A Mathematical Model of the Extensible beam with Multiple Cracks

다중 크랙을 갖는 신장 보의 수리 모델링

  • Shon, Sudeok (Department of Architectural Engineering, Korea University of Technology and Education) ;
  • Ha, Junhong (School of Liberal Arts, Korea University of Technology and Education)
  • 손수덕 (한국기술교육대학교 건축공학과) ;
  • 하준홍 (한국기술교육대학교 교양학부)
  • Published : 2023.06.15

Abstract

Keywords

Acknowledgement

이 원고는 2020년도 정부(교육부)의 재원으로 한국연구재단의 지원을 받아 수행된 기초연구사업임(NRF-2020R1I1A1A01065032)

References

  1. S. Woinowsky-Krieger, "The effect of an axial force on the vibration of hinged bars, Journal of applied Mechanics", Vol.17, pp.35-36, 1950, doi: 10.1115/1.4010053
  2. J.M. Ball., "Initial-boundary value problems for an extensible beam", Journal of Mathematical Analysis and Applications, Vol.42, No.1, pp.61-90, 1973. https://doi.org/10.1016/0022-247X(73)90121-2
  3. Emmrich, Etienne, and Mechthild Thalhammer. "A class of integro-differential equations incorporating nonlinear and nonlocal damping with applications in nonlinear elastodynamics: Existence via time discretization." Nonlinearity 24.9, 2011, doi: 10.1088/0951-7715/24/9/008
  4. 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: 10.1016/j.ijsolstr.2012.11.018
  5. W.M. Ostachowicz & M. Krawczuk., "Analysis of the effect of cracks on the natural frequencies of a cantilever beam", Journal of Sound and Vibration, Vol.150(2), pp.191-201
  6. Ostachowicz, W. M., & Krawczuk, M., "Analysis of the effect of cracks on the natural frequencies of a cantilever beam", Journal of sound and vibration, 150(2), 191-201, 1991, doi: 10.1016/0022-460X(91)90615-Q
  7. Gutman, S., Ha, J., & Shon, S., "Variational setting for cracked beams and shallow arches", Archive of Applied Mechanics, Vol.92, No.7, pp.2225-2236, 2022, doi: 10.1007/s00419-022-02174-6
  8. S. Gutman, J. Ha, S. Shon, "Dynamic behavior of cracked beams ans shallow arches", Journal of the Korean Mathematical Society, Vol.59, No.5, pp.869-890, 2022, doi: 10.4134/JKMS.j210650
  9. Caddemi, S., & Calio, 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.3-5, pp.473-489, doi: 10.1016/j.jsv.2009.07.008
  10. Lin, H. P., Chang, S. C., & Wu, J. D., "Beam vibrations with an arbitrary number of cracks. Journal of Sound Vibration", Vol.258, No.5, pp.987-999, 2002, doi: 10.1006/jsvi.2002.5184