Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Damped forced vibration analysis of layered functionally graded thick beams with porosity

  • Alnujaie, Ali (Mechanical Engineering Department, Faculty of Engineering, Jazan University) ;
  • Akbas, Seref D. (Department of Civil Engineering, Bursa Technical University) ;
  • Eltaher, Mohamed A. (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Assie, Amr E. (Mechanical Engineering Department, Faculty of Engineering, Jazan University)
  • Received : 2020.06.27
  • Accepted : 2020.11.27
  • Published : 2021.04.25
⟨ Previous Next ⟩

Abstract

The following article presents the damped forced vibration of layered functionally graded thick beams including material porosities. In case of very thick beams, beam theories fail to satisfy boundary conditions and to predict the mechanical response accurately. So, the two-dimensional (2D) plane continuum model is exploited to model a thick functionally graded layered beam. The beam is composed from three- layers with functionally graded porous materials. The porosity is described by three different distribution models through the layer thickness. Applied forces to the functionally graded beam are assumed to be sinusoidal harmonic point load in time domain. The Kelvin-Voigt viscoelastic constitutive model is used to simulate damping effect. The governing equations are obtained by using Lagrange's equations. In frame of finite element analysis, twelve -node 2D plane element is exploited to discretize the space domain of thick beam. In the solution of the dynamic problem, the Newmark average acceleration method is used. Numerical studies illustrate effects of porosity distribution, stacking sequence, and graduation constant on the dynamic responses of layered functionally graded porous thick beams. The results show that the porosity function, stacking sequences and the damping ratio have a vital role in dynamic response of functionally graded beams. The proposed model can be used in nuclear, marine, and aerospace technologies.

Keywords

Acknowledgement

The project was funded by Deanship of Scientific Research (DSR) at Jazan University, Jazan, Kingdom of Saudi Arabia under grant no. W41-045. The authors acknowledge with thanks DSR for technical and financial support.

