DOI QR코드

DOI QR Code

Vibration analysis of steel fiber reinforced self-compacting concrete beam on elastic foundation

  • Ozdemir, Mahmut Tunahan (Civil Engineering Department, Institute of Science and Technology, Bursa Uludag University) ;
  • Kobya, Veysel (Civil Engineering Department, Institute of Science and Technology, Bursa Uludag University) ;
  • Yayli, Mustafa Ozgur (Civil Engineering Department, Faculty of Engineering, Bursa Uludag University) ;
  • Mardani-Aghabaglou, Ali (Civil Engineering Department, Faculty of Engineering, Bursa Uludag University)
  • Received : 2020.03.27
  • Accepted : 2020.12.30
  • Published : 2021.02.25

Abstract

In this study, the effect of steel fiber utilization, boundary conditions, different beam cross-section, and length parameter are investigated on the free vibration behavior of fiber reinforced self-compacting concrete beam on elastic foundation. In the analysis of the beam model recommended by Euler-Bernoulli, a method utilizing Stokes transformations and Fourier Sine series were used. For this purpose, in addition to the control beam containing no fiber, three SCC beam elements were prepared by utilization of steel fiber as 0.6% by volume. The time-dependent fresh properties and some mechanical properties of self-compacting concrete mixtures were investigated. In the modelled beam, four different beam specimens produced with 0.6% by volume of steel fiber reinforced and pure (containing no fiber) SCC were analyzed depending on different boundary conditions, different beam cross-sections, and lengths. For this aim, the effect of elasticity of the foundation, cross-sectional dimensions, beam length, boundary conditions, and steel fiber on natural frequency and frequency parameters were investigated. As a result, it was observed that there is a noticeable effect of fiber reinforcement on the dynamic behavior of the modelled beam.

