Advances in nano research

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Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory

  • Matouk, Hakima (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Universite de Sidi Bel Abbes) ;
  • Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Universite de Sidi Bel Abbes) ;
  • Heireche, Houari (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Universite de Sidi Bel Abbes) ;
  • Bourada, Fouad (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Bedia, E.A. Adda (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Tounsi, Abdelouahed (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Mahmoud, S.R. (GRC Department, Jeddah Community College, King Abdulaziz University) ;
  • Tounsi, Abdeldjebbar (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Universite de Sidi Bel Abbes) ;
  • Benrahou, K.H. (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
  • Received : 2019.09.26
  • Accepted : 2020.02.22
  • Published : 2020.05.25
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Abstract

In the current research, the free vibrational behavior of the FG nano-beams integrated in the hygro-thermal environment and reposed on the elastic foundation is investigated using a novel integral Timoshenko beam theory (ITBT). The current model has only three variables unknown and requires the introduction of the shear correction factor because her uniformed variation of the shear stress through the thickness. The effective properties of the nano-beam vary according to power-law and symmetric sigmoid distributions. Three models of the hygro-thermal loading are employed. The effect of the small scale effect is considered by using the nonlocal theory of Eringen. The equations of motion of the present model are determined and resolved via Hamilton principle and Navier method, respectively. Several numerical results are presented thereafter to illustrate the accuracy and efficiency of the actual integral Timoshenko beam theory. The effects of the various parameters influencing the vibrational responses of the P-FG and SS-FG nano-beam are also examined and discussed in detail.

Keywords

Acknowledgement

Authors would like to acknowledge the support provided by the Directorate General for Scientific Research and Technological Development (DGRSDT).

