Structural Engineering and Mechanics

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Eigen analysis of functionally graded beams with variable cross-section resting on elastic supports and elastic foundation

  • Duy, Hien Ta (Department of Civil and Environmental Engineering, Sejong University) ;
  • Van, Thuan Nguyen (Department of Civil and Environmental Engineering, Sejong University) ;
  • Noh, Hyuk Chun (Department of Civil and Environmental Engineering, Sejong University)
  • Received : 2014.02.26
  • Accepted : 2014.08.31
  • Published : 2014.12.10
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Abstract

The free vibration of functionally graded material (FGM) beams on an elastic foundation and spring supports is investigated. Young's modulus, mass density and width of the beam are assumed to vary in thickness and axial directions respectively following the exponential law. The spring supports are also taken into account at both ends of the beam. An analytical formulation is suggested to obtain eigen solutions of the FGM beams. Numerical analyses, based on finite element method by using a beam finite element developed in this study, are performed in order to show the legitimacy of the analytical solutions. Some results for the natural frequencies of the FGM beams are given considering the effect of various structural parameters. It is also shown that the spring supports show the greatest effect on the natural frequencies of FGM beams.

Keywords

Acknowledgement

Supported by : Korea Institute of Energy Technology Evaluation and Planning (KETEP)

References

  1. Abu-Hilal, M. and Mohsen, M. (2000), "Vibration of beams with general boundary conditions due to a moving harmonic load", J. Sound Vib., 232(4), 703-717. https://doi.org/10.1006/jsvi.1999.2771
  2. Alshorbagy, A.E., Eltaher, M.A. and Mahmound, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006
  3. Calim, F.F. (2009), "Free and forced vibrations of non-uniform composite beams", Comput. Struct., 88(3), 413-423. https://doi.org/10.1016/j.compstruct.2008.05.001
  4. Caruntu, D.I. (2009), "Dynamic modal characteristics of transverse vibrations of cantilevers of parabolic thickness", Mech. Res. Commun., 36(3), 391-404. https://doi.org/10.1016/j.mechrescom.2008.07.005
  5. Chakraborty, A., Gopalakrishnan, S. and Reddy, J.N. (2003), "A new beam finite element for the analysis of functionally graded materials", Int. J. Mech. Sci., 45(3), 519-539. https://doi.org/10.1016/S0020-7403(03)00058-4
  6. Ece, M.C., Aydogdu, M. and Taskin, V. (2007), "Vibration of a variable cross-section beam", Mech. Res. Commun., 34, 78-84. https://doi.org/10.1016/j.mechrescom.2006.06.005
  7. Gupta, A. (1985), "Vibration of tapered beams", J. Struct. Eng., 111(1), 19-36. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:1(19)
  8. Gutierrez, R.H., Laura, P.A.A. and Rossi, R.E. (1991), "Vibrations of a timoshenko beam of non-uniform cross-section elastically restrained at one end and carrying a finite mass at the other", Oce. Eng., 18(1-2), 129-145. https://doi.org/10.1016/0029-8018(91)90038-R
  9. Haasen, A.A., Abdelouahed, T., Sid, A.M. and Hichem, A.B. (2011), "Free vibration behavior of exponential functionally graded beams with varying cross-section", J. Vib. Cont., 17(2), 311-318. https://doi.org/10.1177/1077546310370691
  10. Ke, L.L., Yang, J. and Kitipornchai, S. (2010), "An analytical study on the nonlinear vibration of functionally graded beams", Meccanica, 45(6), 743-752. https://doi.org/10.1007/s11012-009-9276-1
  11. Klein, L. (1974), "Transverse vibrations of non-uniform beams", J. Sound Vib., 37(4), 491-505. https://doi.org/10.1016/S0022-460X(74)80029-5
  12. Lardner, T.J. (1968), "Vibration of beams with exponentially varying properties", Acta Mech., 6(2-3), 197-202. https://doi.org/10.1007/BF01170383
  13. Lee, S.Y. and Lin, S.M. (1995), "Vibrations of elastically restrained non-uniform timoshenko beams", J. Sound Vib., 184(3), 403-415. https://doi.org/10.1006/jsvi.1995.0324
  14. Mohanty, S.C., Dash, R.R. and Rout, T. (2011), "Parametric instability of a functionally graded Timoshenko beam on Winkler's elastic foundation", Nucl. Eng. Des., 241(8), 2698-2715. https://doi.org/10.1016/j.nucengdes.2011.05.040
  15. Mohanty, S.C., Dash, R.R. and Rout, T. (2012), "Vibration and dynamic stability analysis of a functionally graded timoshenko beam on pasternak elastic foundation", Int. J. Aero. Light. Struct., 2(3), 383-403.
  16. Mohanty, S.C., Dash, R.R. and Rout, T. (2013), "Free vibration of a functionally graded rotating timoshenko beam using FEM", Adv. Struct. Eng., 16(2), 405-418. https://doi.org/10.1260/1369-4332.16.2.405
  17. Pakar, M.B. (2012), "Accurate analytical solution for nonlinear free vibration of beams", Struct. Eng. Mech., 43(3), 337-347. https://doi.org/10.12989/sem.2012.43.3.337
  18. Ramalingerswara Rao, S. and Ganesan, N. (1995), "Dynamic response of tapered composite beams using higher order shear deformation theory", J. Sound Vib., 187(5), 737-756. https://doi.org/10.1006/jsvi.1995.0560
  19. Sen, Y.L. and Huel Yaw, K. (1990), "Free vibrations of non-uniform beams resting on non-uniform elastic foundation with general elastic end restraints", Comput. Struct., 34(3), 421-429. https://doi.org/10.1016/0045-7949(90)90266-5
  20. Simsek, M. and Cansiz, S. (2012), "Dynamics of elastically connected double-functionally graded beam systems with different boundary conditions under action of a moving harmonic load", Compos. Struct., 94(9), 2861-2878. https://doi.org/10.1016/j.compstruct.2012.03.016
  21. Suppiger, E. and Taleb, N. (1956), "Free lateral vibration of beams of variable cross section", J. Appl. Math. Phys., ZAMP, 7(6), 501-520. https://doi.org/10.1007/BF01601179
  22. Tong, X., Tabarrok, B. and Yeh, K.Y. (1995), "Vibration analysis of timoshenko beams with nonhomogeneity and varying cross-section", J. Sound Vib., 186(5), 821-835. https://doi.org/10.1006/jsvi.1995.0490
  23. Wang, R.T. (1997), "Vibration of multi-span timoshenko beams to a moving force", J. Sound Vib., 207(5), 731-742. https://doi.org/10.1006/jsvi.1997.1188
  24. 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, 209-219. https://doi.org/10.1016/j.compstruct.2007.07.004
  25. Zhou, D. (1993), "A general solution to vibrations of beams on variable winkler elastic foundation", Comput. Struct., 47(1), 83-90. https://doi.org/10.1016/0045-7949(93)90281-H

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