Keywords

References

  1. Abbas, B.A.H. (1984), "Vibrations of timoshenko beams with elastically restrained ends", J. Sound Vib., 97(4), 541-548. https://doi.org/10.1016/0022-460X(84)90508-X.
  2. Akgoz, B. and Civalek, O. (2011), "Nonlinear vibration analysis of laminated plates restingon nonlinear two-parameters elastic foundations", Steel Compos. Struct., 11(5), 403-421. https://doi.org/10.12989/scs.2011.11.5.403.
  3. Akgoz, B. and Civalek, O. (2013), "Free vibration analysis of axially functionally graded tapered Bernoulli-Euler microbeams based on the modified couple stress theory", Compos. Struct., 98, 314-322. https://doi.org/10.1016/j.compstruct.2012.11.020.
  4. Al Rjoub, Y.S. and Hamad, A.G. (2017), "Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method", KSCE J. Civil Eng., 21(3), 792-806. https://doi.org/10.1007/s12205-016-0149-6
  5. Albarracin, C.M. and Grossi, R.O. (2005), "Vibrations of elastically restrained frames", J. Sound Vib., 285(1-2), 467-476. https://doi.org/10.1016/j.jsv.2004.09.013.
  6. Atmane, H.A., Tounsi, A., Mechab, I. and El Abbas, A.B. (2010), "Free vibration analysis of functionally graded plates resting on Winkler-Pasternak elastic foundations using a new shear deformation theory", Int. J. Mech. Mater. Des., 6(2), 113-121. https://doi.org/10.1007/s10999-010-9110-x.
  7. Baferani, A.H., Saidi, A.R. and Ehteshami, H. (2011), "Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation", Compos. Struct., 93(7), 1842-1853. https://doi.org/10.1016/j.compstruct.2011.01.020.
  8. Bahaadini, R. and Saidi, A.R. (2019), "Aerothermoelastic flutter analysis of pre-twisted thin-walled rotating blades reinforced with functionally graded carbon nanotubes", Eur. J. Mech.-A/Solid., 75, 285-306. https://doi.org/10.1016/j.euromechsol.2019.01.018.
  9. Bamonte, P. and Gambarova, P.G. (2012), "A study on the mechanical properties of self-compacting concrete at high temperature and after cooling", Mater. Struct./Materiaux Constr., 45(9), 1375-1387. https://doi.org/10.1617/s11527-012-9839-9.
  10. Bracewell, R.N. (2000), The Fourier Transform and Applications, McGraw Hill.
  11. Bui, T.Q., Khosravifard, A., Zhang, Ch., Hematiyan, M.R. and Golub, M.V. (2013), "Dynamic analysis of sandwich beams with functionally graded core using a truly meshfree radial point interpolation method", Eng. Struct., 47, 90-104. https://doi.org/10.1016/j.engstruct.2012.03.041.
  12. Chung, J.H., Chung, T.Y. and Kim, K.C. (1993), "Vibration analysis of orthotropic mindlin plates with edges elastically restrained against rotation", J. Sound Vib., 163(1), 151-63. https://doi.org/10.1006/JSVI.1993.1154.
  13. Civalek, O. (2004), "Elasti̇ k zemi̇ ne oturan yapilarin hesap yontemleri̇ ne genel birbakis", 45-54.
  14. Civalek, O. (2007), "Nonlinear analysis of thin rectangular plates on Winkler-Pasternak elastic foundations by DSC-HDQ methods", Appl. Math. Model., 31(3), 606-624. https://doi.org/10.1016/j.apm.2005.11.023.
  15. Civalek, O. (2009), "A four-node discrete singular convolution for geometric transformation and its application to numerical solution of vibration problem of arbitrary straight-sided quadrilateral plates", Appl. Math. Model., 33(1), 300-314. https://doi.org/10.1016/j.apm.2007.11.003.
  16. Civalek, O. (2014), "Geometrically nonlinear dynamic and static analysis of shallow spherical shell resting on two-parameters elastic foundations", Int. J. Press. Ves. Pip., 113, 1-9. https://doi.org/10.1016/j.ijpvp.2013.10.014.
  17. Civalek, O. and B. Ozturk. (2010), "Free vibration analysis of tapered beam-column with pinned ends embedded in Winkler-Pasternak elastic foundation", Geomech. Eng., 2(1), 45-56. https://doi.org/10.12989/gae.2010.2.1.045.
  18. De Schutter, G. and Khayat, K.H. (2014), "Introduction and glossary", Mechanical Properties of Self-Compacting Concrete, Springer, Cham.
  19. Deeb, R., Kulasegaram, S. and Karihaloo, B.L. (2014), "3D modelling of the flow of self-compacting concrete with or without steel fibres. Part II: L-box test and the assessment of fibre reorientation during the flow", Comput. Partic. Mech., 1(4), 391-408. https://doi.org/10.1007/s40571-014-0003-x.
  20. Demir, C., Mercan, K., Numanoglu, H.M. and Civalek, O. (2018), "Bending response of nanobeams resting on elastic foundation", J. Appl. Comput. Mech., 4(2), 105-14. https://doi.org/10.22055/jacm.2017.22594.1137.
  21. El-Dieb, A.S. and Reda Taha, M.M. (2012), "Flow characteristics and acceptance criteria of Fiber-Reinforced Self-Compacted Concrete (FR-SCC)", Constr. Build. Mater., 27(1), 585-96. https://doi.org/10.1016/J.CONBUILDMAT.2011.07.004.
  22. Ghane, M., Saidi, A.R. and Bahaadini, R. (2020), "Vibration of fluid-conveying nanotubes subjected to magnetic field based on the thin-walled Timoshenko beam theory", Appl. Math. Model., 80, 65-83. https://doi.org/10.1016/j.apm.2019.11.034.
