Steel and Composite Structures

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Free vibration analysis of axially moving laminated beams with axial tension based on 1D refined theories using Carrera unified formulation

  • Daraei, Behnam (Department of Civil Engineering, Shahid Bahonar University of Kerman) ;
  • Shojaee, Saeed (Department of Civil Engineering, Shahid Bahonar University of Kerman) ;
  • Hamzehei-Javaran, Saleh (Department of Civil Engineering, Shahid Bahonar University of Kerman)
  • Received : 2020.05.04
  • Accepted : 2020.09.29
  • Published : 2020.10.10
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Abstract

In this paper, free vibration finite element analysis of axially moving laminated composite beams subjected to axial tension is studied. It is assumed that the beam has a constant axial velocity and is subject to uniform axial tension. The analysis is based on higher-order theories that have been presented by Carrera Unified Formulation (CUF). In the CUF technique, the three dimensional (3D) displacement fields are expressed as the approximation of the arbitrary order of the displacement unknowns over the cross-section. This higher-order expansion is considered in equivalent single layer (ESL) model. The governing equations of motion are obtained via Hamilton's principle. Finally, several numerical examples are presented and the effect of the ply-angle, travelling speed and axial tension on the natural frequencies and beam stability are demonstrated.

Keywords

References

  1. AL-Bedoor, B.O. and Khulief, Y.A. (1996), "An approximate analytical solution of beam vibrations during axial motion", J. Sound Vib., 192(1), 159-171. https://doi.org/10.1006/jsvi.1996.0181.
  2. Alesadi, A., Galehdari, M. and Shojaee, S. (2017a), "Free vibration and buckling analysis of cross-ply laminated composite plates using Carrera's unified formulation based on Isogeometric approach", Comput. Struct., 183, 38-47. https://doi.org/10.1016/j.compstruc.2017.01.013.
  3. Alesadi, A., Galehdari, M. and Shojaee, S. (2017b), "Free vibration and buckling analysis of composite laminated plates using layerwise models based on isogeometric approach and Carrera unified formulation", Mech. Adv. Mater. Struct., 25, 1018-1032. https://doi.org/10.1080/15376494.2017.1342883.
  4. Alesadi, A., Ghazanfari, S. and Shojaee, S. (2019), "B-spline finite element approach for the analysis of thin-walled beam structures based on 1D refined theories using carrera unified formulation", Thin-Wall. Struct., 130, 313-320. https://doi.org/10.1016/j.tws.2018.05.016
  5. Alesadi, A., Shojaee, S. and Hamzehei-Javaran, S. (2020), "Spherical Hankel-based free vibration analysis of cross-ply laminated plates using refined finite element theories", Iran. J. Sci. Technol. Trans. Civ. Eng., 44, 127-137. https://doi.org/10.1007/s40996-019-00242-6
  6. Bathe, K.J. (1996), Finite Element Procedure, Prentice Hall.
  7. Carrera, E. (1995), "A class of two dimensional theories for multilayered plates analysis", Atti della accad, Delle Sci. Di Torino. Cl. Di Sci. Fis. Mat. e Nat, 19, 1-39.
  8. Carrera, E., Brischetto, S. and Robaldo, A. (2008), "Variable kinematic model for the analysis of functionally graded material plates", AIAA J., 46, 194-203. https://doi.org/10.2514/1.32490.
  9. Carrera, E., Filippi, M., Mahato, P.K.R. and Pagani, A. (2015), "Advanced models for free vibration analysis of laminated beams with compact and thin-walled open/closed sections", J. Comp. Mater., 49(17), 2085-2101. https://doi.org/10.1177/0021998314541570.
  10. Carrera, E., Filippi, M., Mahato, P.K.R. and Pagani, A. (2016a), "Accurate static response of single- and multi-cell laminated box beams", Compos. Struct., 136, 372-383. https://doi.org/10.1016/j.compstruct.2015.10.020.
  11. Carrera, E., Filippi, M., Mahato, P.K.R. and Pagani, A. (2016b), "Free-vibration tailoring of single- and multi-bay laminated box structures by refined beam theories", Thin-Wall. Struct., 109, 40-49. https://doi.org/10.1016/j.tws.2016.09.014.
  12. Carrera, E. and Giunta, g. (2010), "Refined beam theories based on a unified formulation", Int. J. Appl. Mech., 2, 117-143. https://doi.org/10.1142/S1758825110000500.
  13. Carrera, E., Giunta, G. and Petrolo, M. (2011), Beam Structures: Classical and Advanced Theories, John Wiley & Sons Ltd, Chichester, West Sussex, United Kingdom. https://doi.org/10.1002/9781119978565.
