The Journal of the Acoustical Society of Korea (한국음향학회지)

The Acoustical Society of Korea (한국음향학회)
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Analysis of Multi-Mode Reflection and Transmission Coefficients of a Lamb Wave Across a Rectangular Notch

사각형 노치에 대한 램파의 다중 모드 반사와 투과 계수 해석

  • Published : 2008.04.30
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Abstract

The purpose of the present work is to derive the reflection and transmission coefficients of $S_0\;and\;A_0$ mode Lamb waves in relation to the geometry of a rectangular notch when the waves propagate across the notch in an elastic plate. Firstly, the excitable modes of the Lamb wave were analyzed with respect to the plate thickness. The scattering phenomena were divided into three independent processes according to the boundary shape of the notch and the direction of the wave propagation. Linear equations for each process were derived with corresponding free or continuous boundary conditions to analyze the scattered waves. By the rule of linear superposition, the waves scattered at each process were summed for each mode. Then the steady-state reflection and transmission coefficients of the scattered waves were determined so that the difference of energy flux between the incident and the scattered waves would remain within 4%.

본 논문의 목적은 탄성판 내에서 진행하는 기본형 램파 모드인 $S_0,\;A_0$ 모드가 사각형 노치에 의해 산란되었을 때, 노치의 2차원 형상에 따른 각 파의 반사계수와 투과계수를 구하는데 있다. 먼저 노치가 있는 부분의 평판의 두께 변화에 따라 노치 부위에 발생 가능한 램파모드의 변화를 고찰하고, 노치 부위의 경계면 형상과 노치 내부에서 진행하는 입사파의 방향에 따라, 노치에 의한 전체 산란 현상을 3가지의 독립된 산란 프로세스로 구분하였다. 그리고 각 프로세스의 경계면에 자유 경계조건과 연속조건을 적용하여 각 프로세스에서 발생된 산란파의 투과 및 반사 계수를 구하였다. 나아가 중첩의 원리를 이용하여 각 프로세스의 산란파를 모드별로 합산하고, 사각형 노치의 폭과 깊이의 변화에 따른 입력파의 에너지 플럭스의 합과 반사 및 투과파의 에너지 플럭스의 합의 차이가 최대 4%에 들도록 하는 정상상태에서의 반사 및 투과계수를 구하고 분석하였다.

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References

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