  23. Goel, R.P. (1976), "Free vibrations of a beam-mass system with elastically restrained ends", J. Sound Vib., 47(1), 9-14. https://doi.org/10.1016/0022-460X(76)90404-1.
  24. Haciyev, V.C., Sofiyev, A.H. and Kuruoglu. N. (2018), "Free bending vibration analysis of thin bidirectionally exponentially graded orthotropic rectangular plates resting on two-parameter elastic foundations", Compos. Struct., 184, 372-77. https://doi.org/10.1016/J.COMPSTRUCT.2017.10.014.
  25. Hegel, G.W.F. (1986), "This is a reproduction of a library book that was digitized by google as part of an ongoing effort to preserve the information in books and make it universally accessible", Oxford University.
  26. Ho, S.H. and Chen, C.O.K. (1998), "Analysis of general elastically end restrained non-uniform beams using differential transform", Appl. Math. Model., 22(4-5), 219-234. https://doi.org/10.1016/S0307-904X(98)10002-1
  27. Huang, M.H. and Thambiratnam, D.P. (2001a), "Deflection response of plate on Winkler foundation to moving accelerated loads", Eng. Struct., 23(9), 1134-1141. https://doi.org/10.1016/S0141-0296(01)00004-9.
  28. Huang, M.H. and Thambiratnam, D.P. (2001b), "Analysis of plate resting on elastic supports and elastic foundation by finite strip method", Comput. Struct., 79(29-30), 2547-2557. https://doi.org/10.1016/S0045-7949(01)00134-1.
  29. Kamali, M., Shamsi, M. and Saidi, A.R. (2018), "Postbuckling of magneto-electro-elastic CNT-MT composite nanotubes resting on a nonlinear elastic medium in a non-uniform thermal environment", Eur. Phys. J. Plus, 133(3), 1-20. https://doi.org/10.1140/epjp/i2018-11942-y.
  30. Kantar, E., Yuen, T.Y., Kobya, V. and Kuang, J.S. (2017), "Impact dynamics and energy dissipation capacity of fibre-reinforced self-compacting concrete plates", Constr. Build. Mater., 138, 383-397. https://doi.org/10.1016/J.CONBUILDMAT.2017.02.011.
  31. Karlicic, D., Kozic, P. and Pavlovic, R. (2016), "Nonlocal vibration and stability of a multiple-nanobeam system coupled by the Winkler elastic medium", Appl. Math. Model., 40(2), 1599-1614. https://doi.org/10.1016/j.apm.2015.06.036.
  32. Ke, L.L., Yang, J., Kitipornchai, S. and Xiang, Y. (2009), "Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials", Mech. Adv. Mater. Struct., 16(6), 488-502. https://doi.org/10.1080/15376490902781175.
  33. Khodabakhsh, R., Saidi, A.R. and Bahaadini, R. (2020), "An analytical solution for nonlinear vibration and post-buckling of functionally graded pipes conveying fluid considering the rotary inertia and shear deformation effects", Appl. Ocean Res., 101, 102277. https://doi.org/10.1016/j.apor.2020.102277.
  34. Kiani, K. (2013), "Vibration analysis of elastically restrained double-walled carbon nanotubes on elastic foundation subjected to axial load using nonlocal shear deformable beam theories", Int. J. Mech. Sci., 68, 16-34. https://doi.org/10.1016/j.ijmecsci.2012.11.011.
  35. Korte, S., Boel, V., De Corte, W. and De Schutter, G. (2014), "Static and fatigue fracture mechanics properties of selfcompacting concrete using three-point bending tests and wedgesplitting tests", Constr. Build. Mater., 57, 1-8. https://doi.org/10.1016/j.conbuildmat.2014.01.090.
  36. Laura, P.A.A., Maurizi, M.J. and Pombo, J.L. (1975), "A note on the dynamic analysis of an elastically restrained-free beam with a mass at the free end", J. Sound Vib., 41(4), 397-405. https://doi.org/10.1016/S0022-460X(75)80104-0.
  37. Lei, Y., Adhikari, S. and Friswell, M.I. (2013), "Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams", Int. J. Eng. Sci., 66-67, 1-13. https://doi.org/10.1016/j.ijengsci.2013.02.004.
  38. Malekzadeh, P. (2009), "Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations", Compos. Struct., 89(3), 367-373. https://doi.org/10.1016/J.COMPSTRUCT.2008.08.007.
  39. Mustapha, K.B. and Zhong, Z.W. (2010), "Free transverse vibration of an axially loaded non-prismatic single-walled carbon nanotube embedded in a two-parameter elastic medium", Comput. Mater. Sci., 50(2), 742-751. https://doi.org/10.1016/j.commatsci.2010.10.005.
  40. Nardini, D. and Brebbia, C.A. (1983), "A new approach to free vibration analysis using boundary elements", Appl. Math. Model., 7(3), 157-162. https://doi.org/10.1016/0307-904X(83)90003-3.
  41. Natarajan, S., Baiz, P.M., Bordas, S., Rabczuk, T. and Kerfriden, P. (2011), "Natural frequencies of cracked functionally graded material plates by the extended finite element method", Compos. Struct., 93(11), 3082-3092. https://doi.org/10.1016/J.COMPSTRUCT.2011.04.007.
  42. Natsuki, T., Lei, X.W., Ni, Q.Q. and Endo, M. (2010), "Free vibration characteristics of double-walled carbon nanotubes embedded in an elastic medium", Phys. Lett. A, 374(26), 2670-2674. https://doi.org/10.1016/j.physleta.2010.04.040.
  43. Nejadi, M.M. and Mohammadimehr, M. (2020), "Analysis of a functionally graded nanocomposite sandwich beam considering porosity distribution on variable elastic foundation using DQM: Buckling and vibration behaviors", Comput. Concrete, 25(3), 215-224. https://doi.org/10.12989/cac.2020.25.3.215.