  14. Carrera, E., Pagani, A. and Banerjee J.R. (2016), "Linearized buckling analysis of isotropic and composite beam-columns by carrera unified formulation and dynamic stiffness method", Mech. Adv. Mater. Struct., 23(9), 1092-1103. https://doi.org/10.1080/15376494.2015.1121524.
  15. Carrera, E. (2002), "Theories and finite elements for multilayered, anisotropic, composite plates and shells", Arch. Comput. Meth. Eng., 9, 87-140. https://doi.org/10.1007/BF02736649.
  16. Carrera, E. (2003), "Theories and finite elements for multilayered plates and shells: a unified compact formulation with numerical assessment and benchmarking", Arch. Comput. Meth. Eng., 10, 215-296. https://doi.org/10.1007/BF02736224.
  17. Catapano, A., Giunta, G., Belouettar, S. and Carrera, E. (2011), "Static analysis of laminated beams via a unified formulation", Compos. Struct., 94, 75-83. https://doi.org/10.1016/j.compstruct.2011.07.015
  18. Chakraborty, G., Mallik, A.K. and Hatwal, H. (1999), "Non-linear vibration of a traveling beam", Int. J. Nonlinear Mech., 34(4), 655-670. https://doi.org/10.1016/S0020-7462(98)00017-1.
  19. Daraei, B., Shojaee, S. and Hamzehei-Javaran, S. (2020), "Free vibration analysis of composite laminated beams with curvilinear fibers via refined theories", Mech. Adv. Mater. Struct., https://doi.org/10.1080/15376494.2020.1797959.
  20. Ghayesh, M.H. and Amabili, M. (2013), "Steady-state transverse response of an axially moving beam with time-dependent axial speed", Int. J. Non-Linear Mech., 49, 40-49. https://doi.org/10.1016/j.ijnonlinmec.2012.08.003.
  21. Ghayesh, M.H. and Balar, S. (2010), "Non-linear parametric vibration and stability analysis for two dynamic models of axially moving Timoshenko beams", Appl. Math. Model., 34(10), 2850-2859. https://doi.org/10.1016/j.apm.2009.12.019.
  22. Ghayesh, M.H. and Khadem, S.E. (2008), "Rotary inertia and temperature effects on non-linear vibration, steady-state response and stability of an axially moving beam with time-dependent velocity", Int. J. Mech. Sci., 50(3), 389-404. https://doi.org/10.1016/j.ijmecsci.2007.10.006.
  23. Ghazanfari, S., Hamzehei-Javaran, S., Alesadi, A. and Shojaee, S. (2019), "Free vibration analysis of cross-ply laminated beam structures using refined beam theories and B-spline basis functions", Mech. Adv. Mater. Struct., https://doi.org/10.1080/15376494.2019.1574939.
  24. Ghorbanpour Arani, A., Haghparast, E. and BabaAkbar Zarei, H. (2017), "Vibration analysis of functionally graded nanocomposite plate moving in two directions", Steel Compos. Struct., 23(5), 529-541. https://doi.org/10.12989/scs.2017.23.5.529.
  25. Giunta, G., Belouettar, S., Nasser, H., Kiefer-Kamal, E.H. and Thielen, T. (2015), "Hierarchical models for the static analysis of three-dimensional sandwich beam structures", Compos. Struct., 133, 1284-1301. https://doi.org/10.1016/j.compstruct.2015.08.049.
  26. Giunta, G., Metla, N., Koutsawa, Y. and Belouettar, S. (2013), "Free vibration and stability analysis of three-dimensional sandwich beams via hierarchical models", Compos. Part B Eng., 47, 326-338. https://doi.org/10.1016/j.compositesb.2012.11.017.
  27. Ho-Huu, V., Vo-Duy, T., Duong-Gia, D. and Nguyen-Thoi, T. (2018), "An efficient procedure for lightweight optimal design of composite laminated beams", Steel Compos. Struct., 27(3), 297-310. https://doi.org/10.12989/scs.2018.27.3.297.
  28. Hui, Y., Giunta, G., Belouettar, S., Huang, Q., Hu, H. and Carrera, E. (2017), "A free vibration analysis of three-dimensional sandwich beams using hierarchical one-dimensional finite elements", Compos. Part B Eng., 110, 7-19. https://doi.org/10.1016/j.compositesb.2016.10.065.
  29. Hwang, S.J. and Perkins, N.C. (1992), "Supercritical stability of an axially moving beam Part II: Vibration and stability analysis", J. Sound Vib., 154, 397-409. https://doi.org/10.1016/0022-460X(92)90775-S.
  30. Kahya, V., Karaca, S. and Vo, T. (2019), "Shear-deformable finite element for free vibrations of laminated composite beams with arbitrary lay-up", Steel Compos. Struct., 33, 473-487. https://doi.org/10.12989/scs.2019.33.4.473.
  31. Kahya, V. and Turan, M. (2018), "Vibration and buckling of laminated beams by a multi-layer finite element model", Steel Comp. Struct., 28(4), 415-426. https://doi.org/10.12989/scs.2018.28.4.415
