Geomechanics and Engineering

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A refined exponential shear deformation theory for free vibration of FGM beam with porosities

  • Hadji, Lazreg (Universite Ibn Khaldoun) ;
  • Daouadji, T. Hassaine (Universite Ibn Khaldoun) ;
  • Bedia, E. Adda (Laboratoire des Materiaux & Hydrologie, Universite de Sidi Bel Abbes)
  • Received : 2015.03.10
  • Accepted : 2015.05.08
  • Published : 2015.09.25
⟨ Previous Next ⟩

Abstract

In this paper, a refined exponential shear deformation theory for free vibration analysis of functionally graded beam with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton's principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

Keywords

References

  1. Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with properties using various", Struct. Eng. Mech., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  2. Benatta, M.A., Tounsi, A., Mechab, I. and Bachir Bouiadjra, M. (2009), "Mathematical solution for bending of short hybrid composite beams with variable fibers spacing", Appl. Math. Comput., 212(2), 337-348. https://doi.org/10.1016/j.amc.2009.02.030
  3. Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14(1), 5-33. https://doi.org/10.1177/1099636211426386
  4. 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
  5. Hadji, L., Daouadji, T.H., Tounsi, A. and Adda Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., Int. J., 16(5), 507-519. https://doi.org/10.12989/scs.2014.16.5.507
  6. Kadoli, R., Akhtar, K. and Ganesan, N. (2008), "Static analysis of functionally graded beams using higher order shear deformation theory", Appl. Math. Model., 32(12), 2509-2525. https://doi.org/10.1016/j.apm.2007.09.015
  7. Klouche Djedid, I., Benachour, A., Houari, M.S.A., Tounsi, A. and Ameur, M. (2014), "A n-order four variable refined theory for bending and free vibration of functionally graded plates", Steel Compos. Struct., Int. J., 17(1), 21-46. https://doi.org/10.12989/scs.2014.17.1.021
  8. 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
  9. Merazi, M., Hadji, L., Hassaine Dauadji, T., Tounsi, A. and Adda Bedia, E. (2015), "A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position", Geomech. Eng., Int. J., 8(3), 305-321. https://doi.org/10.12989/gae.2015.8.3.305
  10. Nedri, K., El Meiche, N. and Tounsi, A. (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory", Mech. Compos. Mater., 49(6), 641-650. https://doi.org/10.1007/s11029-013-9380-0
  11. Sallai, B.O., Tounsi, A., Mechab, I., Bachir, B.M., Meradjah, M. and Adda Bedia, E.A. (2009), "A theoretical analysis of flexional bending of Al/Al2O3 S-FGM thick beams", Computat. Mater. Sci., 44(4), 1344-1350.
  12. Simsek, M. (2010a), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nucl. Eng. Des., 240(4), 697-705. https://doi.org/10.1016/j.nucengdes.2009.12.013
  13. Simsek, M. (2010b), "Vibration analysis of a functionally graded beam under a moving mass by using different beam theories", Compos. Struct., 92(4), 904-917. https://doi.org/10.1016/j.compstruct.2009.09.030
  14. Sina, S.A., Navazi, H.M. and Haddadpour, H. (2009), "An analytical method for free vibration analysis of functionally graded beams", Mater. Des., 30(3), 741-747. https://doi.org/10.1016/j.matdes.2008.05.015
  15. Tai, H.T. and Vo, P.V. (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
  16. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-112. https://doi.org/10.1016/j.ast.2013.12.002
  17. Wattanasakulpong, N., Prusty, B.G., Kelly, D.W. and Hoffman, M. (2012), "Free vibration analysis of layered functionally graded beams with experimental validation", Mater. Des., 36, 182-190. https://doi.org/10.1016/j.matdes.2011.10.049
  18. 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
  19. Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of $ZrO_2$-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68(1-3), 130-135. https://doi.org/10.1016/S0254-0584(00)00355-2

Cited by

  1. On vibrations of porous nanotubes vol.125, 2018, https://doi.org/10.1016/j.ijengsci.2017.12.009
  2. Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations vol.10, pp.6, 2016, https://doi.org/10.12989/eas.2016.10.6.1429
  3. Static analysis of the FGM plate with porosities vol.21, pp.1, 2016, https://doi.org/10.12989/scs.2016.21.1.123
  4. A new shear deformation plate theory with stretching effect for buckling analysis of functionally graded sandwich plates vol.24, pp.5, 2017, https://doi.org/10.12989/scs.2017.24.5.569
  5. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2015, https://doi.org/10.12989/gae.2017.13.3.385
  6. Analytical analysis of the interfacial shear stress in RC beams strengthened with prestressed exponentially-varying properties plate vol.7, pp.1, 2018, https://doi.org/10.12989/amr.2018.7.1.029
  7. Improved HSDT accounting for effect of thickness stretching in advanced composite plates vol.66, pp.1, 2015, https://doi.org/10.12989/sem.2018.66.1.061
  8. Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates vol.14, pp.6, 2015, https://doi.org/10.12989/gae.2018.14.6.519
  9. Free vibration and buckling analysis of orthotropic plates using a new two variable refined plate theory vol.15, pp.1, 2015, https://doi.org/10.12989/gae.2018.15.1.711
  10. Dynamic analysis for anti-symmetric cross-ply and angle-ply laminates for simply supported thick hybrid rectangular plates vol.7, pp.2, 2015, https://doi.org/10.12989/amr.2018.7.2.119
  11. A new nonlocal HSDT for analysis of stability of single layer graphene sheet vol.6, pp.2, 2015, https://doi.org/10.12989/anr.2018.6.2.147
  12. On the elastic parameters of the strained media vol.67, pp.1, 2015, https://doi.org/10.12989/sem.2018.67.1.053
  13. Geometrically nonlinear analysis of functionally graded porous beams vol.27, pp.1, 2015, https://doi.org/10.12989/was.2018.27.1.059
  14. Nonlinear frequency analysis of beams resting on elastic foundation using max-min approach vol.16, pp.4, 2015, https://doi.org/10.12989/gae.2018.16.4.355
  15. Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory vol.28, pp.1, 2015, https://doi.org/10.12989/was.2019.28.1.019
  16. Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections vol.17, pp.2, 2019, https://doi.org/10.12989/gae.2019.17.2.175
  17. Effect of distribution shape of the porosity on the interfacial stresses of the FGM beam strengthened with FRP plate vol.16, pp.5, 2015, https://doi.org/10.12989/eas.2019.16.5.601
  18. Analyzing nonlinear mechanical-thermal buckling of imperfect micro-scale beam made of graded graphene reinforced composites vol.8, pp.3, 2015, https://doi.org/10.12989/amr.2019.8.3.219
  19. Influence of the distribution shape of porosity on the bending FGM new plate model resting on elastic foundations vol.72, pp.1, 2015, https://doi.org/10.12989/sem.2019.72.1.061
  20. A simple quasi-3D HDST for dynamic behavior of advanced composite plates with the effect of variables elastic foundations vol.22, pp.5, 2015, https://doi.org/10.12989/gae.2020.22.5.415
  21. Analytical solution of free vibration of FG beam utilizing different types of beam theories: A comparative study vol.26, pp.3, 2020, https://doi.org/10.12989/cac.2020.26.3.285
  22. Forced vibration of a functionally graded porous beam resting on viscoelastic foundation vol.24, pp.1, 2015, https://doi.org/10.12989/gae.2021.24.1.091
  23. Modeling and analysis of the imperfect FGM-damaged RC hybrid beams vol.6, pp.2, 2015, https://doi.org/10.12989/acd.2021.6.2.117