Structural Engineering and Mechanics

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Vibration of elastically supported bidirectional functionally graded sandwich Timoshenko beams on an elastic foundation

  • Wei-Ren Chen (Department of Mechanical Engineering, Chinese Culture University) ;
  • Liu-Ho Chiu (Department of Mechanical and Materials Engineering, Tatung University) ;
  • Chien-Hung Lin (Department of Mechanical Engineering, Chinese Culture University)
  • Received : 2024.01.09
  • Accepted : 2024.07.05
  • Published : 2024.07.25
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Abstract

The vibration of elastically supported bidirectional functionally graded (BDFG) sandwich beams on an elastic foundation is investigated. The sandwich structure is composed of upper and lower layers of BDFG material and the core layer of isotropic material. Material properties of upper and lower layers are assumed to vary continuously along the length and thickness of the beam with a power-law function. Hamilton's principle is used to deduce the vibration equations of motion of the sandwich Timoshenko beam. Then, the partial differential equation of motion is spatially discretized into a time-varying ordinary differential equation in terms of Chebyshev differential matrices. The eigenvalue equation associated with the free vibration is formulated to study the influence of various slenderness ratios, material gradient indexes, thickness ratios, foundation and support spring constants on the vibration frequency of BDFG sandwich beams. The present method can provide researchers with deep insight into the impact of various geometric, material, foundation and support parameters on the vibration behavior of BDFG sandwich beam structures.