References

  1. Abo-bakr, R.M., Abo-bakr, H.M., Mohamed, S.A. and Eltaher, M.A. (2020a), "Optimal Weight for Buckling of FG Beam under Variable Axial Load using Pareto Optimality", Compos. Struct., 113193. https://doi.org/10.1016/j.compstruct.2020.113193
  2. Abo-Bakr, H.M., Abo-Bakr, R.M., Mohamed, S.A. and Eltaher, M.A. (2020b), "Weight optimization of axially functionally graded microbeams under buckling and vibration behaviors", Mech. Based Des. Struct. Mach., 1-22. https://doi.org/10.1080/15397734.2020.1838298
  3. Akbas, S.D. (2013), "Geometrically nonlinear static analysis of edge cracked Timoshenko beams composed of functionally graded material", Mathe. Problems Eng., 2013. https://doi.org/10.1155/2013/871815
  4. Akbas, S.D. (2014), "Free vibration of axially functionally graded beams in thermal environment", Int. J. Eng. Appl. Sci., 6(3), 37-51. https://doi.org/10.24107/ijeas.251224
  5. Akbas, S.D. (2015a), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., Int. J., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421
  6. Akbas, S.D. (2015b), "Free vibration and bending of functionally graded beams resting on elastic foundation", Res. Eng. Struct. Mater., 1(1), 25-37. http://dx.doi.org/10.17515/resm2015.03st0107
  7. Akbas, S.D. (2017a), "Nonlinear static analysis of functionally graded porous beams under thermal effect", Coupl. Syst. Mech., Int. J., 6(4), 399-415. https://doi.org/10.12989/csm.2017.6.4.399
  8. Akbas, S.D. (2017b), "Stability of a non-homogenous porous plate by using generalized differantial quadrature method", Int. J. Eng. Appl. Sci., 9(2), 147-155. https://doi.org/10.24107/ijeas.322375
  9. Akbas, S.D. (2018a), "Nonlinear thermal displacements of laminated composite beams", Coupl. Syst. Mech., Int. J., 7(6), 691-705. https://doi.org/10.12989/csm.2018.7.6.691
  10. Akbas, S.D. (2018b), "Post-buckling responses of a laminated composite beam", Steel Compos. Struct., Int. J., 26(6), 733-743. https://doi.org/10.12989/scs.2018.26.6.733
  11. Akbas, S.D. (2018c), "Forced vibration analysis of functionally graded porous deep beams", Compos. Struct., 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013
  12. Akbas, S.D. (2018d), "Geometrically nonlinear analysis of functionally graded porous beams", Wind Struct., Int. J., 27(1), 59-70. https://doi.org/10.12989/was.2018.27.1.059
  13. Akbas, S.D. (2018e), "Thermal post-buckling analysis of a laminated composite beam", Struct. Eng. Mech., Int. J., 67(4), 337-346. http://dx.doi.org/10.12989/sem.2018.67.4.337
  14. Akbas, S.D. (2018f), "Geometrically nonlinear analysis of a laminated composite beam", Struct. Eng. Mech., Int. J., 66(1), 27-36. http://dx.doi.org/10.12989/sem.2018.66.1.027
  15. Akbas, S.D. (2018g), "Investigation on free and forced vibration of a bi-material composite beam", J. Polytech.-Politeknik Dergisi, 21(1), 65-73. http://dx.doi.org/10.2339/politeknik.386841
  16. Akbas, S.D. (2018h), "Investigation of static and vibration behaviors of a functionally graded orthotropic beam", Balikesir universitesi Fen Bilimleri Enstitusu Dergisi, 1-14. https://doi.org/10.25092/baunfbed.343227
  17. Akbas, S.D. (2019a), "Forced vibration analysis of functionally graded sandwich deep beams", Coupl. Syst. Mech., Int. J., 8(3), 259-271. http://dx.doi.org/10.12989/csm.2019.8.3.259
  18. Akbas, S.D. (2019b), "Hygro-thermal nonlinear analysis of a functionally graded beam", J. Appl. Computat. Mech., 5(2), 477-485. http://dx.doi.org/10.22055/JACM.2018.26819.1360
  19. Akbas, S.D. (2019c), "Hygrothermal post-buckling analysis of laminated composite beams", Int. J. Appl. Mech., 11(1), 1950009. https://doi.org/10.1142/S1758825119500091
  20. Akbas, S.D. (2019d), "Hygro-thermal post-buckling analysis of a functionally graded beam", Coupl. Syst. Mech., Int. J., 8(5), 459-471. http://dx.doi.org/10.12989/csm.2019.8.5.459
  21. Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Mathe. Modell., 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006
  22. Asiri, S.A., Akbas, S.D. and Eltaher, M.A. (2020a), "Damped dynamic responses of a layered functionally graded thick beam under a pulse load", Struct. Eng. Mech., Int. J., 75(6), 713-722. https://doi.org/10.12989/sem.2020.75.6.713
  23. Asiri, S.A., Akbas, S.D. and Eltaher, M.A. (2020b), "Dynamic Analysis of Layered Functionally Graded Viscoelastic Deep Beams with Different Boundary Conditions due to a Pulse Load", Int. J. Appl. Mech., 12(5), 2050055. https://doi.org/10.1142/S1758825120500556
  24. Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., Int. J., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457
  25. Chen, X.L. and Liew, K.M. (2004), "Buckling of rectangular functionally graded material plates subjected to nonlinearly distributed in-plane edge loads", Smart Mater. Struct., 13(6), 1430. https://doi.org/10.1088/0964-1726/13/6/014
  26. Civalek, O. (2019), "Vibration of functionally graded carbon nanotube reinforced quadrilateral plates using geometric transformation discrete singular convolution method", Int. J. Numer Methods Eng., 11, 205-216. https://doi.org/10.1002/nme.6254
  27. Ebrahimi, F. and Jafari, A. (2016), "A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities", J. Eng., 2016. http://dx.doi.org/10.1155/2016/9561504
