Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Transient response of functionally graded non-uniform cylindrical helical rods

  • Cuma, Yavuz C. (Department of Civil Engineering, Adana Alparslan Turkes Science and Technology University) ;
  • Calim, Faruk Firat (Department of Civil Engineering, Adana Alparslan Turkes Science and Technology University)
  • Received : 2020.08.25
  • Accepted : 2021.07.14
  • Published : 2021.08.25
⟨ Previous Next ⟩

Abstract

This paper have the objective of investigating forced vibration behaviour of axially functionally graded cylindrical helices with variable cross-section. An algorithm is developed in order to solve corresponding problems. The ordinary differential equations governing the dynamic behaviour of cylindrical helices are determined in Laplace domain by using Timoshenko beam theory. Then transfer matrix method is implemented for the solution, including shear and axial deformation effects. Obtained results are transferred to time domain using Durbin's modified numerical inverse algorithm for Laplace transform. A benchmark problem has been solved to check the accuracy of developed algorithm then a parametric study is conducted considering the effects of material gradient index (βmat), section variation parameter (βsec) and number of active turns (n). Results are compared with solutions attained from ANSYS for verification.

Keywords

References

  1. Abdelrahman, A.A., Eltaher, M.A., Kabeel, A.M., Abdraboh, A.M. and Hendy, A.A. (2019), "Free and forced analysis of perforated beams", Steel Compos. Struct., 31(5), 489-502. https://doi.org/10.12989/scs.2019.31.5.489.
  2. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., 18(3), 659-672. http://doi.org/10.12989/scs.2015.18.3.659.
  3. Busool, W. and Eisenberger, M. (2002), "Free vibration of helicoidal beams of arbitrary shape and variable cross section", J. Vib. Acoust. T.-ASME, 124, 397-409. https://doi.org/10.1115/1.1468870.
  4. Calim, F.F. (2003), "Dynamic analysis of viscoelastic, anisotropic curved spatial systems" Ph.D. Dissertation, Cukurova University, Adana, Turkey. (In Turkish).
  5. Calim, F.F. (2009), "Forced vibration of helical rods of arbitrary shape", Mech. Res. Commun., 36, 882-891. https://doi.org/10.1016/j.mechrescom.2009.07.007.
  6. Calim, F.F. (2012), "Forced vibration of curved beams on two-parameter elastic foundation", Appl. Math. Model., 36, 964-973. https://doi.org/10.1016/j.apm.2011.07.066.
  7. Calim, F.F. (2016a), "Transient analysis of axially functionally graded Timoshenko beams on two-parameter viscoelastic foundation", Compos. Part B Eng., 103, 98-112. http://doi.org/10.1016/j.compositesb.2016.05.040.
  8. Calim, F.F. (2016b), "Free and forced vibration analysis of axially functionally graded Timoshenko beams on two-parameter viscoelastic foundation", Compos. Part B Eng., 103, 98-112. https://doi.org/10.1016/j.compositesb.2016.08.008.
  9. Calim, F.F. (2016c), "Dynamic response of curved Timoshenko beams resting on viscoelastic foundation", Struct. Eng. Mech., 59, 761-774. http://doi.org/10.12989/sem.2016.59.4.761.
  10. Calim, F.F. (2020), "Vibration analysis of functionally graded Timoshenko beams on Winkler-Pasternak elastic foundation", IJST-T Civ. Eng., 44, 901-920. http://.doi.org/10.1007/s40996-019-00283-x.
  11. Calim, F.F. and Cuma, Y.C. (2020), "Vibration analysis of nonuniform hyperboloidal and barrel helices made of functionally graded material", Mech. Based Des. Struc., http://doi.org/10.1080/15397734.2020.1822181.
  12. Cuma, Y.C. and Calim, F.F. (2021), "Free vibration analysis of functionally graded cylindrical helices with variable cross-section", J. Sound Vib., 494, 115856. https://doi.org/10.1016/j.jsv.2020.115856.
  13. Eratli, N., Argeso, H., Calim, F.F., Temel, B. and Omurtag, M.H. (2014), "Dynamic analysis of linear viscoelastic cylindrical and conical helicoidal rods using the mixed FEM", J. Sound Vib., 333, 3671-3690. http://dx.doi.org/10.1016/j.jsv.2014.03.017.
