Structural Engineering and Mechanics

  • 제24권1호
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  • Pages.51-62
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  • 2006
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Analysis of free vibration of beam on elastic soil using differential transform method

  • Catal, Seval (Dokuz Eylul University, Department of Civil Engineering (Applied Mathematics), Faculty of Engineering)
  • 투고 : 2005.11.11
  • 심사 : 2006.04.28
  • 발행 : 2006.09.10
⟨ 이전 논문 다음 논문 ⟩

초록

Differential transform method (DTM) for free vibration analysis of both ends simply supported beam resting on elastic foundation is suggested. The fourth order partial differential equation for free vibration of the beam resting on elastic foundation subjected to bending moment, shear and axial compressive load is obtained by using Winkler hypothesis and small displacement theory. It is assumed that the material is linear-elastic, and that axial load and modulus of subgrade reaction to be constant. In the analysis, shear and axial load effects are considered. The frequency factors of the beam are calculated by using DTM due to the values of relative stiffness; the results are presented in graphs and tables.

키워드

참고문헌

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피인용 문헌

  1. DTM and DQEM for free vibration of axially loaded and semi-rigid-connected Reddy-Bickford beam vol.27, pp.5, 2011, https://doi.org/10.1002/cnm.1313
  2. Solution of free vibration equation of elastically supported Timoshenko columns with a tip mass by differential transform method vol.42, pp.10, 2011, https://doi.org/10.1016/j.advengsoft.2011.06.002
  3. Free vibration analysis of a system of elastically interconnected rotating tapered Timoshenko beams using differential transform method vol.107, 2016, https://doi.org/10.1016/j.ijmecsci.2015.12.027
  4. Flexural–torsional-coupled vibration analysis of axially loaded closed-section composite Timoshenko beam by using DTM vol.306, pp.3-5, 2007, https://doi.org/10.1016/j.jsv.2007.05.049
  5. Free transverse vibrations of an elastically connected simply supported twin pipe system vol.34, pp.5, 2010, https://doi.org/10.12989/sem.2010.34.5.549
  6. Vibration analysis of a rotating tapered Timoshenko beam using DTM vol.45, pp.1, 2010, https://doi.org/10.1007/s11012-009-9221-3
  7. Symmetrically loaded beam on a two-parameter tensionless foundation vol.27, pp.5, 2007, https://doi.org/10.12989/sem.2007.27.5.555
  8. Dynamic stiffness approach and differential transformation for free vibration analysis of a moving Reddy-Bickford beam vol.58, pp.5, 2016, https://doi.org/10.12989/sem.2016.58.5.847
  9. Buckling analysis of semi-rigid connected and partially embedded pile in elastic soil using differential transform method vol.52, pp.5, 2014, https://doi.org/10.12989/sem.2014.52.5.971
  10. Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method vol.31, pp.4, 2009, https://doi.org/10.12989/sem.2009.31.4.453
  11. Free vibrations of a multi-span Timoshenko beam carrying multiple spring-mass systems vol.33, pp.4, 2008, https://doi.org/10.1007/s12046-008-0026-1
  12. Differential transform method and numerical assembly technique for free vibration analysis of the axial-loaded Timoshenko multiple-step beam carrying a number of intermediate lumped masses and rotary inertias vol.53, pp.3, 2015, https://doi.org/10.12989/sem.2015.53.3.537
  13. Solution of free vibration equations of semi-rigid connected Reddy–Bickford beams resting on elastic soil using the differential transform method vol.81, pp.2, 2011, https://doi.org/10.1007/s00419-010-0405-z
  14. Differential transform method for free vibration analysis of a moving beam vol.35, pp.5, 2010, https://doi.org/10.12989/sem.2010.35.5.645
  15. Response of forced Euler-Bernoulli beams using differential transform method vol.42, pp.1, 2006, https://doi.org/10.12989/sem.2012.42.1.095
  16. Differential transform method and Adomian decomposition method for free vibration analysis of fluid conveying Timoshenko pipeline vol.62, pp.1, 2006, https://doi.org/10.12989/sem.2017.62.1.065