This study aims to analyze the natural frequency characteristics of multi-cracked extensible beams. The model and governing equations of the multi-cracked beam were derived using Hamilton's principle while considering crack energy. The eigenmode functions were obtained through eigenvalue analysis by applying the patching conditions of the cracks, and the equations for the discretized cracked beam were formulated and solved. The displacement responses from nonlinear system analysis were used to calculate frequencies via Fast Fourier Transform (FFT), and the frequency characteristics were systematically analyzed with respect to the number of cracks, crack depth, and cross-sectional loss. Additionally, the natural frequencies and orthonormal bases of the linear system were derived by exploring the solutions of the characteristic equation reflecting the cracks. Numerical analyses showed that the natural frequency of a cracked extensible beam was higher than that of a cracked EB beam. However, as the number or depth of cracks increased, the natural frequency gradually decreased. Notably, in extensible beams with large deflections, the dynamic changes caused by cracks demonstrated results that could not be obtained through the EB beam model.

Abstract
1. 서론
2. 다중 크랙 신장 보의 지배방정식
3. 선형 시스템의 고유함수
4. 크랙 신장 보의 주파수 특성
    4.1 Case 1:   
    4.2 Case 2:   
5. 결론
감사의 글
References

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