Keywords

References

  1. Arboleda-Monsalve, L.G., Zapata-Medina, D.G. and Dari'o Aristizabal-Ochoa, J. (2008), "Timoshenko beam-column with generalized end conditions on elastic foundation: Dynamicstiffness matrix and load vector", J. Sound Vib., 310, 1057-1079. https://doi.org/10.1016/j.jsv.2007.08.014.
  2. Belabed, Z., Tounsi, A., Bousahla, A.A., Tounsi, A., Bourada, M. and Al-Osta, M.A. (2024), "Free vibration analysis of BiDirectional Functionally Graded Beams using a simple and efficient finite element model", Struct. Eng. Mech., 90, 233-252. https://doi.org/10.12989/sem.2024.90.3.233.
  3. Benaberrahmane, I., Mekerbi, M., Bouiadjra, R.B., Benyoucef, S., Selim, M.M., Tounsi, A. and Hussain, M. (2021), "Analytical evaluation of frequencies of bidirectional FG thick beams in thermal environment and resting on different foundation", Struct. Eng. Mech., 80(4), 365-375. https://doi.org/10.12989/sem.2021.81.4.365.
  4. Bennai, R., Atmane, H.A. and Tounsi, A. (2015), "A new higherorder shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521.
  5. Birman, V. and Byrd, L.W. (2007), "Modeling and analysis of functionally graded materials and structures", Appl. Mech. Rev., 60, 195-216. https://doi.org/10.1115/1.2777164.
  6. Birman, V. and Kardomateas, G.A. (2018), "Review of current trends in research and applications of sandwich structures", Compos. Part B, 142, 221-240. https://doi.org/10.1016/j.compositesb.2018.01.027.
  7. Calim, F.F. (2016), "Free and forced vibration analysis of axially functionally graded Timoshenko beams on two-parameter viscoelastic foundation", Compos. Part B: Eng., 103, 98-112. https://doi.org/10.1016/j.compositesb.2016.08.008.
  8. Chen, W.R. (2020), "Vibration analysis of axially functionally graded tapered Euler-Bernoulli beams based on Chebyshev collocation method", Int. J. Acoust. Vib., 25, 436-444. https://doi.org/10.20855/ijav.2020.25.31680
  9. Chen, W.R. and Chang, H. (2018), "Vibration analysis of functionally graded Timoshenko beams", Int. J. Struct. Stab. Dyn., 18, 1850007. https://doi.org/10.1142/S0219455418500074.
  10. Chen, W.R. and Chang, H. (2021), "Vibration analysis of bidirectional functionally graded Timoshenko beams using Chebyshev collocation method", Int. J. Struct. Stab. Dyn., 21, 2150009. https://doi.org/10.1142/S0219455421500097.
  11. Comez, I., El-Borgi, S., Kahya, V. and Erdol, R. (2016), "Receding contact problem for two-layer functionally graded media indented by a rigid punch", Acta Mechanica, 227, 2493-2504. https://doi.org/10.1007/s00707-016-1648-8.
  12. Comez, I., Kahya, V.O.L.K.A.N. and Erdol, R. (2018), "Plane receding contact problem for a functionally graded layer supported by two quarter-planes", Arch. Mechanica, 70, 485-504. https://doi.org/10.24423/aom.2846.
  13. Ebrahimi, F. and Farazmandnia, N. (2017), "Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory", Mech. Adv. Mater. Struct., 24, 820-829. https://doi.org/10.1080/15376494.2016.1196786.
  14. Fazzolari, F.A. (2018), "Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations", Compos. Part B: Eng., 136, 254-271. https://doi.org/10.1016/j.compositesb.2017.10.022.
  15. Huynh, T.A., Lieu, X.Q. and Lee, J. (2017), "NURBS-based modeling of bidirectional functionally graded Timoshenko beams for free vibration problem", Compos. Struct., 160, 1178-1190. https://doi.org/10.1016/j.compstruct.2016.10.076.
  16. Kahya, V. and Turan, M. (2017), "Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory", Compos. Part B: Eng., 109, 108-115. https://doi.org/10.1016/j.engstruct.2014.01.029.
  17. Kahya, V. and Turan, M. (2018), "Vibration and stability analysis of functionally graded sandwich beams by a multi-layer finite element", Compos. Part B: Eng., 146, 198-212. https://doi.org/10.1016/j.compositesb.2018.04.011.
  18. Karamanli, A. (2017), "Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3d shear deformation theory", Compos. Struct., 174, 70-86. https://doi.org/10.1016/j.compstruct.2017.04.046.
  19. Karamanli, A. and Aydogdu, M. (2019), "Size dependent flapwise vibration analysis of rotating two-directional functionally graded sandwich porous microbeams based on a transverse shear and normal deformation theory", Int. J. Mech. Sci., 159, 165-181. https://doi.org/10.1016/j.ijmecsci.2019.05.047.
  20. Koutoati, K., Mohri, F. and Daya, E.M. (2021), "Finite element approach of axial bending coupling on static and vibration behaviors of functionally graded material sandwich beams", Mech. Adv. Mater. Struct., 28, 1537-1553. https://doi.org/10.1080/15376494.2019.1685144.
  21. Le, C.I. and Nguyen, D.K. (2023), "Nonlinear vibration of threephase bidirectional functionally graded sandwich beams with influence of homogenization scheme and partial foundation support", Compos. Struct., 307, 116649. https://doi.org/10.1016/j.compstruct.2022.116649.