References

  1. Abdou, M.A., Othman, M.I.A., Tantawi, R.S. and Mansour, N.T. (2019), "Exact solutions of generalized thermoelastic medium with double porosity under L-S theory", Indian J. Phys. https://doi.org/10.1007/s12648-019-01505-8
  2. Akbas, S.D. (2018), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., Int. J., 6(1), 39-55. https://doi.org/10.12989/anr.2018.6.1.039
  3. Akbas, S.D. (2019a), "Hygro-thermal post-buckling analysis of a functionally graded beam", Coupl. Syst. Mech., Int. J., 8(5), 459-471. https://doi.org/10.12989/csm.2019.8.5.459
  4. Akbas, S.D. (2019b), "Forced vibration analysis of functionally graded sandwich deep beams", Coupl. Syst. Mech., Int. J., 8(3), 259-271. https://doi.org/10.12989/csm.2019.8.3.259
  5. Aria, A.I. and Friswell, M.I. (2019), "A nonlocal finite element model for buckling and vibration of functionally graded nanobeams", Compos. Part B., 166, 233-246. https://doi.org/10.1016/j.compositesb.2018.11.071
  6. Aria, A.I., Rabczuk, T. andFriswell, M.I. (2019), "A finite element model for the thermo-elastic analysis of functionally graded porous nanobeams", Eur. J. Mech.-A/Solids. https://doi.org/10.1016/j.euromechsol.2019.04.002
  7. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
  8. Ayat, H., Kellouche, Y., Ghrici, M. and Boukhatem, B. (2018), "Compressive strength prediction of limestone filler concrete using artificial neural networks", Adv. Computat. Des., Int. J., 3(3), 289-302. https://doi.org/10.12989/acd.2018.3.3.289
  9. Barati, M.R. and Shahverdi, H. (2016), "A four-variable plate theory for thermal vibration of embedded FG nanoplates under non-uniform temperature distributions with different boundary conditions", Struct. Eng. Mech., Int. J., 60(4), 707-727. https://doi.org/10.12989/sem.2016.60.4.707
  10. Barati, M.R. and Shahverdi, H. (2019), "Finite element forced vibration analysis of refined shear deformable nanocomposite graphene platelet-reinforced beams", J. Brazil. Soc. Mech. Sci. Eng., 42(1), 33. https://doi.org/10.1007/s40430-019-2118-8
  11. Behera, S. and Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Computat. Des., Int. J., 3(3), 213-232. https://doi.org/10.12989/acd.2017.2.3.165
  12. Belmahi, S., Zidour, M., Meradjah, M., Bensattalah, T. and Dihaj, A. (2018), "Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix", Struct. Eng. Mech., Int. J., 67(5), 517-525. https://doi.org/10.12989/sem.2018.67.5.517
  13. Belmahi, S., Zidour, M. and Meradjah, M. (2019), "Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory", Adv. Aircr. Spacecr. Sci., Int. J, 6(1), 1-18. https://doi.org/10.12989/aas.2019.6.1.001
  14. Bensaid, I., Bekhadda, A. and Kerboua, B. (2018), "Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory", Adv. Nano Res., Int. J., 6(3), 279-298. https://doi.org/10.12989/anr.2018.6.3.279
  15. Bensattalah, T., Zidour, M. and Hassaine Daouadji, T. (2018), "Analytical analysis for the forced vibration of CNT surrounding elastic medium including thermal effect using nonlocal Euler-Bernoulli theory", Adv. Mater. Res., Int. J., 7(3), 163-174. https://doi.org/10.12989/amr.2018.7.3.163
  16. Bensattalah, T., Zidour, M., Hassaine Daouadji, T. and Bouakaz, K. (2019), "Theoretical analysis of chirality and scale effects on critical buckling load of zigzag triple walled carbon nanotubes under axial compression embedded in polymeric matrix", Struct. Eng. Mech., Int. J., 70(3), 269-277. https://doi.org/10.12989/sem.2019.70.3.269
  17. Bozyigit, B. and Yesilce, Y. (2016), "Dynamic stiffness approach and differential transformation for free vibration analysis of a moving Reddy-Bickford beam", Struct. Eng. Mech., Int. J., 58(5), 847-868. https://doi.org/10.12989/sem.2016.58.5.847
  18. Daouadji, T.H. (2017), "Analytical and numerical modeling of interfacial stresses in beams bonded with a thin plate", Adv. Computat. Des., Int. J., 2(1), 57-69. https://doi.org/10.12989/acd.2017.2.1.057
  19. Ebrahimi, F. and Barati, M.R. (2016a), "Nonlocal strain gradient theory for damping vibration analysis of viscoelastic inhomogeneous nano-scale beams embedded in visco-Pasternak foundation", J. Vib. Control, 24(10), 2080-2095. https://doi.org/10.1177/1077546316678511
  20. Ebrahimi, F. and Barati, M.R. (2016b), "A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment", Appl. Phys. A, 122, 792. https://doi.org/10.1007/s00339-016-0322-2
