Structural Engineering and Mechanics

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Free vibration analysis of edge cracked symmetric functionally graded sandwich beams

  • Cunedioglu, Yusuf (Mechanical Engineering Department, Faculty of Engineering, Nigde University)
  • Received : 2015.05.01
  • Accepted : 2015.11.24
  • Published : 2015.12.25
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Abstract

In this study, free vibration analysis of an edge cracked multilayered symmetric sandwich beams made of functionally graded materials are investigated. Modelling of the cracked structure is based on the linear elastic fracture mechanics theory. Material properties of the functionally graded beams change in the thickness direction according to the power and exponential laws. To represent functionally graded symmetric sandwich beams more realistic, fifty layered beam is considered. Composition of each layer is different although each layer is isotropic and homogeneous. The considered problem is carried out within the Timoshenko first order shear deformation beam theory by using finite element method. A MATLAB code developed to calculate natural frequencies for clamped and simply supported conditions. The obtained results are compared with published studies and excellent agreement is observed. In the study, the effects of crack location, depth of the crack, power law index and slenderness ratio on the natural frequencies are investigated.

Keywords

References

  1. Akbas, S.D. (2013), "Geometrically nonlinear static analysis of edge cracked Timoshenko beams composed of functionally graded material", Math. Prob. Eng., Article ID 871815, 14.
  2. Akbas, S.D. (2013), "Free vibration characteristics of edge cracked functionally graded beams by using finite element method", IJETT, 4(10), 4590-4597.
  3. Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, 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
  4. Aydin, K. (2013), "Free vibration of functionally graded beams with arbitrary number of surface cracks", Eur. J. Mech. A-Solid., 42, 112-124. https://doi.org/10.1016/j.euromechsol.2013.05.002
  5. 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
  6. Cunedioglu, Y. and Beylergil, B. (2014), "Free vibration analysis of laminated composite beam under room and high temperatures", Struct. Eng. Mech., 51(1), 111-130. https://doi.org/10.12989/sem.2014.51.1.111
  7. Demir, E., Callioglu, H. and Sayer, M. (2013), "Free vibration of symmetric FG sandwich Timoshenko beam with simply supported edges", Indian J. Eng. Mater. S, 20(6), 515-521.
  8. Elishakoff, I. and Candan, S. (2001), "Apparently first closed-form solution for vibrating: inhomogeneous beams", Int. J. Solid. Struct., 38(19), 3411-3441. https://doi.org/10.1016/S0020-7683(00)00266-3
  9. Ferezqi, H.Z., Tahani, M. and Toussi, H.E. (2010), "Analytical approach to free vibrations of cracked Timoshenko beams made of functionally graded materials", Mech. Adv. Mater. Struct., 17(5), 353-365. https://doi.org/10.1080/15376494.2010.488608
  10. Gibson, R.F. (1994), Principles of Composite Materials, First Edition, McGraw-Hill, New York.
  11. Giunta, G., Crisafulli, D., Belouettar, S. and Carrera, E. (2011), "Hierarchical theories for the free vibration analysis of functionally graded beams", Compos. Struct., 94(1), 68-74. https://doi.org/10.1016/j.compstruct.2011.07.016
  12. Ke, L.L., Yang, J., Kitipornchai, S. and Xiang, Y. (2009), "Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials", Mech. Adv. Mater. Struct., 16(6), 488-502. https://doi.org/10.1080/15376490902781175
  13. Kisa, M. (2004), "Free vibration analysis of a cantilever composite beam with multiple cracks", Compos. Sci. Technol., 64(9), 1391-1402. https://doi.org/10.1016/j.compscitech.2003.11.002
  14. Kisa, M. and Brandon, J. (2000), "The effects of closure of cracks on the dynamics of a cracked cantilever beam", J. Sound. Vib., 238(1), 1-18. https://doi.org/10.1006/jsvi.2000.3099
  15. Kisa, M., Brandon, J. and Topcu, M. (1998), "Free vibration analysis of cracked beams by a combination of finite elements and component mode synthesis methods", Comput. Struct., 67(4), 215-223. https://doi.org/10.1016/S0045-7949(98)00056-X
  16. Kitipornchai, S., Ke, L.L., Yang, J. and Xiang, Y. (2009), "Nonlinear vibration of edge cracked functionally graded Timoshenko beams", J. Sound. Vib., 324(3-5), 962-982. https://doi.org/10.1016/j.jsv.2009.02.023
  17. Li, S., Hu, J.J., Zhai, C.H. and Xie, L.L. (2013), "A unified method for modeling of axially and/or transversally functionally graded beams with variable cross-section profile", Mech. Bas. Des. Struc., 41(2), 168-188. https://doi.org/10.1080/15397734.2012.709466
  18. 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
  19. Matbuly, M.S., Ragb, O. and Nassar, M. (2009), "Natural frequencies of a functionally graded cracked beam using the differential quadrature method", Appl. Math. Comput., 215(6), 2307-2316. https://doi.org/10.1016/j.amc.2009.08.026
  20. Petyt, M. (1990), Introduction toFfinite Element Vibration Analysis, First Edition, Cambridge University Press, Cambridge.
  21. Pradhan, K.K. and Chakraverty, S. (2013), "Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method", Compos. Part B-Eng., 51, 175-184. https://doi.org/10.1016/j.compositesb.2013.02.027
  22. 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-Eng., 42(4), 801-808.
  23. Simsek, M., Kocaturk, T. and Akbas, S.D. (2012), "Dynamic behavior of an axially functionally graded beam under action of a moving harmonic load", Compos. Struct., 94(8), 2358-2364. https://doi.org/10.1016/j.compstruct.2012.03.020
  24. Su, H. and Banerjee, J.R. (2015), "Development of dynamic stiffness method for free vibration of functionally graded Timoshenko beams", Comput. Struct,. 147, 107-116. https://doi.org/10.1016/j.compstruc.2014.10.001
  25. Thai, H.T. and Vo, T.P. (2012), "Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories", Int. J. Mech. Sci., 62(1), 57-66. https://doi.org/10.1016/j.ijmecsci.2012.05.014
  26. Wattanasakulpong, N., Prusty, G.B. and Kelly, D.W. (2013), "Free and forced vibration analysis using improved third-order shear deformation theory for functionally graded plates under high temperature loading", J. Sandw. Struct. Mater., 15(5), 583-606. https://doi.org/10.1177/1099636213495751
  27. Wei, D., Liu, Y.H. and Xiang, Z.H. (2012), "An analytical method for free vibration analysis of functionally graded beams with edge cracks", J. Sound Vib., 331(7), 1686-1700. https://doi.org/10.1016/j.jsv.2011.11.020
  28. Yan, T., Kitipornchai, S. and Yang, J. (2011), "Parametric instability of functionally graded beams with an open edge crack under axial pulsating excitation", Compos. Struct., 93(7), 1801-1808. https://doi.org/10.1016/j.compstruct.2011.01.019
  29. Yan, T., Kitipornchai, S., Yang, J. and He, X.Q. (2011), "Dynamic behaviour of edge-cracked shear deformable functionally graded beams on an elastic foundation under a moving load", Compos. Struct., 93(11), 2992-3001. https://doi.org/10.1016/j.compstruct.2011.05.003
  30. Yan, T. and Yang, J. (2011), "Forced vibration of edge-cracked functionally graded beams due to a transverse moving load", Procedia Eng., 14, 3293-3300. https://doi.org/10.1016/j.proeng.2011.07.416
  31. 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

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