Geomechanics and Engineering

  • 제25권5호
  • /
  • Pages.383-394
  • /
  • 2021
  • /
  • 2005-307X(pISSN)
  • /
  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Investigating of free vibration behavior of bidirectional FG beams resting on variable elastic foundation

  • Benaberrahmane, Ismail (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Benyoucef, Samir (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Sekkal, Mohamed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Mekerbi, Mohamed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Bouiadjra, Rabbab Bachir (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Selim, Mahmoud M. (Department of Mathematics, Al-Aflaj College of Science and Humanities, Prince Sattam bin Abdulaziz University) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Hussain, Muzamal (Department of Mathematics, Government College University Faisalabad)
  • 투고 : 2021.01.15
  • 심사 : 2021.05.28
  • 발행 : 2021.06.10
⟨ 이전 논문 다음 논문 ⟩

초록

In the present study, the free vibration of bidirectional functionally graded (FG) beams resting on variable elastic foundation are comprehensively investigated. The beam's behavior is modeled using 2D displacement field that contain undetermined integral terms and involves a reduced unknown functions. The material properties of the FG beam are assumed to be graded in both the thickness and longitudinal directions according to a power law. The beams are considered simply supported and resting on variable elastic foundation. The differential equation system governing the free vibration behavior of bidirectional beams is derived based on the Hamilton principle. The problem is then solved using the Navier solution for a simply supported beam. The accuracy of the used model can be noticed by comparing it with other solutions available in the literature where a good conformance was obtained. A detailed parametric study is conducted to explore the influences of material composition and variable elastic parameters on the vibration characteristics of the beams. The results reveal that the grading indexes in one or both directions as well as the parameters of the elastic foundation strongly impact the fundamental frequencies.

