University, Hanoi, Vietnam

2. Faculty of Mathematics, Mechanics and Informatics, VNU University of Science, Hanoi, Vietnam

Abstract

The existence of Rayleigh waves (propagating in isotropic elastic half-spaces) with the tangential and normal impedance boundary conditions was investigated. It has been shown that for the tangential impedance boundary condition (TIBC), there always exists a unique Rayleigh wave, while for the normal impedance boundary condition (NIBC), there exists a domain (of impedance and material parameters) in which exactly one Rayleigh wave is possible and outside this domain a Rayleigh wave is impossible. In this paper, we consider the existence of Rayleigh waves with the full impedance boundary condition (FIBC) that contains both TIBC and NIBC. It is shown that the existence picture of Rayleigh waves for this general case is more complicated. It contains domain for which exactly one Rayleigh wave exists, domain where a Rayleigh wave is impossible, and domain for which all three possibilities may occur: two Rayleigh waves exist, one Rayleigh wave exists, and no Rayleigh wave exists at all. The obtained existence results recover the existence results established previously for the cases of TIBC and NIBC. The formulas for the Rayleigh wave velocity are derived. As these formulas are totally explicit, they are very useful in various practical applications, especially in the non-destructive evaluation of the mechanical properties of structures. In order to establish the existence results and derive formulas for the Rayleigh wave velocity, the complex function method, which is based on the Cauchy-type integrals, is employed.

Funder

Vietnam National Foundation for Science and Technology Development

Publisher

SAGE Publications

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3