Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 721294, 9 pages
http://dx.doi.org/10.1155/2013/721294
Research Article

Free Vibration Analysis of an Euler Beam of Variable Width on the Winkler Foundation Using Homotopy Perturbation Method

Department of Civil Engineering, Kocaeli University, 41380 Kocaeli, Turkey

Received 24 February 2013; Accepted 30 March 2013

Academic Editor: Safa Bozkurt Coşkun

Copyright © 2013 Utkan Mutman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Balkaya, M. O. Kaya, and A. Saǧlamer, “Analysis of the vibration of an elastic beam supported on elastic soil using the differential transform method,” Archive of Applied Mechanics, vol. 79, no. 2, pp. 135–146, 2009. View at Publisher · View at Google Scholar · View at Scopus
  2. B. Ozturk and S. B. Coskun, “The Homotopy Perturbation Method for free vibration analysis of beam on elastic foundation,” Structural Engineering and Mechanics, vol. 37, no. 4, pp. 415–425, 2011. View at Google Scholar · View at Scopus
  3. I. E. Avramidis and K. Morfidis, “Bending of beams on three-parameter elastic foundation,” International Journal of Solids and Structures, vol. 43, no. 2, pp. 357–375, 2006. View at Publisher · View at Google Scholar · View at Scopus
  4. M. A. De Rosa, “Free vibrations of Timoshenko beams on two-parameter elastic foundation,” Computers and Structures, vol. 57, no. 1, pp. 151–156, 1995. View at Google Scholar · View at Scopus
  5. H. Matsunaga, “VIbration and buckling of deep beam-columns on two-parameter elastic foundations,” Journal of Sound and Vibration, vol. 228, no. 2, pp. 359–376, 1999. View at Google Scholar · View at Scopus
  6. M. El-Mously, “Fundamental frequencies of Timoshenko beams mounted on Pasternak foundation,” Journal of Sound and Vibration, vol. 228, no. 2, pp. 452–457, 1999. View at Google Scholar · View at Scopus
  7. C. N. Chen, “Vibration of prismatic beam on an elastic foundation by the differential quadrature element method,” Computers and Structures, vol. 77, no. 1, pp. 1–9, 2000. View at Publisher · View at Google Scholar · View at Scopus
  8. C. N. Chen, “DQEM vibration analyses of non-prismatic shear deformable beams resting on elastic foundations,” Journal of Sound and Vibration, vol. 255, no. 5, pp. 989–999, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. I. Coşkun, “The response of a finite beam on a tensionless Pasternak foundation subjected to a harmonic load,” European Journal of Mechanics, A/Solids, vol. 22, no. 1, pp. 151–161, 2003. View at Publisher · View at Google Scholar · View at Scopus
  10. W. Q. Chen, C. F. Lü, and Z. G. Bian, “A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation,” Applied Mathematical Modelling, vol. 28, no. 10, pp. 877–890, 2004. View at Publisher · View at Google Scholar · View at Scopus
  11. P. Maheshwari, S. Chandra, and P. K. Basudhar, “Response of beams on a tensionless extensible geosynthetic-reinforced earth bed subjected to moving loads,” Computers and Geotechnics, vol. 31, no. 7, pp. 537–548, 2004. View at Publisher · View at Google Scholar · View at Scopus
  12. N. M. Auciello and M. A. De Rosa, “Two approaches to the dynamic analysis of foundation beams subjected to subtangential forces,” Computers and Structures, vol. 82, no. 6, pp. 519–524, 2004. View at Publisher · View at Google Scholar · View at Scopus
  13. J. H. He, “Coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. J. H. He, “The homotopy perturbation method for nonlinear oscillators with discontinuities,” Applied Mathematics and Computation, vol. 151, no. 1, pp. 287–292, 2004. View at Publisher · View at Google Scholar · View at Scopus
  15. J. H. He, “Application of homotopy perturbation method to nonlinear wave equations,” Chaos, Solitons & Fractals, vol. 26, no. 3, pp. 695–700, 2005. View at Publisher · View at Google Scholar · View at Scopus
  16. J. H. He, “Asymptotology by homotopy perturbation method,” Applied Mathematics and Computation, vol. 156, no. 3, pp. 591–596, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. J. H. He, “Homotopy perturbation method for solving boundary value problems,” Physics Letters A, vol. 350, no. 1-2, pp. 87–88, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. J. H. He, “Limit cycle and bifurcation of nonlinear problems,” Chaos, Solitons & Fractals, vol. 26, no. 3, pp. 827–833, 2005. View at Publisher · View at Google Scholar · View at Scopus