키워드

참고문헌

  1. Al-Basyouni, K. S., Ghandourah, E., Mostafa, H.M. and Algarni, A. (2020), "Effect of the rotation on the thermal stress wave propagation in non-homogeneous viscoelastic body", Geomech. Eng., 21(1), 1-9. https://doi.org/10.12989/gae.2020.21.1.001.
  2. Ali Rachedi, M., Benyoucef, S., Bouhadra, A., Bachir Bouiadjra, R., Sekkal, M. and Benachour, A. (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. Eng., 22(1), 65-80. http://doi.org/10.12989/gae.2020.22.1.065.
  3. Al-Osta, M.A. (2019), "Shear behaviour of RC beams retrofitted using UHPFRC panels epoxied to the sides", Comput. Concrete, 24(1), 37-49. http://doi.org/10.12989/cac.2019.24.1.037
  4. Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.
  5. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. https://doi.org/10.12989/SCS.2015.19.6.1421.
  6. Attia, M.A. (2017), "On the mechanics of functionally graded nanobeams with the account of surface elasticity", Int. J. Eng. Sci., 115, 73-101. https://doi.org/10.1016/j.ijengsci.2017.03.011.
  7. 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.
  8. Bachir Bouiadjra, R., Bachiri, A., Benyoucef, S., Fahsi, B. and Bernard, F. (2020), "An investigation of the thermodynamic effect of FG beam on elastic foundation", Struct. Eng. Mech., 76(1), 115-127. https://doi.org/10.12989/sem.2020.76.1.115.
  9. Bachiri, A., Bourada, M., Mahmoudi, A., Benyoucef, S. and Tounsi, A. (2018), "Thermodynamic effect on the bending response of elastic foundation FG plate by using a novel four variable refined plate theory", J. Therm. Stresses, 41(8), 1042-1062. https://doi.org/10.1080/01495739.2018.1452169.
  10. Benferhat, R., Daouadji, T.H. and Adim, B. (2016), "A novel higher order shear deformation theory based on the neutral surface concept of FGM plate under transverse load", Adv. Mater. Res., 5(2), 107-120. https://doi.org/10.12989/amr.2016.5.2.107.
  11. Bhattacharya, S. and Das, D. (2019), "Free vibration analysis of bidirectional-functionally graded and double-tapered rotating micro-beam in thermal environment using modified couple stress theory", Compos. Struct., 215, 471-492. https://doi.org/10.1016/j.compstruct.2019.01.080.
  12. Boulal, A., Bensattalah, T., Karas, A., Zidour, M., Heireche, H. and Adda Bedia, E.A. (2020), "Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle", Struct. Eng. Mech., 73(2), 209-223. https://doi.org/10.12989/sem.2020.73.2.209.
  13. 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 response of functionally graded beam resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.
  14. Chami., K., Massafer, T. and Hadji, L. (2020), "Analytical modeling of bending and free vibration of thick advanced composite beams resting on Winkler-Pasternak elastic foundation", Earthq. Struct., 19(2), 91-101. http://doi.org/10.12989/eas.2020.19.2.091.
  15. Civalek, O., Dastjerdi, S., Akbas, S. and Akgoz, B. (2021), "Vibration analysis of carbon nanotube-reinforced composite microbeams", Math. Meth. Appl. Sci. https://doi.org/10.1002/mma.7069.
  16. Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H. and Abdel-Wahab, M., (2020), "A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA", Compos. Struct., 259, 113216. https://doi.org/10.1016/j.compstruct.2020.113216.
  17. Cuong-Le, T., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel-Wahab, M. (2020), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. Comput., 1-12. https://doi.org/10.1007/s00366-020-01154-0.
  18. Demir., C. and Civalek, O. (2017), "On the analysis of microbeams", Int. J. Eng. Sci., 121, 14-33. https://doi.org/10.1016/j.ijengsci.2017.08.016.
  19. Eisenberger, M. and Clastornik, J. (1987), "Vibrations and buckling of a beam on a variable Winkler elastic foundation", J. Sound Vib., 115, 233-241. https://doi.org/10.1016/0022-460X(87)90469-X.
  20. Fariborz, J. and Batra, R.C. (2019), "Free vibration of bidirectional functionally graded material circular beams using shear deformation theory employing logarithmic function of radius", Compos. Struct., 210, 217-230. https://doi.org/10.1016/j.compstruct.2018.11.036.
  21. Faroughi, S., Rahmani, A. and Friswell, M.I. (2020), "On wave propagation in two-dimensional functionally graded porous rotating nano-beams using a general nonlocal higher-order beam model", Appl. Math. Model., 80, 169-190. https://doi.org/10.1016/j.apm.2019.11.040.
  22. Hadji, L. (2020), "Influence of the distribution shape of porosity on the bending of FGM beam using a new higher order shear deformation model", Smart Struct. Syst., 26(2), 253-262. http://doi.org/10.12989/sss.2020.26.2.25.
