Abstract
References
- J.P. Den Hartog, Advanced Strength of Materials, Dover Publications Inc., New York, pp. 286–290, 1952.
- S.P. Timoshenko D.H. Young and W. Weaver, Vibration Problems in Engineering, John Wiley, New York, 1974.
- R.D. Blevins, Formulas for Natural Frequency and Mode Shape, New York, 1979.
- S.K. Jang and C.W. Bert, “Free Vibration of Stepped Beams: Exact and Numerical Solutions”, Journal of Sound and Vibration, vol. 130, pp. 342-346, 1989.
- Y.C. Lai, B.Y. Ting, W.S. Lee and W.R. Becker, “Dynamic Response of Beams on Elastic Foundations”, J. Struct. Engng. ASCE, vol. 118, pp. 853-858, 1992.
- J. Wang, “Vibration of Stepped Beams on Elastic Foundations”, Journal of Sound and Vibration, vol. 149, no. 2, pp. 315-322, 1991.
- S. Kukla, “Free vibration of a beam supported on a stepped elastic foundation”, Journal of Sound and Vibration, vol. 149, no. 2, pp. 259-265, 1991.
- P.M. Belles, M.J. Maurizi, and D.H. Di Luca, “Vibration of stepped beams on non-uniform elastic foundations”, Journal of Sound and Vibration, vol. 169, no. 1, pp. 127-128, 1994.
- D. Thambiratnam and Y.Zhuge, “Free vibration analysis of beams on elastic foundation”, Computers and Structures, vol. 60, pp. 971-980, 1996.
- O.F. Durgun, “Elastik Zemin Uzerindeki Kademeli Kirişin Homotopi Pertürbasyon Yönetimi ile Serbest Titreşim Analizi”, M.Sc.Thesis, in Turkish, 2015.
- G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Springer, Netherlands, 1994.
- CSI, SAP 2000, Ver. 21.02, integrated software for structural analysis and design. Computers and Structures Inc., Berkeley, CA, USA, 2019.
Semi-Analytical and Finite Element Investigations of the Vibration of a Stepped Beam on an Elastic Foundation
Abstract
In this study free vibration behavior of a stepped beam on an elastic foundation is considered. The vibration of uniform beams on an elastic foundation has been previously studied extensively and various solutions are available in the literature. However, the problem considered in current study appears not to have been widely covered in the literature and analytical solutions are strictly limited. To this aim, semi-analytical solutions are obtained first by using Adomian decomposition method, then finite element solutions are computed via structural finite element analysis software (SAP 2000). The free vibration analysis of stepped beam considering the combinations of different support conditions at each end are performed employing semi-analytical and finite element methods. The findings of the analysis are compared and discussed in detail.
References
- J.P. Den Hartog, Advanced Strength of Materials, Dover Publications Inc., New York, pp. 286–290, 1952.
- S.P. Timoshenko D.H. Young and W. Weaver, Vibration Problems in Engineering, John Wiley, New York, 1974.
- R.D. Blevins, Formulas for Natural Frequency and Mode Shape, New York, 1979.
- S.K. Jang and C.W. Bert, “Free Vibration of Stepped Beams: Exact and Numerical Solutions”, Journal of Sound and Vibration, vol. 130, pp. 342-346, 1989.
- Y.C. Lai, B.Y. Ting, W.S. Lee and W.R. Becker, “Dynamic Response of Beams on Elastic Foundations”, J. Struct. Engng. ASCE, vol. 118, pp. 853-858, 1992.
- J. Wang, “Vibration of Stepped Beams on Elastic Foundations”, Journal of Sound and Vibration, vol. 149, no. 2, pp. 315-322, 1991.
- S. Kukla, “Free vibration of a beam supported on a stepped elastic foundation”, Journal of Sound and Vibration, vol. 149, no. 2, pp. 259-265, 1991.
- P.M. Belles, M.J. Maurizi, and D.H. Di Luca, “Vibration of stepped beams on non-uniform elastic foundations”, Journal of Sound and Vibration, vol. 169, no. 1, pp. 127-128, 1994.
- D. Thambiratnam and Y.Zhuge, “Free vibration analysis of beams on elastic foundation”, Computers and Structures, vol. 60, pp. 971-980, 1996.
- O.F. Durgun, “Elastik Zemin Uzerindeki Kademeli Kirişin Homotopi Pertürbasyon Yönetimi ile Serbest Titreşim Analizi”, M.Sc.Thesis, in Turkish, 2015.
- G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Springer, Netherlands, 1994.
- CSI, SAP 2000, Ver. 21.02, integrated software for structural analysis and design. Computers and Structures Inc., Berkeley, CA, USA, 2019.
Details
| Primary Language | English |
|---|---|
| Subjects | Civil Engineering |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | December 1, 2020 |
| Submission Date | March 23, 2020 |
| Acceptance Date | October 7, 2020 |
| Published in Issue | Year 2020 Volume: 24 Issue: 6 |
Cite
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.