Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Dynamic contact response of a finite beam on a tensionless Pasternak foundation under symmetric and asymmetric loading

  • Coskun, Irfan (Faculty of Civil Engineering, Yildiz Technical University)
  • Received : 2009.05.13
  • Accepted : 2009.11.06
  • Published : 2010.02.20
⟨ Previous Next ⟩

Abstract

The dynamic response of a finite Bernoulli-Euler beam resting on a tensionless Pasternak foundation and subjected to a concentrated harmonic load is investigated in this study. This load may be applied at the center of the beam, or it may be offset from the center. Since the elastic foundation is assumed to be tensionless, the beam may lift off the foundation, resulting in contact and non-contact regions in the system. An analytical/numerical solution is obtained from the governing equations of the contact and non-contact regions to determine the coordinates of the lift-off points. Although there is no nonlinear term in the equations, the problem appears to be nonlinear since the contact regions are not known in advance. Due to that nonlinearity, the essentials of the problem (the coordinates of the lift-off points) are calculated numerically using the Newton-Raphson technique. The results, which represent the symmetric and asymmetric responses of the beam, are presented graphically in this work. They illustrate the effects of the forcing frequency and the beam length on the extent of the contact regions and displacements.

Keywords

References

  1. Celep, Z., Malaika, A. and Abu-Hussein, M. (1989), "Forced vibrations of a beam on a tensionless foundation", J. Sound Vib., 128, 235-246. https://doi.org/10.1016/0022-460X(89)90768-2
  2. Celep, Z. and Demir, F. (2005), "Circular rigid beam on a tensionless two-parameter elastic foundation", ZAMMZ. Angew. Math. Me., 85(6), 431-439. https://doi.org/10.1002/zamm.200310183
  3. Celep, Z. and Demir, F. (2007), "Symmetrically loaded beam on a two-parameter tensionless foundation", Struct. Eng. Mech., 27(5), 555-574. https://doi.org/10.12989/sem.2007.27.5.555
  4. Chen, W.Q., Lu, C.F. and Bian, Z.G. (2004), "A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation", Appl. Math. Model., 28, 877-890. https://doi.org/10.1016/j.apm.2004.04.001
  5. Choros, J. and Adams, G.G. (1979), "A steadily moving load on an elastic beam resting on a tensionless Winkler foundation", J. Appl. Mech., 46, 175-180. https://doi.org/10.1115/1.3424492
  6. Co kun, . and Engin, H. (1999), "Non-linear vibrations of a beam on an elastic foundation", J. Sound Vib., 223(3), 335-354. https://doi.org/10.1006/jsvi.1998.1973
  7. Coskun, I. (2000), "Non-linear vibrations of a beam resting on a tensionless Winkler fundation", J. Sound Vib., 236(3), 401-411. https://doi.org/10.1006/jsvi.2000.2982
  8. Coskun, I. (2003), "The response of a finite beam on a tensionless Pasternak foundation subjected to a harmonic load", Eur. J. Mech. A-Solid., 22, 151-161. https://doi.org/10.1016/S0997-7538(03)00011-1
  9. Coskun, I., Engin, H. and Ozmutlu, A. (2008), "Response of a finite beam on a tensionless Pasternak foundation under symmetric and asymmetric loading", Struct. Eng. Mech., 30(1), 21-36. https://doi.org/10.12989/sem.2008.30.1.021
  10. De Rosa, M.A. (1995), "Free vibrations of Timoshenko beams on two-parameter elastic foundation", Comput. Struct., 57(1), 151-156. https://doi.org/10.1016/0045-7949(94)00594-S
  11. De Rosa, M.A. and Maurizi, M.J. (1998), "The influence of concentrated masses and Pasternak soil on the free vibrations of Euler beams-exact solution", J. Sound Vib., 212(4), 573-581. https://doi.org/10.1006/jsvi.1997.1424
  12. Dutta, S.C. and Roy, R. (2002), "A critical review on idealization and modeling for interaction among soilfoundation- structure system", Comput. Struct., 80, 1579-1594. https://doi.org/10.1016/S0045-7949(02)00115-3
  13. Filipich, C.P. and Rosales, M.B. (2002), "A further study about the behaviour of foundation piles and beams in a Winkler-Pasternak soil", Int. J. Mech. Sci., 44(1), 21-36. https://doi.org/10.1016/S0020-7403(01)00087-X
  14. Franciosi, C. and Masi, A. (1993) "Free vibrations of foundation beams on two-parameter elastic soil", Comput. Struct., 47(3), 419-426. https://doi.org/10.1016/0045-7949(93)90237-8
  15. Hetényi, M. (1946), Beams on Elastic Foundation, The University of Michigan Press, Ann Arbor, USA.
