Journal of the Computational Structural Engineering Institute of Korea (한국전산구조공학회논문집)

Computational Structural Engineering Institute of Korea (한국전산구조공학회)
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Consistent Boundary Condition for Horizontally-Polarized Shear (SH) Waves Propagated in Layered Waveguides

층상 waveguide에서의 SH파 전파 해석을 위한 경계조건

  • Lee, Jin Ho (Department of Ocean Engineering, Pukyong National University)
  • 이진호 (부경대학교 해양공학과)
  • Received : 2021.01.07
  • Accepted : 2021.01.20
  • Published : 2021.04.30
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Abstract

The wave-propagation phenomenon in an infinite medium has been used to describe the physics in many fields of engineering and natural science. Analytical or numerical methods have been developed to obtain solutions to problems related to the wave-propagation phenomenon. Energy radiation into infinite regions must be accurately considered for accurate solutions to these problems; hence, various numerical and mechanical models as well as boundary conditions have been developed. This paper proposes a new boundary condition that can be applied to scalar-wave or horizontally-polarized shear-wave (or SH-wave) propagation problems in layered waveguides. A governing equation is obtained for the SH waves by applying finite-element discretization in the vertical direction of the waveguide and subsequently modified to derive the boundary condition for the infinite region of the waveguide. Using the orthogonality of the eigenmodes for the SH waves in a layered waveguide, the new boundary condition is shown to be equivalent to the existing root-finding absorbing boundary condition; further, the accuracy is shown to increase with the degree of the new boundary condition, and its stability can be proven. The accuracy and stability are then demonstrated by applying the proposed boundary condition to wave-propagation problems in layered waveguides.

무한 매질에서의 파전파 현상은 공학과 자연과학의 여러 분야에서 다양한 물리적 현상을 서술하는데 활용되고 있고, 이 문제에 대한 해를 얻기 위하여 해석적 방법 또는 수치적 방법이 개발되어 사용되고 있다. 이 문제에 대한 정확한 해를 얻기 위해서는 무한 영역으로의 에너지 방사를 정확히 고려해야 하고, 이를 위해 다양한 수치적 또는 역학적 모형 또는 경계조건이 개발되었다. 이 연구에서는 층상 waveguide에서의 scalar wave 또는 SH파 전파 문제에 적용할 수 있는 새로운 경계조건을 제안하고자 한다. 이를 위해 waveguide의 수직방향으로 유한요소 이산화를 적용하여 얻은 SH파의 지배방정식을 변형하여 waveguide의 무한 영역의 영향을 나타내는 경계조건을 유도한다. 층상 waveguide에서의 SH파에 대한 고유모드의 직교성을 이용하여, 새로운 경계조건은 기존의 root-finding absorbing boundary condition와 동등함을 보이고, 이로부터 새로운 경계조건의 차수가 증가할수록 정확성이 증가하고, 또한 이산화된 수준에서도 안정함을 유도할 수 있다. 제안된 경계조건을 층상 waveguide에서의 파전파 문제에 적용하여 그 정확성과 안정성을 검증한다.

Keywords

Acknowledgement

본 연구는 산업통상자원부(MOTIE)와 한국에너지기술평가원(KETEP)의 지원을 받아 수행한 연구 과제입니다(No. 20201510100020).

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