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Free vibration analysis of tapered beam-column with pinned ends embedded in Winkler-Pasternak elastic foundation

  • Civalek, Omer (Akdeniz University, Civil Engineering Department) ;
  • Ozturk, Baki (Nigde University, Civil Engineering Department)
  • Received : 2009.10.03
  • Accepted : 2010.01.15
  • Published : 2010.03.25

Abstract

The current study presents a mathematical model and numerical method for free vibration of tapered piles embedded in two-parameter elastic foundations. The method of Discrete Singular Convolution (DSC) is used for numerical simulation. Bernoulli-Euler beam theory is considered. Various numerical applications demonstrate the validity and applicability of the proposed method for free vibration analysis. The results prove that the proposed method is quite easy to implement, accurate and highly efficient for free vibration analysis of tapered beam-columns embedded in Winkler- Pasternak elastic foundations.

References

  1. Civalek, O. (2006), "An efficient method for free vibration analysis of rotating truncated conical shells", Int. J. Press. Vess. Piping, 83, 1-12. https://doi.org/10.1016/j.ijpvp.2005.10.005
  2. Civalek, O. (2006a), "Free vibration analysis of composite conical shells using the discrete singular convolution algorithm", Steel Compos. Struct., 6(4), 353-366. https://doi.org/10.12989/scs.2006.6.4.353
  3. Civalek, O. (2007), "Numerical analysis of free vibrations of laminated composite conical and cylindrical shells: discrete singular convolution (DSC) approach", J. Comput. Appl. Math., 205, 251-271. https://doi.org/10.1016/j.cam.2006.05.001
  4. Civalek, O. (2007a), "Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method", Int. J. Mech. Sci., 49, 752-765. https://doi.org/10.1016/j.ijmecsci.2006.10.002
  5. Civalek O. (2007b), "Frequency analysis of isotropic conical shells by discrete singular convolution (DSC)", Struct. Eng. Mech., 25(1), 127-131. https://doi.org/10.12989/sem.2007.25.1.127
  6. De Rosa, M.A. and Maurizi, M.J. (1999), "Dynamic analysis of multistep piles on Pasternak soil subjected to axial tip forces", J. Sound Vib., 219, 771-783. https://doi.org/10.1006/jsvi.1998.1826
  7. Doyle, P.F. and Pavlovic, M.N. (1982), "Vibration of beams on partial elastic foundations", Earthq. Eng. Struct. Dyn., 10, 663-674. https://doi.org/10.1002/eqe.4290100504
  8. Eisenberger, M. (1995), "Dynamics stiffness matrix for variable cross-section Timoshenko beams", Commun. Numer. Meth. En., 11, 507-513. https://doi.org/10.1002/cnm.1640110605
  9. Halabe, U.B. and Jain, S.K. (1996), "Lateral free vibration of a single pile with or without an axial load", J. Sound Vib., 195, 531-544. https://doi.org/10.1006/jsvi.1996.0443
  10. Kameswara Rao, N.S.V. and Das, Y.C. (1975), "Anandakrishnan M, Dynamic response of beams on generalized elastic foundation", Int. J. Solids Struct., 11, 255-273. https://doi.org/10.1016/0020-7683(75)90067-0
  11. Lee, J. and Schultz, W.W. (2004), "Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral method", J. Sound Vib., 269, 609-621. https://doi.org/10.1016/S0022-460X(03)00047-6
  12. Matsunaga, H. (1999), "Vibration and buckling of deep beam-columns on two parameter elastic foundations", J. Sound Vib., 228(2), 359-376. https://doi.org/10.1006/jsvi.1999.2415
  13. Simsek, M. (2009), "Static analysis of a functionally graded beam under a uniformly distributed load by ritz method", Int. J. Eng. Appl. Sci., 1(3), 1-11.
  14. Simsek, M. and Kocaturk, T. (2009), "Non-linear dynamic analysis of an eccentrically prestressed damped beam under a concentrated moving harmonic load", J. Sound Vib., 320, 235-253. https://doi.org/10.1016/j.jsv.2008.07.012
  15. Valsangkar, A.J. and Pradhanang, R. (1988), "Vibrations of beam-columns on two-parameter elastic foundations", Earthq. Eng. Struct. Dyn., 16, 217-225. https://doi.org/10.1002/eqe.4290160205
  16. Yankelevsky, D.Z. and Eisenberger, M. (1986), "Analysis of a beam-column on elastic foundations", Comput. Struct., 23(3), 351-356. https://doi.org/10.1016/0045-7949(86)90226-9
  17. Yokoyama, T. (1991), "Vibrations of Timoshenko beam-columns on two-parameter elastic foundations", Earthq. Eng. Struct. Dyn., 20, 355-370. https://doi.org/10.1002/eqe.4290200405
  18. Wei, G.W. (2000), "Wavelets generated by using discrete singular convolution kernels", J. Phys. A - Math. Gen., 33, 8577-8596. https://doi.org/10.1088/0305-4470/33/47/317
  19. Wei, G.W. (2001), "A new algorithm for solving some mechanical problems", Comput. Meth. Appl. Mech. Eng., 190, 2017-2030. https://doi.org/10.1016/S0045-7825(00)00219-X
  20. Wei, G.W. (2001a), "Vibration analysis by discrete singular convolution", J. Sound Vib., 244, 535-553. https://doi.org/10.1006/jsvi.2000.3507
  21. Wei, G.W. (2001b), "Discrete singular convolution for beam analysis", Eng. Struct., 23, 1045-1053. https://doi.org/10.1016/S0141-0296(01)00016-5
  22. Wie, G.W., Zhao, Y.B. and Xiang, Y. (2002), "Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm", Int. J. Numer. Meth. Eng., 55, 913-946. https://doi.org/10.1002/nme.526
  23. Wei, G.W., Zhao, Y.B. and Xiang, Y. (2002a), "A novel approach for the analysis of high-frequency vibrations", J. Sound Vib., 257(2), 207-246. https://doi.org/10.1006/jsvi.2002.5055
  24. West, H.H. and Mafi, M. (1984), "Eigenvalues for beam-columns on elastic supports", J. Struct. Eng. - ASCE, 110(6), 1305-1320. https://doi.org/10.1061/(ASCE)0733-9445(1984)110:6(1305)
  25. Zhao, Y.B., Wei, G.W. and Xiang, Y. (2002), "Discrete singular convolution for the prediction of high frequency vibration of plates", Int. J. Solids Struct., 39, 65-88. https://doi.org/10.1016/S0020-7683(01)00183-4
  26. Zhao, Y.B., Wei, G.W. and Xiang, Y. (2002a), "Plate vibration under irregular internal supports", Int. J. Solids Struct., 39, 1361-1383. https://doi.org/10.1016/S0020-7683(01)00241-4
  27. Zhaohua, F. and Cook, R.D. (1983), "Beams elements on two-parameter elastic foundations", J. Eng. Mech. - ASCE, 109(6), 1390-1401. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:6(1390)

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