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램파의 분산성과 파 반사가 시간반전과정에 미치는 영향의 이해

Understanding the Effects of the Dispersion and Reflection of Lamb Waves ona Time Reversal Process

김승범|손훈|박현우
한국전산구조공학회 (The Computational Structural Engineering Institute Of Korea)|2009.02|한국전산구조공학회논문집 (Journal of the Computational Structural Engineering Institute of Korea)|제22권 제1호|pp. 89-103

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참고문헌

키워드

파 반사wave reflectionstructural health monitoring능동탐지램파시간반전과정시간반전성내부모드분산다중모드분산구조물건전성감시Lamb wavetime reversal processtime reversibilitywithin-mode dispersionmultimode dispersionactive sensing

초록

이 연구에서는 얇은 판형구조물의 손상탐지에 널리 사용되어오는 램파에 시간반전(time reversal)개념의 적용성을 이론적으로 규명한다. 고전적 시간반전 음향학에 의하면, 센서에서의 출력신호를 시간영역에서 반전 후 재입사시켜 원래의 가진점으로 돌려보내면, 그 가진점에서 원래 입력신호가 복원된다. 그러나 램파에 시간반전과정을 적용하게 되면 램파 고유의 분산성과 판 경계에서의 파 반사로 인해 시간반전성이 복잡한 양상을 띠게 된다. 이러한 램파의 시간반전성을 보다 잘 이해하기 위해 이 연구에서는 램파의 시간반전과정을 이론적으로 규명한다. 특히, 램파의 내부모드분산, 다중모드분산, 그리고 판 경계면에서의 램파의 반사가 시간반전성에 미치는 영향을 정식화하였다. 간단한 수치예제를 통해 이 연구에서 제시된 이론적 발견들의 타당성을 검증한다.

Abstract

This study investigates the applicability of the time reversal concept in modern acoustics to the Lamb waves, which have been widely studied for defect detection in plate-like structures. According to conventional time reversal acoustics, an input signal can be reconstructed at an excitation point if an output signal recorded at another point is reversed in the time domain and emitted back to the original source point. However, the application of a time reversal process(TRP) to Lamb wave propagations is complicated due to velocity and amplitude dispersion characteristics of Lamb waves and reflections from the boundaries of a structure. In this study, theoretical investigations are presented to better understand the time reversibility of Lamb waves. In particular, the effects of within-mode dispersion, multimode dispersion, amplitude dispersion, and reflections from boundaries on the TRP are theoretically formulated. Simple numerical case studies are conducted to validate the theoretical findings of this study.

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