  28. Eltaher, M.A. and Akbas, S.D. (2020), "Transient response of 2D functionally graded beam structure", Struct. Eng. Mech., Int. J., 75(3), 357-367. https://doi.org/10.12989/sem.2020.75.3.357
  29. Eltaher, M.A., Omar, F.A., Abdraboh, A.M., Abdalla, W.S. and Alshorbagy, A.E. (2020a), "Mechanical behaviors of piezoelectric nonlocal nanobeam with cutouts", Smart Struct. Syst., Int. J., 25(2), 219-228. https://doi.org/10.12989/sss.2020.25.2.219
  30. Eltaher, M.A. and Mohamed, N.A. (2020b), "Vibration of nonlocal perforated nanobeams with general boundary conditions", Smart Struct. Syst., Int. J., 25(4), 501-514. https://doi.org/10.12989/sss.2020.25.4.501
  31. Farokhi, H., Ghayesh, M.H. and Hussain, S. (2016), "Three-dimensional nonlinear global dynamics of axially moving viscoelastic beams", J. Vib. Acoust., 138(1). https://doi.org/10.1115/1.4031600
  32. 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
  33. Ghayesh, M.H. (2012), "Nonlinear dynamic response of a simply-supported Kelvin-Voigt viscoelastic beam, additionally supported by a nonlinear spring", Nonlinear Anal.: Real World Applic., 13(3), 1319-1333. https://doi.org/10.1016/j.nonrwa.2011.10.009
  34. Ghayesh, M.H. (2018a), "Nonlinear vibration analysis of axially functionally graded shear-deformable tapered beams", Appl. Mathe. Modell., 59, 583-596. https://doi.org/10.1016/j.apm.2018.02.017
  35. Ghayesh, M.H. (2018b), "Dynamics of functionally graded viscoelastic microbeams", Int. J. Eng. Sci., 124, 115-131. https://doi.org/10.1016/j.ijengsci.2017.11.004
  36. Ghayesh, M.H. (2019a), "Viscoelastic mechanics of Timoshenko functionally graded imperfect microbeams", Compos. Struct., 225, 110974. https://doi.org/10.1016/j.compstruct.2019.110974
  37. Ghayesh, M.H. (2019b), "Mechanics of viscoelastic functionally graded microcantilevers", Eur. J. Mech.-A/Solids, 73, 492-499. https://doi.org/10.1016/j.euromechsol.2018.09.001
  38. Ghayesh, M.H. (2019c), "Asymmetric viscoelastic nonlinear vibrations of imperfect AFG beams", Appl. Acoust., 154, 121-128. https://doi.org/10.1016/j.apacoust.2019.03.022
  39. Ghayesh, M.H. (2019d), "Dynamical analysis of multilayered cantilevers", Commun. Nonlinear Sci. Numer. Simul., 71, 244-253. https://doi.org/10.1016/j.cnsns.2018.08.012
  40. Ghayesh, M.H. (2019e), "Nonlinear oscillations of FG cantilevers", Appl. Acoust., 145, 393-398. https://doi.org/10.1016/j.apacoust.2018.08.014
  41. Ghayesh, M.H. (2019f), "Viscoelastic dynamics of axially FG microbeams", Int. J. Eng. Sci., 135, 75-85. https://doi.org/10.1016/j.ijengsci.2018.10.005
  42. Ghayesh, M.H. and Amabili, M. (2012), "Nonlinear dynamics of axially moving viscoelastic beams over the buckled state", Comput. Struct., 112, 406-421. https://doi.org/10.1016/j.compstruc.2012.09.005
  43. Ghayesh, M.H. and Moradian, N. (2011), "Nonlinear dynamic response of axially moving, stretched viscoelastic strings", Archive Appl. Mech., 81(6), 781-799. https://doi.org/10.1007/s00419-010-0446-3
  44. Ghayesh, M.H., Kazemirad, S. and Darabi, M.A. (2011), "A general solution procedure for vibrations of systems with cubic nonlinearities and nonlinear/time-dependent internal boundary conditions", J. Sound Vib., 330(22), 5382-5400. https://doi.org/10.1016/j.jsv.2011.06.001
  45. Jouneghani, F.Z., Dimitri, R. and Tornabene, F. (2018), "Structural response of porous FG nanobeams under hygro-thermoechanical loadings", Compos. Part B: Eng., 152, 71-78. https://doi.org/10.1016/j.compositesb.2018.06.023
  46. Pegios, I.P. and Hatzigeorgiou, G.D. (2018), "Finite element free and forced vibration analysis of gradient elastic beam structures", Acta Mechanica, 229(12), 4817-4830. https://doi.org/10.1007/s00707-018-2261-9
  47. 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., Int. J., 33(6), 865-875. http://dx.doi.org/10.12989/scs.2019.33.6.865
  48. Ramteke, P.M., Mahapatra, B.P., Panda, S.K. and Sharma, N. (2020), "Static deflection simulation study of 2D Functionally graded porous structure", Materials Today: Proceedings. https://doi.org/10.1016/j.matpr.2020.03.537
  49. Sheng, G.G. and Wang, X. (2019), "Nonlinear forced vibration of functionally graded Timoshenko microbeams with thermal effect and parametric excitation", Int. J. Mech. Sci., 155, 405-416. https://doi.org/10.1016/j.ijmecsci.2019.03.015
  50. Taati, E. and Fallah, F. (2019), "Exact solution for frequency response of sandwich microbeams with functionally graded cores", J. Vib. Control, 25(19-20), 2641-2655. https://doi.org/10.1177/1077546319864645
  51. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002
  52. Wu, D., Liu, A., Huang, Y., Huang, Y., Pi, Y. and Gao, W. (2018), "Dynamic analysis of functionally graded porous structures through finite element analysis", Eng. Struct., 165, 287-301. https://doi.org/10.1016/j.engstruct.2018.03.023
  53. Yang, J., Chen, D. and Kitipornchai, S. (2018), "Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method", Compos. Struct., 193, 281-294. https://doi.org/10.1016/j.compstruct.2018.03.090
  54. Zhao, J., Xie, F., Wang, A., Shuai, C., Tang, J. and Wang, Q. (2019), "Vibration behavior of the functionally graded porous (FGP) doubly-curved panels and shells of revolution by using a semi-analytical method", Compos. Part B: Eng., 157, 219-238. https://doi.org/10.1016/j.compositesb.2018.08.087