Computers and Concrete

  • 제26권3호
  • /
  • Pages.285-292
  • /
  • 2020
  • /
  • 1598-8198(pISSN)
  • /
  • 1598-818X(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Analytical solution of free vibration of FG beam utilizing different types of beam theories: A comparative study

  • 투고 : 2020.07.29
  • 심사 : 2020.09.11
  • 발행 : 2020.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

In engineering structures, to having the projected structure to serve all the engineering purposes, the theory to be used during the modeling stage is also of great importance. In the present work, an analytical solution of the free vibration of the beam composed of functionally graded materials (FGMs) is presented utilizing different beam theories. The comparison of supposed beam theory for free vibration of functionally graded (FG) beam is examined. For this aim, Euler-Bernoulli, Rayleigh, Shear, and Timoshenko beam theories are employed. The functionally graded material properties are assumed to vary continuously through the thickness direction of the beam with respect to the volume fraction of constituents. The governing equations of free vibration of FG beams are derived in the frameworks of four beam theories. Resulting equations are solved versus simply supported boundary conditions, analytically. To verify the results, comparisons are carried out with the available results. Parametrical studies are performed for discussing the effects of supposed beam theory, the variation of beam characteristics, and FGM properties on the free vibration of beams. In conclusion, it is found that the interaction between FGM properties and the supposed beam theory is of significance in terms of free vibration of the beams and that different beam theories need to be used depending on the characteristics of the beam in question.

키워드

과제정보

The financial support of the Suleyman Demirel University Scientific Research Projects Unit (SDU-BAP) with Grand No. 4857-YL1-17 is gratefully acknowledged. The authors would like to thank institution.