  16. Horibe, T. and Asano, N. (2001), "Large deflection analysis of beams on two-parameter elastic foundation using the boundary integral equation method", JSME Int. J. A-Solid. M., 44(2), 231-236. https://doi.org/10.1299/jsmea.44.231
  17. Ioakimidis, N.I. (1996), "Beams on tensionless elastic foundation: Approximate quantifier elimination with Chebyshev series", Int. J. Numer. Meth. Eng., 39(4), 663-686. https://doi.org/10.1002/(SICI)1097-0207(19960229)39:4<663::AID-NME875>3.0.CO;2-8
  18. Kaschiev, M.S. and Mikhajlov, K. (1995), "A beam resting on a tensionless Winkler foundation", Comput. Struct., 55(2), 261-264. https://doi.org/10.1016/0045-7949(94)00445-9
  19. Kerr, A.D. (1964), "Elastic and viscoelastic foundation models", J. Appl. Mech-T. ASME 31, 491-498. https://doi.org/10.1115/1.3629667
  20. Kerr, A.D. and Coffin, D.W. (1991), "Beams on a two-dimensional Pasternak base subjected to loads that cause lift-off", Int. J. Solids Struct., 28(4), 413-422. https://doi.org/10.1016/0020-7683(91)90057-M
  21. Lancioni, G. and Lenci, S. (2007), "Forced nonlinear oscillations of a semi-infinite beam resting on a unilateral elastic soil: Analytical and numerical solutions", J. Comput. Nonlinear Dyn., 2(2), 155-166. https://doi.org/10.1115/1.2447406
  22. Lin, L. and Adams, G.G. (1987), "Beam on tensionless elastic foundation", J. Eng. Mech-ASCE, 113, 542-553. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:4(542)
  23. Maheshwari, P., Chandra, S. and Basudhar, P.K. (2004), "Response of beams on a tensionless extensible geosynthetic-reinforced earth bed subjected to moving loads", Comput. Geotech., 31, 537-548. https://doi.org/10.1016/j.compgeo.2004.07.005
  24. Malekzadeh, P. and Karami, G. (2008), "A mixed differential quadrature and finite element free vibration and buckling analysis of thick beams on two-parameter elastic foundations", Appl. Math. Model., 32, 1381-1394. https://doi.org/10.1016/j.apm.2007.04.019
  25. Rao, N.V.S.K. (1974), "Onset of separation betwen a beam and tensionless elastic foundation due to moving loads", J. Appl. Mech-T. ASME, 41, 303-305. https://doi.org/10.1115/1.3423257
  26. Rao, G.V. (2003), "Large-amplitude free vibrations of uniform beams on Pasternak foundation", J. Sound Vib., 263(4), 954-960. https://doi.org/10.1016/S0022-460X(02)01486-4
  27. Silveira, R.A.M., Pereira, W.L.A. and Gonçalves, P.B. (2008), "Nonlinear analysis of structural elements under unilateral contact constraints by a Ritz type approach", Int. J. Solids Struct., 45, 2629-2650. https://doi.org/10.1016/j.ijsolstr.2007.12.012
  28. Tsai, N.C. and Westmann, R.E. (1967), "Beams on tensionless foundation", J. Eng. Mech-ASCE, 93, 1-12.
  29. Valsangkar, A.J. and Pradhanang, R. (1988), "Vibrations of a beam-column on two-parameter elastic foundation", Earthq. Eng. Struct., D, 16, 217-225. https://doi.org/10.1002/eqe.4290160205
  30. Weitsman, Y. (1970), "On foundations that react in compression only", J. Appl. Mech.-T. ASME, 37(7), 1019-1030. https://doi.org/10.1115/1.3408653
  31. Weitsman, Y. (1971), "Onset of separation between a beam and tensionless elastic foundation under a moving load", Int. J. Mech. Sci., 13, 707-711. https://doi.org/10.1016/0020-7403(71)90070-1
  32. Weitsman, Y. (1972), "A tensionless contact between a beam and an elastic half-space", Int. J. Eng. Sci., 10, 73-81. https://doi.org/10.1016/0020-7225(72)90075-4
  33. Zhang, Y. and Murphy, D.K. (2004), "Response of a finite beam in contact with a tensionless foundation under symmetric and asymmetric loading", Int. J. Solids Struct., 41, 6745-6758. https://doi.org/10.1016/j.ijsolstr.2004.05.028
  34. Zhaohua, F. and Cook, R.D. (1983), "Beam elements on two-parameter elastic foundations", J. Eng. Mech-ASCE 109, 1390-1402. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:6(1390)
  35. Zhang, Y. (2008), "Tensionless contact of a finite beam resting on Reissner foundation", Int. J. Mech. Sci., 50, 1035-1041. https://doi.org/10.1016/j.ijmecsci.2008.02.006

Cited by

  1. A numerical approach for equilibrium and stability analysis of slender arches and rings under contact constraints vol.50, pp.1, 2013, https://doi.org/10.1016/j.ijsolstr.2012.09.015
  2. Vibration attenuation in periodic composite Timoshenko beams on Pasternak foundation vol.40, pp.3, 2010, https://doi.org/10.12989/sem.2011.40.3.373