  23. Hadji, L. and Avcar, M. (2021), "Free vibration analysis of FG porous sandwich plates under various boundary conditions", J. Appl. Comput. Mech., 7(2), 505-519. http://doi.org/10.22055/JACM.2020.35328.2628.
  24. Hao, D. and Wei, C. (2016), "Dynamic characteristics analysis of bi-directional functionally graded Timoshenko beams", Compos. Struct., 141, 253-263. https://doi.org/10.1016/j.compstruct.2016.01.051.
  25. Jalaei, M.H. and Civalek, O. (2019), "On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam", Int. J. Eng. Sci., 143, 14-32. https://doi.org/10.1016/j.ijengsci.2019.06.013.
  26. Karamanli, A. (2017a), "Elastostatic analysis of two-directional functionally graded beams using various beam theories and symmetric smoothed particle hydrodynamics method", Compos. Struct., 160, 653-669. http://doi.org/10.1016/j.compstruct.2016.10.065.
  27. Karamanli, A. (2017b), "Bending behaviour of two directional functionally gradedsandwich beams by using a quasi-3d shear deformation theory", Compos. Struct., 174, 70-86. https://doi.org/10.1016/j.compstruct.2017.04.046
  28. Kar, V.R. and Panda, S.K. (2020), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693.
  29. Kiani, Y. (2019), "NURBS-based thermal buckling analysis of graphene platelet reinforced composite laminated skew plates", J. Therm. Stresses, 1-19. https://doi.org/10.1080/01495739.2019.1673687.
  30. Li, J., Guan, Y., Wang, G., Zhao, G., Lin, J., Naceur, H. and Coutellier, D. (2018), "Meshless modeling of bending behavior of bi-directional functionally graded beam structures", Compos. Part B Eng., 155, 104-111. https://doi.org/10.1016/j.compositesb.2018.08.029.
  31. Lu, Y. and Chen, X. (2020), "Nonlinear parametric dynamics of bidirectional functionally graded beams", Shock Vib., 8840833, https://doi.org/10.1155/2020/8840833.
  32. Merzoug, M., Bourada, M., Sekkal, M., Abir, A.C., Chahrazed, B., Benyoucef, S. and Benachour, A. (2020), "2D and quasi 3D computational models for thermoelastic bending of FG beams on variable elastic foundation: Effect of the micromechanical models", Geomech. Eng., 22(4), 361-374. http://doi.org/10.12989/gae.2020.22.4.361.
  33. Madenci, E. (2019), "A refined functional and mixed formulation to static analyses of fgm beams", Struct. Eng. Mech., 69(4), 427-437. https://doi.org/10.12989/sem.2019.69.4.427.
  34. Madenci, E., Ozkilic, Y.O. and Gemi, L. (2020), "Experimental and theoretical investigation on flexure performance of pultruded GFRP composite beams with damage analyses", Compos. Struct., 242, 112162. https://doi.org/10.1016/j.compstruct.2020.112162.
  35. Madenci, E., Ozkilic, T.O. and Gemi, L. (2020), "Buckling and free vibration analyses of pultruded GFRP laminated composites: Experimental, numerical and analytical investigations", Compos. Struct., 254, 112806. https://doi.org/10.1016/j.compstruct.2020.112806.
  36. Madenci, E., Ozkilic, T.O. and Gemi, L. (2020), "Theoretical investigation on static analysis of pultruded GFRP composite beams", Akademik Platform Muhendislik ve Fen Bilimleri Dergisi, 8(3), 483-490. https://doi.org/10.21541/apjes.734770.
  37. Madenci, E. and Ozutok, A. (2020), "Variational approximate for high order bending analysis of laminated composite plates", Struct. Eng. Mech., 73(1), 97-108. https://doi.org/10.12989/sem.2020.73.1.097.
  38. Madenci, E. and Ozutok, A. (2017), "Variational approximate and mixed-finite element solution for static analysis of laminated composite plates", Solid State Phenom., 267, 35-39. https://doi.org/10.4028/www.scientific.net/SSP.267.35
  39. Madenci, E. and Gulcu, S. (2020), "Optimization of flexure stiffness of FGM beams via artificial neural networks by mixed FEM", Struct. Eng. Mech., 75(5), 633-642. https://doi.org/10.12989/sem.2020.75.5.633.
  40. Nemati, A.R. and Mahmoodabadi, M.J. (2019), "Effect of micromechanical models on stability of functionally graded conical panels resting on Winkler-Pasternak foundation in various thermal environments", Arch. Appl. Mech., 1-33. https://doi.org/10.1007/s00419-019-01646-6.
  41. Nguyen, D.K., Nguyen, Q.H., Tran, T.T. and Bui, V.T. (2017), "Vibration of bi-dimensional functionally graded Timoshenko beams excited by a moving load", Acta Mech., 228(1), 141-155. http://doi.org/10.1007/s00707-016-1705-3.
  42. Ouldlarbi, L., Kaci, A., Houari, M.S.A. and Tounsi, A., (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Based Des. Struct. Mach., 41(4), 421-433. https://doi.org/10.1080/15397734.2013.763713.