참고문헌

  1. Akgoz, B. and Civalek, O. (2017), "Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams", Compos. B Eng., 129, 77-87. https://doi.org/10.1016/j.compositesb.2017.07.024.
  2. Al Rjoub, Y.S. and Hamad, A.G. (2017), "Free vibration of functionally Euler-Bernoulli and Timoshenko graded porous beams using the transfer matrix method", KSCE J. Civil Eng., 21, 792-806. https://doi.org/10.1007/s12205-016-0149-6.
  3. Alsaid-Alwan, H.H.S. (2017), "Free vibration analysis of functionally graded beam with different engineering theories", Master of Science Thesis, Suleyman Demirel University, Graduate School of Natural and Applied Sciences, Department of Civil Engineering, Isparta.
  4. Anil, K.L., Panda, S.K., Sharma, N., Hirwani, C.K. and Topal, U. (2020), "Optimal fiber volume fraction prediction of layered composite using frequency constraints-A hybrid FEM approach", Comput. Concrete, 25(4), 303-310. https://doi.org/10.12989/cac.2020.25.4.303.
  5. Avcar M. (2015), "Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam", Struct. Eng. Mech., 55, 871-884. https://doi.org/10.12989/sem.2015.55.4.871.
  6. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.
  7. Avcar, M. and Alsaid-Alwan, H. (2017a), "Free vibration of functionally graded Rayleigh beam", Int. J. Eng. Appl. Sci., 9, 127-137. http://dx.doi.org/10.24107/ijeas.322884.
  8. Avcar, M. and Alsaid-Alwan, H. (2017b), "Free vibration analysis of functionally graded beams using different engineering theories", 4th International Conference on Computational and Experimental Science and Engineering (ICCESEN 2017), Antalya, Turkey.
  9. Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11(10), 232. https://doi.org/10.1007/s12517-018-3579-2.
  10. Ayache, B., Bennai, R., Fahsi, B., Fourn, H., Atmane, H.A. and Tounsi, A. (2018), "Analysis of wave propagation and free vibration of functionally graded porous material beam with a novel four variable refined theory", Earthq. Struct., 15(4), 369-382. https://doi.org/10.12989/eas.2018.15.4.369.
  11. Aydogdu, M., Arda, M. and Filiz, S. (2018), "Vibration of axially functionally graded nano rods and beams with a variable nonlocal parameter", Adv. Nano Res., Int. J., 6(3), 257-278. http://dx.doi.org/10.12989/anr.2018.6.3.257.
  12. Balubaid, M., Tounsi, A., Dakhel, B. and Mahmoud, S.R. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete, 24(6), 579-586. http://dx.doi.org/10.12989/cac.2019.24.6.579.
  13. Birman, V. and Byrd, L.W. (2007), "Modeling and analysis of functionally graded materials and structure", ASME Appl. Mech. Rev., 60(5), 195-216. https://doi.org/10.1115/1.2777164.
  14. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 1, 409-423. https://doi.org/10.12989/scs.2015.18.2.409.
  15. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras A., Bousahla A.A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. http://dx.doi.org/10.12989/sem.2019.71.2.185.
  16. Chakraverty, S. and Pradhan, K.K. (2016), Vibration Of Functionally Graded Beams and Plates, Academic Press.
  17. Civalek, O. and Kiracioglu, O. (2010), "Free vibration analysis of Timoshenko beams by DSC method", Int. J. Numer. Meth. Bio., 26(12), 1890-1898. https://doi.org/10.1002/cnm.1279.
  18. Civalek, O. and Ozturk, B. (2010), "Free vibration analysis of tapered beam-column with pinned ends embedded in Winkler-Pasternak elastic foundation", Geomech. Eng., 2(1), 45-56. http://dx.doi.org/10.12989/gae.2010.2.1.045.
  19. Dewangan, H.C., Panda, S.K. and Sharma, N. (2020a), "Experimental validation of role of cut-out parameters on modal responses of laminated composite-a coupled FE approach", Int. J. Appl. Mech., 2050068. https://doi.org/10.1142/S1758825120500684.
  20. Dewangan, H.C., Sharma, N., Hirwani, C.K. and Panda, S.K. (2020b), "Numerical eigenfrequency and experimental verification of variable cutout (square/rectangular) borne layered glass/epoxy flat/curved panel structure", Mech. Bas. Des. Struct. Mach., 1-18. https://doi.org/10.1080/15397734.2020.1759432.
  21. Ebrahimi, F., Barati, M.R. and Civalek, O (2020), "Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures", Eng. Comput., 36, 953-964. https://doi.org/10.1007/s00366-019-00742-z.
  22. Hadji, L., Daouadji, T.H. and Bedia, E.A. (2015), "A refined exponential shear deformation theory for free vibration of FGM beam with porosities", Geomech. Eng.., 9(3), 361-372. https://doi.org/10.12989/gae.2015.9.3.361.
  23. Hadji, L., Daouadji, T.H., Tounsi, A. and Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., 16(5), 507-519. http://dx.doi.org/10.12989/scs.2014.16.5.507.
  24. Han, M.S., Benaroya, H. and Wei, T. (1999), "Dynamics of transversely vibrating beams using four engineering theories", J. Sound Vib., 225, 935-988. https://doi.org/10.1006/jsvi.1999.2257.
  25. Hirwani, C.K. and Panda, S.K. (2019), "Nonlinear thermal free vibration frequency analysis of delaminated shell panel using FEM", Compos. Struct., 224, 111011. https://doi.org/10.1016/j.compstruct.2019.111011.
  26. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Bedia, E.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and free vibration analysis", Comput. Concrete, 25(1), 37-57. http://dx.doi.org/10.12989/cac.2020.25.1.037.
  27. Kahya, V. and Turan, M. (2018), "Vibration and buckling of laminated beams by a multi-layer finite element model", Steel Compos. Struct., 28(4), 415-426. http://dx.doi.org/10.12989/scs.2018.28.4.415.
  28. Kieback, B., Neubrand, A. and Riedel, H. (2003), "Processing techniques for functionally graded materials", Mater. Sci. Eng. A, 362, 81-106. https://doi.org/10.1016/S0921-5093(03)00578-1.