  14. Eratli, N., Yilmaz, M., Darilmaz, K. and Omurtag, M.H. (2016), "Dynamic analysis of helicoidal bars with non-circular cross-sections via mixed FEM", Struct. Eng. Mech., 57(2), 221-238. https://doi.org/10.12989/sem.2016.57.2.221.
  15. Huang, Y., Yang, L.E. and Luo, Q.Z. (2013), "Free vibration of axially functionally graded Timoshenko beams with nonuniform cross-section", Compos. Part B Eng., 45, 1493-1498. https://doi.org/10.1016/j.compositesb.2012.09.015.
  16. Jiang, W., Jones, W.K., Wang, T.L. and Wu, K.H. (1991), "Free vibration of helical springs", J. Appl. Mech., 58, 222-228. https://doi.org/10.1115/1.2897154.
  17. Lee, J. And Thompson, D.J. (2001), "Dynamic stiffness formulation, free vibration and wave motion of helical springs", J. Sound Vib., 239, 297-320. https://doi.org/10.1006/jsvi.2000.3169.
  18. Lin, Y. and Pisano, A.P. (1987), "General dynamic equations of helical springs with static solution and experimental verification", J. Appl. Mech. T.-ASME, 54, 910-917. https://doi.org/10.1115/1.3173138.
  19. Massoud, M.P. (1965), "Vectorial derivation of the equations for small vibrations of twisted curved beams", J. Appl. Mech., 32, 439-440. https://doi.org/10.1115/1.3625823.
  20. Mottershead, J.E. (1980), "Finite elements for dynamical analysis of helical rods", Int. J. Mech. Sci., 22, 267-283. https://doi.org/10.1016/0020-7403(80)90028-4.
  21. Nagaya, K. (1989), "Dynamic stress analysis of a coil spring of arbitrary cross-section to general transient excitations", J. Sound Vib., 128, 307-319. https://doi.org/10.1016/0022-460X(89)90774-8.
  22. Omurtag, M.H. and Akoz, A.Y. (1992), The mixed finite element solution of helical beams with variable cross-section under arbitrary loading", Comput. Struct., 43, 325-331. https://doi.org/10.1016/0045-7949(92)90149-T.
  23. Pearson, D. (1982) "The transfer matrix method for the vibration of compressed helical springs", J. Mech. Eng. Sci., 24, 163-171. https://doi.org/10.1243/JMES_JOUR_1982_024_033_02.
  24. She, G.L., Liu, H. B. and Karami, B. (2020), "On resonance behavior of porous FG curved nanobeams", Steel Compos. Struct., 36(2), 179-186. http://doi.org/10.12989/scs.2020.36.2.179.
  25. Temel, B. and Calim, F.F. (2003), "Forced vibration of cylindrical helical rods subjected to impulsive loads", J. Appl. Mech., 70, 281-291. https://doi.org/10.1115/1.1554413.
  26. Temel, B., Calim, F.F. and Tutuncu, N. (2004), "Quasi-static and dynamic response of viscoelastic helical rods", J. Sound Vib., 271, 921-935. https://doi.org/10.1016/S0022-460X(03)00760-0.
  27. Temel, B., Calim, F.F. and Tutuncu, N. (2005), "Forced vibration of composite cylindrical helical rods", Int. J. Mech. Sci., 47, 998-1022. https://doi.org/10.1016/j.ijmecsci.2005.04.003.
  28. Wang, G., Zhu, L., Higuchi, K., Fan, W. and Li, L. (2019), "Solution for free vibration of spatial curved beams", Eng. Comput., 37, 1597-1616. https://doi.org/10.1108/EC-03-2019-0097.
  29. Wittrick, W.H. (1966), "On elastic wave propagation in helical springs", Int. J. Mech. Sci., 8, 25-47. https://doi.org/10.1016/0020-7403(66)90061-0.
  30. Xiong, Y. and Tabarrok, B. (1992), "A finite element model for the vibration of spatial rods under various applied loads" Int. J. Mech. Sci., 34, 41-51. https://doi.org/10.1016/0020-7403(92)90052-I.
  31. Yildirim, V. (1996), "Investigation of parameters affecting free vibration frequency of helical springs", Int. J. Numer. Methods Eng., 39, 99-114. https://doi.org/10.1002/(SICI)1097-0207(19960115)39:1<99::AID-NME850>3.0.CO;2-M.
  32. Yildirim, V. (1999), "An efficient numerical method for predicting the natural frequencies of cylindrical helical springs," Int. J. Mech. Sci., 41, 919-939. https://doi.org/10.1016/s0020-7403(98)00065-4.