Steel and Composite Structures

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Vibration analysis of functionally graded material (FGM) grid systems

  • Darilmaz, Kutlu (Istanbul Technical University, Civil Engineering Department)
  • Received : 2013.12.17
  • Accepted : 2014.07.27
  • Published : 2015.02.25
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Abstract

The paper considers the free vibration analysis of FGM grid systems. Up to now, very little work has been done on this type of system and the paper aspires to fill this gap. Based on the hybrid-stress finite element formulation free vibration solutions for FGM grid systems of various aspect ratios, different types of gradations functions, and support conditions are determined. The tabulation of these results, not available thus far, should be useful to designers and researchers who may use them.

Keywords

References

  1. Anandrao, K.S., Gupta, R.K., Ramchandran, P. and Rao, G.V. (2012), "Non-linear free vibrations and post-buckling analysis of shear flexible functionally graded beams", Struct. Eng. Mech., Int. J., 44(3) , 339-361. https://doi.org/10.12989/sem.2012.44.3.339
  2. Atmane, H.A., Tounsi, A., Ziane, N. and Mechab, I. (2011), "Mathematical solution for free vibration of sigmoid functionally graded beams with varying cross-section", Steel Compos. Struct., Int. J., 11(6), 489-504. https://doi.org/10.12989/scs.2011.11.6.489
  3. ANSYS (1997), Swanson Analysis Systems, Swanson J. ANSYS 5.4, USA.
  4. Aydogdu, M. and Taskin, V. (2007), "Free vibration analysis of functionally graded beams with simply supported edges", Mater. Des., 28(5), 1651-1656. https://doi.org/10.1016/j.matdes.2006.02.007
  5. Chakraborty, A. and Gopalakrishnan, S. (2003), "A spectrally formulated finite element for wave propagation analysis in functionally graded beams", Int. J. Solid Struct., 40(10), 2421-2448. https://doi.org/10.1016/S0020-7683(03)00029-5
  6. 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
  7. Ching, H.K. and Yen, S.C. (2005), "Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads", J. Compos. Part B: Eng., 36(3), 223-240. https://doi.org/10.1016/j.compositesb.2004.09.007
  8. Ching, H.K. and Yen, S.C. (2006), "Transient thermoelastic deformations of 2D functionally graded beams under nonuniformly convective heat supply", Compos. Struct., 73, 381-393. https://doi.org/10.1016/j.compstruct.2005.02.021
  9. Darilmaz, K. (2011), "Influence of aspect ratio and fibre orientation on the stability of simply supported orthotropic skew plates", Steel Compos. Struct., Int. J., 11(5), 359-374. https://doi.org/10.12989/scs.2011.11.5.359
  10. Darilmaz, K. (2012), "Analysis of sandwich plates: A three-dimensional assumed stress hybrid finite element", J. Sandw. Struct. Mater., 14(4), 487-501. https://doi.org/10.1177/1099636212443916
  11. Kapuria, S., Bhattacharyya, M. and Kumar, A.N. (2008), "Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation", Compos. Struct., 82(3), 390-402. https://doi.org/10.1016/j.compstruct.2007.01.019
  12. Kim, J. and Paulino, G.H. (2002), "Finite element evaluation of mixed mode stress intensity factors in functionally graded materials", Int. J. Numer. Meth. Eng., 53(8), 1903-1935. https://doi.org/10.1002/nme.364
  13. Li, X.F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams", J. Sound Vib., 318(4-5), 1210-1229. https://doi.org/10.1016/j.jsv.2008.04.056
  14. Li, S.R. and Batra, R.C. (2013), "Relations between buckling loads of functionally graded Timoshenko and homogeneous Euler-Bernoulli beams", Compos. Struct., 95, 5-9. https://doi.org/10.1016/j.compstruct.2012.07.027
  15. Pian, T.H.H. and Chen, D.P. (1983), "On the suppression of zero energy deformation modes", Int. J. Numer. Meth. Eng., 19(12), 1741-1752. https://doi.org/10.1002/nme.1620191202
  16. Pradhan, K.K. and Chakraverty, S. (2013), "Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method", Compos.: Part B, 51, 175-184. https://doi.org/10.1016/j.compositesb.2013.02.027
  17. Qian, L.F. and Ching, H.K. (2004), "Static and dynamic analysis of 2D functionally graded elasticity by using meshless local Petrov-Galerkin method", J. Chinese Inst. Eng., 27, 491-503. https://doi.org/10.1080/02533839.2004.9670899
  18. Sankar, B.V. (2001), "An elasticity solution for functionally graded beams", Compos. Sci. Technol., 61(5), 689-696. https://doi.org/10.1016/S0266-3538(01)00007-0
  19. Simsek, M. and Kocaturk, T. (2009), "Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load", Compos. Struct., 90(4), 465-473. https://doi.org/10.1016/j.compstruct.2009.04.024
  20. Tajalli, S.A., Rahaeifard M., Kahrobaiyan, M.H., Movahhedy, M.R., Akbari, J. and Ahmadian, M.T. (2013), "Mechanical behavior analysis of size-dependent micro-scaled functionally graded Timoshenko beams by strain gradient elasticity theory", Compos. Struct., 102, 72-80. https://doi.org/10.1016/j.compstruct.2013.03.001
  21. Wakashima, K., Hirano, T. and Niino, M. (1990), "Space applications of advanced structural materials", ESA SP-303: 97.
  22. Xiang, H.J. and Yang, J. (2008), "Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction", J. Compos.: Part B., 39(2), 292-303. https://doi.org/10.1016/j.compositesb.2007.01.005
  23. Yang, J. and Chen, Y. (2008), "Free vibration and buckling analyses of functionally graded beams with edge cracks", Compos. Struct., 83(1), 48-60. https://doi.org/10.1016/j.compstruct.2007.03.006
  24. Yang, J., Chen, Y., Xiang, Y. and Jia, X.L. (2008), "Free and forced vibration of cracked inhomogeneous beams under an axial force and a moving load", J. Sound Vib., 312(1-2), 166-181. https://doi.org/10.1016/j.jsv.2007.10.034
  25. Ying, J., Lue, C.F. and Chen, W.Q. (2008), "Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations", Compos. Struct., 84(3), 209-219. https://doi.org/10.1016/j.compstruct.2007.07.004
  26. Zhong, Z. and Yu, T. (2007), "Analytical solution of a cantilever functionally graded beam", Compos. Sci. Technol., 67(3-4), 481-488. https://doi.org/10.1016/j.compscitech.2006.08.023

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