Acknowledgement
이 논문은 2023년도 정부(교육부)의 재원으로 한국연구재단의 지원을 받아 수행된 기초연구사업임(RS-2023-00248809)
References
- Ostachowicz, W.M. & Krawczuk, M., "Analysis of the effect of cracks on the natural frequencies of a cantilever beam," Journal of Sound and Vibration, Vol.150, No.2, pp.191-201, 1991. https://doi.org/10.1016/0022-460X(91)90615-Q
- Lin, H.P., Chang, S. & Wu, J., "Beam vibrations with an arbitrary number of cracks," Journal of Sound and Vibration, Vol.258, pp.987-999, 2002. https://doi.org/10.1006/jsvi.2002.5184
- Caddemi, S. & Cali'o, I., "Exact closed-form solution for the vibration modes of the Euler-Bernoulli beam with multiple open cracks," Journal of Sound and Vibration, Vol.327, No.3, pp.473-489, 2009. https://doi.org/10.1016/j.jsv.2009.07.008
- Caddemi, S. & Morassi, A., "Multi-cracked Euler-Bernoulli beams: Mathematical modeling and exact solutions," International Journal of Solids and Structures, Vol.50, No.6, pp.944-956, 2013. DOI:https://doi.org/10.1016/j.ijsolstr.2012.11.018
- Gutman, S., Ha, J.H. & Shon, S.D., "Equations of motion for cracked beams and shallow arches," Nonlinear Functional Analysis and Applications, Vol.27, No.2, pp.405-432, 2022. DOI:https://doi.org/10.48550/arXiv.2110.11197
- Gutman, S., Ha, J.H. & Shon, S.D., "Variational setting for cracked beams and shallow arches," Archive of Applied Mechanics, Vol.92, pp.2225-2236, 2022. DOI:https://doi.org/10.1007/s00419-022-02174-6
- Gutman, S., Ha, J.H. & Shon, S.D., "Dynamic behavior of cracked beams ans shallow arches," Journal of the Korean Mathematical Society, Vol. 59, No.5, pp.869-890, 2022. DOI:https://doi.org/10.4134/JKMS.j210650
- Woinowsky-Krieger, S., "The effect of an axial force on the vibration of hinged bars," Journal of applied Mechanics, Vol.17, pp.35-36, 1950. https://doi.org/10.1115/1.4010053
- Ball, J.M., "Initial-boundary value problems for an extensible beam," Journal of Mathematical Analysis and Applications, Vol.42, No.1, pp.61-90, 1973. DOI:https://www.sciencedirect.com/science/article/pii/0022247X73901212?via%3Dihub https://doi.org/10.1016/0022-247X(73)90121-2
- Shon, S.D., Ha, J.H. & Lee, S.J., "Dynamic model and governing equations of a shallow arches with moving boundary", Journal of Korean Association for Spatial Structures, Vol.22, No.2 pp.57~64, 2022. DOI:https://doi.org/10.9712/KASS.2022.22.1.57