  43. Ozutok, A. and Madenci, E. (2017), "Static analysis of laminated composite beams based on higher-order shear deformation theory by using mixed-type finite element method", Int. J. Mech. Sci., 130, 234-243. https://doi.org/10.1016/j.ijmecsci.2017.06.013.
  44. Panjehpour, M., Loh, E.W.K. and Deepak, T.J. (2018), "Structural insulated panels: State-of-the-Art", Trends Civ. Eng. Arch., 3(1), 336-340. https://doi.org/10.32474/TCEIA.2018.03.000151.
  45. Pradhan, S.C. and Murmu, T. (2009), "Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method", J. Sound Vib., 321, 342-362. https://doi.org/10.1016/j.jsv.2008.09.018.
  46. Pydah, A. and Sabale, A. (2017), "Static analysis of bi-directional functionally graded curved beams", Compos. Struct., 160, 867-876. https://doi.org/10.1016/j.compstruct.2016.10.120.
  47. Rahmani, A., Faroughi, S. and Friswell, M.I. (2020), "The vibration of two-dimensional imperfect functionally graded(2D-FG) porous rotating nanobeams based on general nonlocaltheory", Mech. Syst. Signal Process., 144, 106854. https://doi.org/10.1016/j.ymssp.2020.106854.
  48. Rahmani, M., Mohammadi, Y. and Kakavand, F. (2019), "Vibration analysis of sandwich truncated conical shells with porous FG face sheets in various thermal surroundings", Steel Compos. Struct., 32(2), 239-252. http://doi.org/10.12989/scs.2019.32.2.239.
  49. Rajasekaran, S. and Khaniki, H.B. (2018), "Free vibration analysis of bi-directional functionally graded single/multi-cracked beams", Int. J. Mech. Sci., 144, 341-356. https://doi.org/10.1016/j.ijmecsci.2018.06.004.
  50. 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. http://doi.org/10.12989/scs.2019.33.6.865.
  51. Shahmohammadi, M.A., Azhari, M. and Saadatpou, M.M. (2020), "Free vibration analysis of sandwich FGM shells using isogeometric B-spline finite strip method", Steel Compos. Struct., 34(3), 361-376. http://doi.org/10.12989/scs.2020.34.3.361.
  52. Selmi, A. (2020), "Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam", Smart Struct. Syst., 26(3), 361-371. https://doi.org/10.12989/SSS.2020.26.3.361.
  53. Shafiei, N., Mirjavadi, S.S., Mohasel Afshari, B., Rabby, S. and Kazemi, M. (2017), "Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams", Comput. Meth. Appl. Mech. Eng., 322, 615-632. https://doi.org/10.1016/j.cma.2017.05.007.
  54. Simsek, M. (2010), "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.
  55. simsek, M. (2015), "Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions", Compos. Struct., 133, 968-978. http://doi.org/10.1016/j.compstruct.2015.08.021.
  56. simsek, M. (2016), "Buckling of Timoshenko beams composed of two-dimensional functionally graded material (2D-FGM) having different boundary conditions", Compos. Struct., 149, 304-314. https://doi.org/10.1016/j.compstruct.2016.04.034.
  57. Si Tayeb, T., Zidour, M., Bensattalah, T., Heireche, H., Benahmed, A. and Adda Bedia, E.A. (2020), "Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle", Adv. Nano Res., 8(2), 135-148. https://doi.org/10.12989/anr.2020.8.2.135.
  58. Sobhy, M. (2015), "Thermoelastic response of FGM plates with temperature-dependent properties resting on variable elastic foundations", J. Appl. Mech., 7(6), 1550082. https://doi.org/10.1142/S1758825115500829.
  59. Timesli, A. (2020), "Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation", Comput. Concrete, 26(1), 53-62. https://doi.org/10.12989/cac.2020.26.1.053.
  60. Tang, Y. and Ding, Q. (2019), "Nonlinear vibration analysis of a bi-directional functionally graded beam under hygro-thermal loads", Compos. Struct., 225,111076. https://doi.org/10.1016/j.compstruct.2019.111076.
  61. Tran, T.T. and Nguyen D.K. (2018), "Free vibration analysis of 2-DFGM beams in thermal environment based on a newthird-order shear deformation theory", Vietnam J. Mech., 40(2), 121-140. https://doi.org/10.15625/0866-7136/10503.
  62. Vinyas, M. (2020), "On frequency response of porous functionally graded magneto-electro-elastic circular and annular plates with different electro-magnetic conditions using HSDT", Compos. Struct., 240, 112044. https://doi.org/10.1016/j.compstruct.2020.112044.
  63. Wang, Z.H., Wang, X.H., Xu, G.D., Cheng, S. and Zeng, T. (2016), "Free vibration of two-directional functionally graded beams", Compos. Struct., 135, 191-198. http://doi.org/10.1016/j.compstruct.2015.09.013.
  64. Yaghoobi, H. and Taheri, F. (2020), "Analytical solution and statistical analysis of buckling capacity of sandwich plates with uniform and non-uniform porous core reinforced with graphene nanoplatelets", Compos. Struct.,252, 112700. https://doi.org/10.1016/j.compstruct.2020.112700
  65. 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.