Structural Engineering and Mechanics

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Timoshenko theory effect on the vibration of axially functionally graded cantilever beams carrying concentrated masses

  • Rossit, Carlos A. (Department of Engineering, Universidad Nacional del Sur(UNS) Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET)) ;
  • Bambill, Diana V. (Department of Engineering, Universidad Nacional del Sur(UNS) Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET)) ;
  • Gilardi, Gonzalo J. (Department of Engineering, Universidad Nacional del Sur(UNS) Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET))
  • Received : 2017.10.26
  • Accepted : 2018.03.19
  • Published : 2018.06.25
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Abstract

In this paper is studied the effect of considering the theory of Timoshenko in the vibration of AFG beams that support ground masses. As it is known, Timoshenko theory takes into account the shear deformation and the rotational inertia, provides more accurate results in the general study of beams and is mandatory in the case of high frequencies or non-slender beams. The Rayleigh-Ritz Method is employed to obtain approximated solutions of the problem. The accuracy of the procedure is verified through results available in the literature that can be represented by the model under study. The incidence of the Timoshenko theory is analyzed for different cases of beam slenderness, variation of its cross section and compositions of its constituent material, as well as different amounts and positions of the attached masses.

Keywords

References

  1. Chen, D.W. and Liu, T.L. (2006), "Free and forced vibrations of a tapered cantilever beam carrying multiple point masses", Struct. Eng. Mech., 23(2), 209-216. https://doi.org/10.12989/sem.2006.23.2.209
  2. Chen, D.W., Sun, D.L. and Li, X.F. (2017), "Surface effects on resonance frequencies of axially functionally graded Timoshenko nanocantilevers with attached nanoparticle", Compos. Struct., 173(1), 116-126. https://doi.org/10.1016/j.compstruct.2017.04.006
  3. Elishakoff, I., Kaplunov, J. and Nolde, E. (2015), "Celebrating the centenary of Timoshenko's study of effects of shear deformation and rotary inertia", Appl. Mech. Rev., 67(6), 060802. https://doi.org/10.1115/1.4031965
  4. Gan, B.S., Trinh, T.H., Le, T.H. and Nguyen, D.K. (2015), "Dynamic response of non-uniform Timoshenko beams made of axially FGM subjected to multiple moving point loads", Struct. Eng. Mech., 53(5), 981-995. https://doi.org/10.12989/sem.2015.53.5.981
  5. He, P., Liu, Z. and Li, C. (2013), "An improved beam element for beams with variable axial parameters", Shock Vibr., 20(4), 601-617. https://doi.org/10.1155/2013/708910
  6. Huang, Y., Yang, L. and Luo, Q. (2013), "Free vibration of axially functionally graded Timoshenko beams with non-uniform cross-section", Compos.: Part B, 45(1), 1493-1498. https://doi.org/10.1016/j.compositesb.2012.09.015
  7. Ilanko, S. and Monterrubio, L.E. (2014), The Rayleigh-Ritz Method for Structural Analysis, John Wiley & Sons Inc., London, U.K.
  8. Nikolic, A. (2017), "Free vibration analysis of a non-uniform axially functionally graded cantilever beam with a tip body", Arch. Appl. Mech., 87(7), 1227-1241. https://doi.org/10.1007/s00419-017-1243-z
  9. Rajasekaran, S. and Norouzzadeh Tochaei, E. (2014), "Free vibration analysis of axially functionally graded tapered Timoshenko beams using differential transformation element method and differential quadrature element method of lowest-order", Meccan., 49(4), 995-1009. https://doi.org/10.1007/s11012-013-9847-z
  10. Rossit, C.A., Bambill, D.V. and Gilardi, G.J. (2017), "Free vibrations of AFG cantilever tapered beams carrying attached masses", Struct. Eng. Mech., 61(5), 685-691. https://doi.org/10.12989/sem.2017.61.5.685
  11. Sarkar, K. and Ganguli, R. (2014), "Closed-form solutions for axially functionally graded Timoshenko beams having uniform cross-section and fixed-fixed boundary condition", Compos.: Part B, 58, 361-370. https://doi.org/10.1016/j.compositesb.2013.10.077
  12. Shahba, A., Attarnejad, R., Marvi, M.T. and Hajilar, S. (2011), "Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions", Compos.: Part B, 42(4), 801-808.
  13. Su, H., Banerjee, J.R. and Cheung, C.W. (2013), "Dynamic stiffness formulation and free vibration analysis of functionally graded beams", Compos. Struct., 106, 854-862. https://doi.org/10.1016/j.compstruct.2013.06.029
  14. Sun, D.L., Li, X.F. and Wang, C.Y. (2016), "Buckling of standing tapered Timoshenko columns with varying flexural rigidity under combined loadings", Int. J. Struct. Stab. Dyn., 16(6), 1550017. https://doi.org/10.1142/S0219455415500170
  15. Tang, A.Y., Wu, J.X., Li, X.F. and Lee, K.Y. (2014), "Exact frequency equations of free vibration of exponentially non-uniform functionally graded Timoshenko beams", Int. J. Mech. Sci., 89, 1-11. https://doi.org/10.1016/j.ijmecsci.2014.08.017
  16. Timoshenko, S.P. (1921), "On the correction for shear of the differential equation for transverse vibration of prismatic bar", Philosoph. Mag., 41(245), 744-746.
  17. Timoshenko, S.P. (1922), "On the transverse vibrations of bars of uniform cross section", Philosoph. Mag., 43(253), 125-131.
  18. Torabi, K., Afshari, H. and Heidari-Rarani M. (2013), "Free vibration analysis of a non-uniform cantilever Timoshenko beam with multiple concentrated masses using DQEM", Eng. Sol. Mech., 1(1), 9-20.
  19. Tudjono, S., Han, A., Nguyen, D., Kiryu, S. and Gan, B. (2017), "Exact shape functions for Timoshenko beam element", IOSR J. Comput. Eng., 19(3), 12-20.
  20. Zhao, Y., Huang, Y. and Guo, M. (2017), "A novel approach for free vibration of axially functionally graded beams with non-uniform cross-section based on Chebyshev polynomials theory", Compos. Struct., 168, 277-284. https://doi.org/10.1016/j.compstruct.2017.02.012