  29. Koizumi, M. (1993), "The concept of FGM", Ceram. Tran. Funct. Grad. Mater., 34, 3-10. https://doi.org/10.1080/10426919508935030.
  30. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B Eng., 28, 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9.
  31. Lee, J.W. and Lee, J.Y. (2019), "An exact transfer matrix method for coupled bending and bending vibrations of a twisted Timoshenko beam", Struct. Eng. Mech., 72(6), 797-807. http://dx.doi.org/10.12989/sem.2019.72.6.797.
  32. Li, S., Wan, Z. and Zhang, J. (2014), "Free vibration of functionally graded beams based on both classical and first-order shear deformation beam theories", Appl. Math. Mech., 35, 591-606. https://doi.org/10.1007/s10483-014-1815-6.
  33. Mahamood, R.M., Akinlabi, E.T., Shukla, M. and Pityana, S. (2012), "Functionally graded material: an overview", Proceedings of the World Congress on Engineering, Vol III, WCE 2012, London, UK.
  34. Mehar, K., Mishra, P.K. and Panda, S.K. (2020), "Numerical investigation of thermal frequency responses of graded hybrid smart nanocomposite (CNT-SMA-Epoxy) structure", Mech. Adv. Mater. Struct., 1-13. https://doi.org/10.1080/15376494.2020.1725193.
  35. Nejadi, M.M. and Mohammadimehr, M. (2020), "Analysis of a functionally graded nanocomposite sandwich beam considering porosity distribution on variable elastic foundation using DQM: Buckling and vibration behaviors", Comput. Concrete, 25(3), 215-224. https://doi.org/10.12989/cac.2020.25.3.215.
  36. Nguyen, T.K., Vo, T.P. and Thai, H.T. (2013), "Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory", Compos. B Eng., 55, 147-157. https://doi.org/10.1016/j.compositesb.2013.06.011.
  37. Pandey, H.K., Hirwani, C.K., Sharma, N., Katariya, P.V., Dewangan, H.C. and Panda, S.K. (2019), "Effect of nano glass cenosphere filler on hybrid composite eigenfrequency responses-An FEM approach and experimental verification", Adv. Nano Res., 7(6), 419-429. https://doi.org/10.12989/anr.2019.7.6.419.
  38. Patle, B.K., Hirwani, C.K., Singh, R.P. and Panda, S.K. (2018), "Eigenfrequency and deflection analysis of layered structure using uncertain elastic properties-a fuzzy finite element approach", Int. J. Approx. Reason., 98, 163-176. https://doi.org/10.1016/j.ijar.2018.04.013.
  39. Rahmani, M.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A., Mahmoud, S.R., Benrahou, K.H. and Tounsi, A. (2020), "Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory", Comput. Concrete, 25(3), 225-244. http://dx.doi.org/10.12989/cac.2020.25.3.225.
  40. Ramteke, P.M., Panda, S.K. and Sharma, N. (2019), "Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure", Steel Compos. Struct., 33(6), 865-875 https://doi.org/10.12989/scs.2019.33.6.865.
  41. Rao, S.S. (2007), Vibration of Continuous Systems, Wiley, New York, USA.
  42. Sahoo, S.S., Panda, S.K., Mahapatra, T.R. and Hirwani, C.K. (2019), "Numerical analysis of transient responses of delaminated layered structure using different mid-plane theories and experimental validation", Iran J. Sci. Technol. Tran. Mech. Eng., 43, 41-56. https://doi.org/10.1007/s40997-017-0111-3.
  43. Sahouane, A., Hadji, L. and Bourada, M. (2019), "Numerical analysis for free vibration of functionally graded beams using an original HSDBT", Earthq. Struct., 17(1), 31-37. https://doi.org/10.12989/eas.2019.17.1.031.
  44. Sahu, P., Sharma, N. and Panda, S.K. (2020), "Numerical prediction and experimental validation of free vibration responses of hybrid composite (Glass/Carbon/Kevlar) curved panel structure", Compos. Struct., 241, 112073. https://doi.org/10.1016/j.compstruct.2020.112073.
  45. Shokravi, M. (2017), "Vibration analysis of silica nanoparticles-reinforced concrete beams considering agglomeration effects", Comput. Concrete, 19(3), 333-338. http://dx.doi.org/10.12989/cac.2017.19.3.333.
  46. Suresh, S. and Mortensen, A. (1998), Fundamentals of Functionally Graded Materials: Processing and Thermomechanical Behavior of Graded Metals and Metal-Ceramic Composites, IOM Communications, London, UK.
  47. 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.2012.05.0143
  48. Timoshenko, S.P. (1937), Vibration Problems in Engineering, D. Van Nostrand, Princeton, NJ, USA.
  49. Wang, J.R., Liu, T.L. and Chen, D.W. (2007), "Free vibration analysis of a Timoshenko beam carrying multiple spring-mass systems with the effects of shear deformation and rotary inertia", Struct Eng. Mech., 26(1), 1-14. http://dx.doi.org/10.12989/sem.2007.26.1.001.
  50. Wang, X. and Li, S. (2016), "Free vibration analysis of functionally graded material beams based on Levinson beam theory", Appl. Math. Mech., 37, 861-878. https://doi.org/10.1007/s10483-016-2094-9.
  51. Wattanasakulpong, N. and Ungbhakorn, V. (2012), "Free vibration analysis of functionally graded beams with general elastically end constraints by DTM", World J. Mech., 2, 297-310. https://doi.org/10.4236/wjm.2012.26036.
  52. Yildirim, V. and Kiral, E. (2000), "Investigation of the rotary inertia and shear deformation effects on the out-of-plane bending and torsional natural frequencies of laminated beams", Compos. Struct., 49(3), 313-320. https://doi.org/10.1016/S0263-8223(00)00063-5.

피인용 문헌

  1. Coupled Vibration Characteristics Analysis of Hot Rolling Mill with Structural Gap vol.2021, 2020, https://doi.org/10.1155/2021/5581398
  2. Vibration behavior of bi-dimensional functionally graded beams vol.77, pp.5, 2020, https://doi.org/10.12989/sem.2021.77.5.587
  3. Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory vol.10, pp.3, 2020, https://doi.org/10.12989/anr.2021.10.3.281