참고문헌
- 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.
- 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.
- 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.
- Calim, F.F. (2003), "Dynamic analysis of viscoelastic, anisotropic curved spatial systems" Ph.D. Dissertation, Cukurova University, Adana, Turkey. (In Turkish).
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.