Journal of Korean Association for Spatial Structures (한국공간구조학회논문집)

Korean Association for Spatial Structures (한국공간구조학회)
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Crack Energy and Governing Equation of an Extensible Beam with Multiple Cracks

다중 균열을 갖는 신장 보의 균열 에너지와 지배방정식

  • Shon, Sudeok (Dept. of Architectural Engineering, KoreaTECH)
  • 손수덕 (한국기술교육대학교 건축공학과 )
  • Received : 2024.02.09
  • Accepted : 2024.02.26
  • Published : 2024.03.15
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Abstract

This paper aims to advance our understanding of extensible beams with multiple cracks by presenting a crack energy and motion equation, and mathematically justifying the energy functions of axial and bending deformations caused by cracks. Utilizing an extended form of Hamilton's principle, we derive a normalized governing equation for the motion of the extensible beam, taking into account crack energy. To achieve a closed-form solution of the beam equation, we employ a simple approach that incorporates the crack's patching condition into the eigenvalue problem associated with the linear part of the governing equation. This methodology not only yields a valuable eigenmode function but also significantly enhances our understanding of the dynamics of cracked extensible beams. Furthermore, we derive a governing equation that is an ordinary differential equation concerning time, based on orthogonal eigenmodes. This research lays the foundation for further studies, including experimental validations, applications, and the study of damage estimation and detection in the presence of cracks.

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Acknowledgement

이 논문은 2023년도 정부(교육부)의 재원으로 한국연구재단의 지원을 받아 수행된 기초연구사업임(RS-2023-00248809)

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