  32. Kong, L. and Parker, R.G. (2004), "Approximate eigensolutions of axially moving beams with small flexural stiffness", J. Sound Vib., 276(1-2), 459-469. https://doi.org/10.1016/j.jsv.2003.11.027
  33. Lee, U. and Jang, I. (2007), "On the boundary conditions for axially moving beams", J. Sound Vib., 306(3-5), 675-690. https://doi.org/10.1016/j.jsv.2007.06.039
  34. Lee, U., Kim, J. and Oh, H. (2004), "Spectral analysis for the transverse vibration of an axially moving Timoshenko beam", J. Sound Vib., 271(3-5), 685-703. https://doi.org/10.1016/S0022-460X(03)00300-6.
  35. Liu, B., Zhao, L., Ferreira, A.J.M., Xing, Y.F., Neves, A.M.A. and Wang, J. (2017), "Analysis of viscoelastic sandwich laminates using a unified formulation and a differential quadrature hierarchical finite element method", Compos. Part B Eng., 110, 185-192. https://doi.org/10.1016/j.compositesb.2016.11.028.
  36. Mokhtari, A. and Mirdamadi, H.R. (2018), "Study on vibration and stability of an axially translating viscoelastic Timoshenko beam: Non-transforming spectral element analysis", Appl. Math. Model., 56, 342-358. https://doi.org/10.1016/j.apm.2017.12.007.
  37. Oz, H.R. (2001), "On the vibrations of an axially traveling beam on fixed supports with variable velocity", J. Sound Vib., 239(3), 556-564. https://doi.org/10.1006/jsvi.2000.3077
  38. Oz, H.R. and Pakdemirli, M. (1999), "Vibrations of an axially moving beam with time dependent velocity", J. Sound Vib., 227(2), 239-257. https://doi.org/10.1006/jsvi.1999.2247.
  39. Ozkaya, E. and Oz, H.R. (2002), "Determination of natural frequencies and stability regions of axially moving beams using artificial neural networks method", J. Sound Vib., 252(4), 782-789. https://doi.org/10.1006/jsvi.2001.3991.
  40. Pagani, A., Carrera, E., Boscolo, M. and Banerjee, J.R. (2014), "Refined dynamic stiffness elements applied to free vibration analysis of generally laminated composite beams with arbitrary boundary conditions", Compos. Struct., 110, 305-316. https://doi.org/10.1016/j.compstruct.2013.12.010.
  41. Pagani, A., Carrera, E. and Ferreira, A.J.M. (2016), "Higher-order theories and radial basis functions applied to free vibration analysis of thin-walled beams", Mech. Adv. Mater. Struct., 23, 1080-1091. https://doi.org/10.1080/15376494.2015.1121555.
  42. Pagani, A. and Carrera, E. (2018), "Unified formulation of geometrically nonlinear refined beam theories", Mech. Adv. Mater. Struct., 25, 15-31. https://doi.org/10.1080/15376494.2016.1232458.
  43. Pakdemirli, M. and Ozkaya, E. (1998), "Approximate boundary layer solution of a moving beam problem", Math. Comput. Appl., 3(2), 93-100. https://doi.org/10.3390/mca3020093.
  44. Reddy, J.N. (2013), An Introduction to Continuum Mechanics, Cambridge University Press, Second Edition.
  45. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, Boca Raton, FL, Second Edition.
  46. Rezaee, M. and Lotfan, S. (2015), "Non-linear nonlocal vibration and stability analysis of axially moving nanoscale beams with time-dependent velocity", Int. J. Mech. Sci., 96, 36-46. https://doi.org/10.1016/j.ijmecsci.2015.03.017.
  47. Simpson, A. (1973), "Transverse modes and frequencies of beams translating between fixed end supports", J. Mech. Eng. Sci., 15(3), 159-164. https://doi.org/10.1243/JMES_JOUR_1973_015_031_02.
  48. Siylianou, M. and Tabarrok, B. (1994), "Finite element analysis of an axially-moving beam, part II: Stability analysis", J. Sound Vib., 178(4), 455-481. https://doi.org/10.1006/jsvi.1994.1498.
  49. Wickert, J.A. and Mote, C.D. (1990), "Classical vibration analysis of axially moving continua", J. Appl. Mech., 57(3), 738-744. https://doi.org/10.1115/1.2897085
  50. Wickert, J.A. and Mote, C.D. (1988), "Current research on the vibration and stability of axially moving materials", Shock Vib. Dig., 20, 3-13. https://doi.org/10.1177/058310248802000503
  51. Wickert, J.A. (1992), "Non-linear vibration of a traveling tensioned beam", Int. J. Non-Linear Mech., 27(3), 503-517. https://doi.org/10.1016/0020-7462(92)90016-Z.
  52. Yan, Y., Carrera, E., Pagani, A., Kaleel, I. and Miguel, A.G.d. (2020), "Isogeometric analysis of 3D straight beam-type structures by Carrera Unified Formulation", Appl. Math. Model., 79, 768-792. https://doi.org/10.1016/j.apm.2019.11.003

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