Table of Contents Author Guidelines Submit a Manuscript
Shock and Vibration
Volume 2014 (2014), Article ID 159213, 7 pages
http://dx.doi.org/10.1155/2014/159213
Research Article

An Efficient Analytical Method for Vibration Analysis of a Beam on Elastic Foundation with Elastically Restrained Ends

Faculty of Engineering, Department of Civil Engineering, Bilecik Şeyh Edebali University, Gülümbe Kampüsü, 11210 Bilecik, Turkey

Received 27 February 2014; Revised 22 April 2014; Accepted 30 April 2014; Published 14 May 2014

Academic Editor: Toshiaki Natsuki

Copyright © 2014 Mustafa Özgür Yayli et al. 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. K. R. Chun, “Free vibration of a beam with one end spring-hinged and the other free,” Journal of Applied Mechanics, Transactions ASME, vol. 39, no. 4, pp. 1154–1155, 1972. View at Google Scholar · View at Scopus
  2. M. J. Maurizi, R. E. Rossi, and J. A. Reyes, “Vibration frequencies for a uniform beam with one end spring-hinged and subjected to a translational restraint at the other end,” Journal of Sound and Vibration, vol. 48, no. 4, pp. 565–568, 1976. View at Google Scholar · View at Scopus
  3. P. F. Doyle and M. N. Pavlovic, “Vibration of beams on partial elastic foundations,” Earthquake Engineering Structural Dynamics, vol. 10, no. 5, pp. 663–674, 1982. View at Google Scholar · View at Scopus
  4. P. A. A. Laura, P. Verniere de Irassar, and G. M. Ficcadenti, “A note on transverse vibrations of continuous beams subject to an axial force and carrying concentrated masses,” Journal of Sound and Vibration, vol. 86, no. 2, pp. 279–284, 1983. View at Google Scholar · View at Scopus
  5. B. A. H. Abbas, “Vibrations of Timoshenko beams with elastically restrained ends,” Journal of Sound and Vibration, vol. 97, no. 4, pp. 541–548, 1984. View at Google Scholar · View at Scopus
  6. G. V. Rao and N. R. Naidu, “Free vibration and stability behaviour of uniform beams and columns with non-linear elastic end rotational restraints,” Journal of Sound and Vibration, vol. 176, no. 1, pp. 130–135, 1994. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Kacar, H. T. Tan, and M. O. Kaya, “A note free vibration analysis of beams on variable Winkler elastic foundation by using the differential transform method,” Mathematical and Computational Applications, vol. 16, pp. 773–783, 2001. View at Google Scholar
  8. Ö. Civalek, “Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns,” Engineering Structures, vol. 26, no. 2, pp. 171–186, 2004. View at Publisher · View at Google Scholar · View at Scopus
  9. H. K. Kim and M. S. Kim, “Vibration of beams with generally restrained boundary conditions using fourier series,” Journal of Sound and Vibration, vol. 245, no. 5, pp. 771–784, 2001. View at Publisher · View at Google Scholar · View at Scopus
  10. M. Hetenyi, “Beams and plates on elastic foundation,” Applied Mechanics Reviews, vol. 19, pp. 95–102, 1966. View at Google Scholar
  11. C. Miranda and K. Nair, “Finite beams on elastic foundation,” Journal Structural Division, vol. 92, pp. 2131–2142, 1966. View at Google Scholar
  12. D. Z. Yankelevsky and M. Eisenberger, “Analysis of a beam column on elastic foundation,” Computers and Structures, vol. 23, no. 3, pp. 351–356, 1986. View at Google Scholar · View at Scopus
  13. M. Eisenberger and J. Clastornik, “Vibrations and buckling of a beam on a variable winkler elastic foundation,” Journal of Sound and Vibration, vol. 115, no. 2, pp. 233–241, 1987. View at Google Scholar · View at Scopus
  14. M. A. De Rosa, “Stability and dynamics of beams on Winkler elastic foundations,” Earthquake Engineering & Structural Dynamics, vol. 18, no. 3, pp. 377–388, 1989. View at Google Scholar · View at Scopus
  15. J. Wang, “Vibration of stepped beams on elastic foundations,” Journal of Sound and Vibration, vol. 149, no. 2, pp. 315–322, 1991. View at Google Scholar · View at Scopus
  16. Y. C. Lai, B. Y. Ting, W.-S. Lee, and B. R. Becker, “Dynamic response of beams on elastic foundation,” Journal of Structural Engineering ACSE, vol. 118, no. 3, pp. 853–858, 1992. View at Google Scholar · View at Scopus
  17. D. Zhou, “A general solution to vibrations of beams on variable winkler elastic foundation,” Computers and Structures, vol. 47, no. 1, pp. 83–90, 1993. View at Google Scholar · View at Scopus
  18. D. Thambiratnam and Y. Zhuge, “Free vibration analysis of beams on elastic foundation,” Composite Structure, vol. 60, pp. 971–980, 1996. View at Google Scholar
  19. D. N. Paliwal and R. K. Pandey, “The free vibration of a cylindrical shell on an elastic foundation,” Journal of Vibration and Acoustics, Transactions of the ASME, vol. 120, no. 1, pp. 63–71, 1998. View at Google Scholar · View at Scopus
  20. P. Gülkan and B. N. Alemdar, “Exact finite element for a beam on a two-parameter elastic foundation: a revisit,” Structural Engineering and Mechanics, vol. 7, no. 3, pp. 259–276, 1999. View at Google Scholar · View at Scopus
  21. K. Al-Hosani, S. Fadhil, and A. El-Zafrany, “Fundamental solution and boundary element analysis of thick plates on Winkler foundation,” Computers and Structures, vol. 70, no. 3, pp. 325–336, 1999. View at Google Scholar · View at Scopus
  22. J.-H. Yin, “Closed-form solution for reinforced Timoshenko beam on elastic foundation,” Journal of Engineering Mechanics, vol. 126, no. 8, pp. 868–874, 2000. View at Publisher · View at Google Scholar · View at Scopus
  23. J.-H. Yin, “Comparative modeling study of reinforced beam on elastic foundation,” Journal of Geotechnical and Geoenvironmental Engineering, vol. 126, no. 3, pp. 265–271, 2000. View at Publisher · View at Google Scholar · View at Scopus
  24. D. M. Santee and P. B. Gonçalves, “Oscillations of a beam on a non-linear elastic foundation under periodic loads,” Shock and Vibration, vol. 13, no. 4-5, pp. 273–284, 2006. View at Google Scholar · View at Scopus
  25. P. A. A. Laura and R. H. Gutierrez, “Analysis of vibrating Timoshenko beams using the method of differential quadrature,” Shock and Vibration, vol. 1, pp. 89–93, 1993. View at Google Scholar
  26. A. Kacar, H. T. Tan, and M. O. Kaya, “Free vibration analysis of beams on variable winkler elastic foundation by using the differential transform method,” Mathematical Computational Applications, vol. 16, pp. 773–783, 2011. View at Google Scholar
  27. 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