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Smart Structures and Systems Volume 29, Number 2, February 2022 , pages 279-286 DOI: https://doi.org/10.12989/sss.2022.29.2.279 |
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Theoretical formulations of current and unique Rayleigh waves with impedance boundary condition embedding normal stress |
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Xuan Quynh Nguyen and Dongkyu Lee
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| Abstract | ||
| In this article, a novel propagation formulation of Rayleigh waves in a compressible isotropic half-space with impedance boundary condition is proposed by embedding the normal stress. In a two-dimensional case, it is assumed that a design boundary is free of normal traction and a shear traction depends on linearly a normal component of displacements multiplied by frequencies. Therefore, impedance boundary conditions affect the normal stress, where the impedance parameters correspond to dimensions of stresses over velocity. On the other hand, vanished impedance values are traction-free boundary conditions. The main purpose of this article is to present theoretically the existence and uniqueness of a Rayleigh wave formulation relying on secular equation's mathematical analyses. Its velocity varies along with the impedance parameters. Moreover, numerical experiments with different values for the velocity of Rayleigh waves are carried out. The present Rayleigh waves study is a fundamental step in analyzing the cause and effect of physical states such as building or structure damages resulting from natural dynamics. The results of the study generate a basic design formulation theory to test the effects of Rayleigh waves affecting structures when an earthquake occurs. The presence and uniqueness of the proposed formulation is verified by mutual comparisons of several numerical examples. | ||
| Key Words | ||
| existence and uniqueness; impedance boundary condition; normal stress; Rayleigh waves; velocity waves elastic | ||
| Address | ||
| Department of Architectural Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul 05006, Republic of Korea. | ||