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.

1. 서론
2. 균열의 에너지 모델
3. 운동 방정식과 균열의 경계조건
4. 고유치와 고유함수
5. 균열을 갖는 신장 보의 지배방정식
6. 결론
References

• 손수덕(한국기술교육대학교 건축공학과 연구교수, 공학박사) | Shon, Sudeok (Dept. of Architectural Engineering, KoreaTECH)