  44. Numanoglu, H.M., Akgoz, B. and Civalek, O. (2018), "On dynamic analysis of nanorods", Int. J. Eng. Sci., 130, 33-50. https://doi.org/10.1016/j.ijengsci.2018.05.001.
  45. Omurtag, M.H. and Kadioglu, F. (1998), "Free vibration analysis of orthotropic plates resting on pasternak foundation by mixed finite element formulation", Comput. Struct., 67(4), 253-265. https://doi.org/10.1016/S0045-7949(97)00128-4.
  46. Omurtag, M.H., Ozutok, A., Akoz, A.Y. and OeZCELIKOeRS, Y. U.N.U.S. (1997), "Free vibration analysis of Kirchhoff plates resting on elastic foundation by mixed finite element formulation based on Gateaux differential", Int. J. Numer. Meth. Eng., 40(2), 295-317. https://doi.org/10.1002/(SICI)1097-0207(19970130)40:2<295::AID-NME66>3.0.CO;2-2
  47. Pasternak, P.L. (1954), "On a new method of an elastic foundation by means of two foundation constants", Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstuve i Arkhitekture.
  48. Reissner, E. (1958), "A note on deflections of plates on a viscoelastic foundation", J. Appl. Mech., ASME, 25, 144-145. https://doi.org/10.1115/1.4011704
  49. Rezaei, A.S. and Saidi, A.R. (2015), "Exact solution for free vibration of thick rectangular plates made of porous materials", Compos. Struct., 134, 1051-1060. https://doi.org/10.1016/j.compstruct.2015.08.125.
  50. Rezaei, A.S., Saidi, A.R., Abrishamdari, M. and Mohammadi, M.H.P. (2017), "Natural frequencies of functionally graded plates with porosities via a simple four variable plate theory: An analytical approach", Thin Wall. Struct., 120, 366-377. https://doi.org/10.1016/j.tws.2017.08.003.
  51. Self-Compacting Concrete European Project Group (2005), The European Guidelines for Self-Compacting Concrete: Specification, Production and Use, International Bureau for Precast Concrete (BIBM).
  52. Shen, Z.B., Li, X.F., Sheng, L.P. and Tang, G.J. (2012), "Transverse vibration of nanotube-based micro-mass sensor via nonlocal Timoshenko beam theory", Comput. Mater. Sci., 53(1), 340-346. https://doi.org/10.1016/j.commatsci.2011.09.023.
  53. Thambiratnam, D. and Zhuge, Y. (1996), "Dynamic analysis of beams on an elastic foundation subjected to moving loads", J. Sound Vib., 198(2), 149-169. https://doi.org/10.1006/jsvi.1996.0562.
  54. Vlasov, V.Z. (1966), "Beams, plates and shells on elastic foundation", Israel Program for Scientific Translation.
  55. Wang, T.M. and Gagnon, L.W. (1978), "Vibrations of continuous timoshenko beams on Winkler-Pasternak foundations", J. Sound Vib., 59(2), 211-20. https://doi.org/10.1016/0022-460X(78)90501-1.
  56. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002.
  57. Winkler, E. (1867), "Die lehre von elastizitat und festigkeit (on elasticity and fixity)", Prag. https://archive.org/details/bub_gb_25E5AAAAcAAJ/page/n3.
  58. Yanik, F. and Yayli, M.O. (2015), "Rijit olmayan sinir kosullarinda elastik zemine oturan bir cubugun eksenel titresim analizi", Bilecik Seyh Edebali Universitesi Fen Bilimleri Dergisi, 2(1), 35-44.
  59. Yas, M.H. and Samadi, N. (2012), "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation", Int. J. Press. Ves. Pip., 98, 119-28. https://doi.org/10.1016/J.IJPVP.2012.07.012.
  60. Yayli, M.O. (2017), "Buckling analysis of a cantilever single-walled carbon nanotube embedded in an elastic medium with an attached spring", Micro Nano Lett., 12(4), 255-259. https://doi.org/10.1049/mnl.2016.0662.
  61. Yayli, M.O. (2018), "On the torsional vibrations of restrained nanotubes embedded in an elastic medium", J. Brazil. Soc. Mech. Sci. Eng., 40(9), 419. https://doi.org/10.1007/s40430-018-1346-7
  62. Yayli, M.O., Aras, M. and Aksoy, S. (2014), "An efficient analytical method for vibration analysis of a beam on elastic foundation with elastically restrained ends", Shock Vib., 2014, Article ID 159213. https://doi.org/10.1155/2014/159213
  63. Yayli, M.O., Yanik, F. and Kandemir, S.Y. (2015), "Longitudinal vibration of nanorods embedded in an elastic medium with elastic restraints at both ends", Micro Nano Lett., 10(11), 641-644. https://doi.org/10.1049/mnl.2014.0680.
  64. Ying, J., Lu, C.F. and Chen. W.Q. (2008), "Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations", Compos. Struct., 84(3), 209-219. https://doi.org/10.1016/J.COMPSTRUCT.2007.07.004.
  65. Zhou, D. (2001), "Vibrations of Mindlin Rectangular Plates with Elastically Restrained Edges Using Static Timoshenko Beam Functions with the Rayleigh-Ritz Method", International Journal of Solids and Structures 38 (32-33), 5565-80. https://doi.org/10.1016/S0020-7683(00)00384-X.
  66. Zhou, D., Y. K. Cheung, S. H. Lo, and F. T.K. Au. (2004), "Three-dimensional vibration analysis of rectangular thick plates on Pasternak foundation", Int. J. Numer. Meth. Eng., 59(10), 1313-1334. https://doi.org/10.1002/nme.915.