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Year 2019, Volume: 2 Issue: 2, 28 - 33, 30.11.2019
https://doi.org/10.34088/kojose.491345

Abstract

References

  • Doyle P. F., Pavlovic M. N., 1982. Vibration of Beams on Partial Elastic Foundations. Earthquake Engineering and Structural Dynamics, 10(5), 663-674.
  • Eisenberger M., Yankelevsky D. Z., Adin M. A., 1985. Vibrations of Beams Fully or Partially Supported on Elastic Foundations. Earthquake Engineering and Structural Dynamics, 13(5), 651-660.
  • Laura P. A. A., Cortinez V. H., 1987. Vibrating Beam Partially Embedded in Winkler-Type Foundation. Journal of Engineering Mechanics, 113(1), 143-147.
  • Kukla S., 1991. Free Vibration of a Beam Supported on a Stepped Elastic Foundation. Journal of Sound and Vibration, 149(2), 259-265.
  • Thambiratnam D., Zhuge Y., 1996. Free Vibration Analysis of Beams on Elastic Foundation. Computers & Structures, 60(6), 971-980.
  • Motaghian S. E., Mofida M., Alanjari P., 2011. Exact Solution to Free Vibration of Beams Partially Supported by an Elastic Foundation. Scientia Iranica, 18(4), 861-866.
  • Cazzani A., 2013. On the Dynamics of a Beam Partially Supported by an Elastic Foundation: An Exact Solution Set. International Journal of Structural Stability and Dynamics, doi: 10.1142/S0219455413500454.
  • Coşkun S. B., Mutman U., Çinçin C., 2015. Free Vibration Analysis of A Beam Partially Supported on Elastic Foundation Using Adomian Decomposition Method. 5th International Earthquake Symposium, Kocaeli, Turkey, 10-12 June.
  • Çinçin C., 2018. Analysis of Vibration A Beam Partially Supported on Elastic Foundation Using Adomian Decomposition Method. M. Sc. Thesis, Kocaeli University, Kocaeli.
  • Adomian G., 1994. Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston.
  • Wazwaz A. M., 1998. A Comparison between Adomian Decomposition Method and Taylor Series Method in the Series Solutions. Applied Mathematics and Computation, 97(1), 37-44.
  • Mao Q., Pietrzko S., 2010. Free Vibration Analysis of Stepped Beams by Using Adomian Decomposition Method. Applied Mathematics and Computation, 217(7), 3429-3441.
  • Mao Q., Pietrzko S., 2012. Free Vibration Analysis of a Type of Tapered Beams by Using Adomian Decomposition Method. Applied Mathematics and Computation, 219(6), 3264-3271.
  • Coşkun S. B., Atay M. T., Öztürk B., 2011. Transverse Vibration Analysis of Euler-Bernoulli Beams Using Analytical Approximate Techniques, Advances in Vibration Analysis Research, ed: Ebrahimi F., Intech Press, pp. 1-22, doi: 10.5772/639.
  • Coşkun S. B., Öztürk B., Mutman U., 2014. Adomian Decomposition Method for Vibration of Nonuniform Euler Beams on Elastic Foundation, Proceedings of the 9th International Conference on Structural Dynamics (EURODYN 2014), 1935-1940.

Analysis of Beam Vibrations on Partial Elastic Foundation Using Adomian Decomposition Method

Year 2019, Volume: 2 Issue: 2, 28 - 33, 30.11.2019
https://doi.org/10.34088/kojose.491345

Abstract

In this study, the natural frequencies of beams
partially supported on elastic foundations are

investigated. In the analysis, Euler-Bernoulli beam theory and Winkler
foundation model are used.
Adomian Decomposition
Method (ADM) is used for the free vibration analysis for the beams considered.
Free vibration modes are determined
according to obtained results and first few modes are presented in
tables and figures for beams with
different support conditions.
In the
last chapter, proposed method and
obtained
results are
discussed.

References

  • Doyle P. F., Pavlovic M. N., 1982. Vibration of Beams on Partial Elastic Foundations. Earthquake Engineering and Structural Dynamics, 10(5), 663-674.
  • Eisenberger M., Yankelevsky D. Z., Adin M. A., 1985. Vibrations of Beams Fully or Partially Supported on Elastic Foundations. Earthquake Engineering and Structural Dynamics, 13(5), 651-660.
  • Laura P. A. A., Cortinez V. H., 1987. Vibrating Beam Partially Embedded in Winkler-Type Foundation. Journal of Engineering Mechanics, 113(1), 143-147.
  • Kukla S., 1991. Free Vibration of a Beam Supported on a Stepped Elastic Foundation. Journal of Sound and Vibration, 149(2), 259-265.
  • Thambiratnam D., Zhuge Y., 1996. Free Vibration Analysis of Beams on Elastic Foundation. Computers & Structures, 60(6), 971-980.
  • Motaghian S. E., Mofida M., Alanjari P., 2011. Exact Solution to Free Vibration of Beams Partially Supported by an Elastic Foundation. Scientia Iranica, 18(4), 861-866.
  • Cazzani A., 2013. On the Dynamics of a Beam Partially Supported by an Elastic Foundation: An Exact Solution Set. International Journal of Structural Stability and Dynamics, doi: 10.1142/S0219455413500454.
  • Coşkun S. B., Mutman U., Çinçin C., 2015. Free Vibration Analysis of A Beam Partially Supported on Elastic Foundation Using Adomian Decomposition Method. 5th International Earthquake Symposium, Kocaeli, Turkey, 10-12 June.
  • Çinçin C., 2018. Analysis of Vibration A Beam Partially Supported on Elastic Foundation Using Adomian Decomposition Method. M. Sc. Thesis, Kocaeli University, Kocaeli.
  • Adomian G., 1994. Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston.
  • Wazwaz A. M., 1998. A Comparison between Adomian Decomposition Method and Taylor Series Method in the Series Solutions. Applied Mathematics and Computation, 97(1), 37-44.
  • Mao Q., Pietrzko S., 2010. Free Vibration Analysis of Stepped Beams by Using Adomian Decomposition Method. Applied Mathematics and Computation, 217(7), 3429-3441.
  • Mao Q., Pietrzko S., 2012. Free Vibration Analysis of a Type of Tapered Beams by Using Adomian Decomposition Method. Applied Mathematics and Computation, 219(6), 3264-3271.
  • Coşkun S. B., Atay M. T., Öztürk B., 2011. Transverse Vibration Analysis of Euler-Bernoulli Beams Using Analytical Approximate Techniques, Advances in Vibration Analysis Research, ed: Ebrahimi F., Intech Press, pp. 1-22, doi: 10.5772/639.
  • Coşkun S. B., Öztürk B., Mutman U., 2014. Adomian Decomposition Method for Vibration of Nonuniform Euler Beams on Elastic Foundation, Proceedings of the 9th International Conference on Structural Dynamics (EURODYN 2014), 1935-1940.
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Cebrail Çinçin This is me

Safa Bozkurt Coşkun

Publication Date November 30, 2019
Acceptance Date August 28, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA Çinçin, C., & Coşkun, S. B. (2019). Analysis of Beam Vibrations on Partial Elastic Foundation Using Adomian Decomposition Method. Kocaeli Journal of Science and Engineering, 2(2), 28-33. https://doi.org/10.34088/kojose.491345