  22. Le, C.I., Le, N.A.T. and Nguyen, D.K. (2021), "Free vibration and buckling of bidirectional functionally graded sandwich beams using an enriched third-order shear deformation beam element", Compos. Struct., 261, 113309. https://doi.org/10.1016/j.compstruct.2020.113309.
  23. Le, T.N.A., Vu, T.A.N., Tran, V.L. and Nguyen, D.K. (2020), "Free vibration of bidirectional functionally graded sandwich beams using a first-order shear deformation finite element formulation", J. Sci. Tech. Civil Eng., 14, 136-150. https://doi.org/10.1016/j.compstruct.2020.113309.
  24. Nguyen, D.K., Vu, A.N.T., Le, N.A.T. and Pham, V.N. (2020), "Dynamic behavior of a bidirectional functionally graded sandwich beam under nonuniform motion of a moving load", Shock Vib., 2020, 1-15. https://doi.org/10.1155/2020/8854076.
  25. Nguyen, T.K., Vo, T.P., Nguyen, B.D. and Lee, J. (2016), "An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory", Compos. Struct., 156, 238-252. https://doi.org/10.1016/j.compstruct.2015.11.074.
  26. Pang, M., Zhou, S.M., Hu, B.L. and Zhang, Y.Q. (2023), "Free vibration analysis of a bidirectional functionally graded carbon nanotube reinforced composite beam", J. Appl. Mech. Tech. Phys., 64, 878-889. https://doi.org/10.1134/S0021894423050176.
  27. Pham, V.N., Nguyen, D.K. and Gan, B.S. (2019), "Vibration analysis of two directional functionally graded sandwich beams using a shear deformable finite element formulation", Adv. Tech. Innov., 4, 152-164.
  28. 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.
  29. Sayyad, A.S. and Ghugal, Y.M. (2019), "Modeling and analysis of functionally graded sandwich beams: A review", Mech. Adv. Mater. Struct., 26, 1776-1795. https://doi.org/10.1080/15376494.2018.1447178.
  30. Selmi, A. (2021), "Vibration behavior of bi-dimensional functionally graded beams", Struct. Eng. Mech., 77(5), 587-599. https://doi.org/10.12989/sem.2021.77.5.587.
  31. 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. https://doi.org/10.1016/j.compstruct.2015.08.021.
  32. Songsuwan, W., Pimsarn, M. and Wattanasakulpong, N. (2018), "Dynamic responses of functionally graded sandwich beams resting on elastic foundation under harmonic moving loads", Int. J. Struct. Stab. Dyn., 18, 181850112. https://doi.org/10.1142/S0219455418501122.
  33. 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.
  34. Su, Z., Jin, G., Wang, Y. and Ye, X. (2016), "A general Fourier formulation for vibration analysis of functionally graded sandwich beams with arbitrary boundary condition and resting on elastic foundations", Acta Mechanica, 227, 1493-1514. https://doi.org/10.1007/s00707-016-1575-8.
  35. Taleb, O., Sekkal, M., Bouiadjra, R.B., Benyoucef, S., Khedher, K.M., Salem, M.A. and Tounsi, A. (2024), "On the free vibration behavior of temperature-dependent bidirectional functionally graded curved porous beams", Int. J. Struct. Stab. Dyn., 24, 2450112. https://doi.org/10.1142/S0219455424501128.
  36. Tossapanon, P. and Wattanasakulpong, N. (2016), "Stability and free vibration of functionally graded sandwich beams resting on two parameter elastic foundation", Compos. Struct., 142, 215-225. https://doi.org/10.1016/j.compstruct.2016.01.085.
  37. Trefethen, L.N. (2000), Spectral Methods in MATLAB, Software, Environments, and Tools, SIAM, Philadelphia, USA.
  38. Trinh, L.C., Vo, T.P., Osofero, A.I. and Lee, J. (2016), "Fundamental frequency analysis of functionally graded sandwich beams based on the state space approach", Compos. Struct., 156, 263-275. https://doi.org/10.1016/j.compstruct.2015.11.010.
  39. Turan, M. and Kahya, V. (2021), "Free vibration and buckling analysis of functionally graded sandwich beams by Navier's method", J. Facil. Eng. Arch. Gazi Univ., 36, 743-757. https://doi.org/10.17341/gazimmfd.599928.
  40. Turan, M., Adiyaman, G., Kahya, V. and Birinci, A. (2016), "Axisymmetric analysis of a functionally graded layer resting on elastic substrate", Struct. Eng. Mech., 58(3), 423-442. https://doi.org/10.12989/sem.2016.58.3.423.
  41. Vu, T.A.N. (2021), "Fundamental frequencies of bidirectional functionally graded sandwich beams partially supported by foundation using different beam theories", Trans. Commun. Sci. J., 72, 452-467. https://doi.org/10.47869/tcsj.72.4.5
  42. Vu, T.A.N., Le, T.N.A. and Nguyen, D.K. (2020), "Free vibration of a 2D-FGSW beam based on a shear deformation theory", Viet. J. Mech., 42, 189-205. https://doi.org/10.15625/0866-7136/14817.
  43. Wattanasakulpong, N. and Bui, T.Q. (2017), "Vibration analysis third-order shear deformation FGM beams with elastic support by Chebyshev collocation method", Int. J. Struct. Stab. Dyn., 18, 1850071. https://doi.org/10.1142/S0219455418500712.
  44. Yahiaoui, M., Tounsi, A., Fahsi, B., Bouiadjra, R.B. and Benyoucef, S. (2018), "The role of micromechanical models in the mechanical response of elastic foundation FG sandwich thick beams", Struct. Eng. Mech., 68(1), 53-66. https://doi.org/10.12989/sem.2018.68.1.053.