  21. Ebrahimi, F. and Barati, M.R. (2017), "Buckling analysis of nonlocal strain gradient axially functionally graded nanobeams resting on variable elastic medium", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 232(11), 2067-2078. https://doi.org/10.1177/0954406217713518
  22. Ebrahimi, F. and Daman, M. (2017), "Dynamic characteristics of curved inhomogeneous nonlocal porous beams in thermal environment", Struct. Eng. Mech., Int. J., 64(1), 121-133. https://doi.org/10.12989/sem.2017.64.1.121
  23. Ebrahimi, F. and Heidari, E. (2018), "Vibration characteristics of advanced nanoplates in humid-thermal environment incorporating surface elasticity effects via differential quadrature method", Struct. Eng. Mech., Int. J., 68(1), 131-157. http://dx.doi.org/10.12989/sem.2018.68.1.131
  24. Ebrahimi, F. and Salari, E. (2015), "Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature dependent FG nanobeams", Mech. Adv. Mater. Struct., 23(12), 1379-1397. https://doi.org/10.1080/15376494.2015.1091524
  25. Eltaher, M.A., El-Borgi, S. and Reddy, J.N. (2016), "Nonlinear analysis of size-dependent and material-dependent nonlocal CNTs", Compos. Struct., 153, 902-913. https://doi.org/10.1016/j.compstruct.2016.07.013
  26. Eltaher, M.A., Agwa, M. and Kabeel, A. (2018a), "Vibration Analysis of Material Size-Dependent CNTs Using Energy Equivalent Model", J. Appl. Computat. Mech., 4(2), 75-86. https://doi.org/10.22055/JACM.2017.22579.1136
  27. Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018b), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazil. Soc. Mech. Sci. Eng., 40, 141. https://doi.org/10.1007/s40430-018-1065-0
  28. Eltaher, M.A., Omar, F.A., Abdalla, W.S. and Gad, E.H. (2019a), "Bending and vibrational behaviors of piezoelectric nonlocal nanobeam including surface elasticity", Waves Random Complex Media, 29(2), 264-280. https://doi.org/10.1080/17455030.2018.1429693
  29. Eltaher, M.A., Almalki, T.A., Almitani, K.H. and Ahmed, K.I.E. (2019b), "Participation factor and vibration of carbon nanotube with vacancies", J. Nano Res., 57, 158-174. https://doi.org/10.4028/www.scientific.net/JNanoR.57.158
  30. Eltaher, M.A., Almalki, T.A., Ahmed, K.I.E. and Almitani, K.H. (2019c), "Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach", Adv. Nano Res., Int. J., 7(1), 39-49. https://doi.org/10.12989/anr.2019.7.1.039
  31. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  32. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803
  33. Esmaeili, M. and Beni, Y.T. (2019), "Vibration and buckling analysis of functionally graded flexoelectric smart beam", J. Appl. Computat. Mech., 5(5), 900-917. https://doi.org/10.22055/JACM.2019.27857.1439
  34. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007
  35. Forsat, M., Badnava, S., Mirjavadi, S.S., Barati, M.R. and Hamouda, A.M.S. (2020), "Small scale effects on transient vibrations of porous FG cylindrical nanoshells based on nonlocal strain gradient theory", Eur. Phys. J. Plus, 135(1), 81. https://doi.org/10.1140/epjp/s13360-019-00042-x
  36. Hadji, L., Zouatnia, N. and Bernard, F. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., Int. J., 69(2), 231-241. https://doi.org/10.12989/sem.2019.69.2.231
  37. Hajmohammad, M.H., Farrokhian, A. and Kolahchi, R. (2018), "Smart control and vibration of viscoelastic actuator-multiphase nanocomposite conical shells-sensor considering hygrothermal load based on layerwise theory", Aerosp. Sci. Technol., 78, 260270. https://doi.org/10.1016/j.ast.2018.04.030
  38. Hamidi, A., Zidour, M., Bouakkaz, K. and Bensattalah, T. (2018), "Thermal and small-scale effects on vibration of embedded armchair single-walled carbon nanotubes", J. Nano Res., 51, 24-38. https://doi.org/10.4028/www.scrientific.net/JNanoR.51.24
  39. Hosseini, H. and Kolahchi, R. (2018), "Seismic response of functionally graded-carbon nanotubes-reinforced submerged viscoelastic cylindrical shell in hygrothermal environment", Physica E: Low-dimens. Syst. Nanostruct., 102, 101-109. https://doi.org/10.1016/j.physe.2018.04.037
  40. Hussain, M. and Naeem, M.N. (2019), "Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes", Appl. Mathe. Model., 75, 506-520. https://doi.org/10.1016/j.apm.2019.05.039
  41. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2017), "Effect of different temperature load on thermal post buckling behaviour of functionally graded shallow curved shell panels", Compos. Struct., 160, 1236-1247. https://doi.org/10.1016/j.compstruct.2016.10.125
  42. Katariya, P.V., Hirwani, C.K. and Panda, S.K. (2019), "Geometrically nonlinear deflection and stress analysis of skew sandwich shell panel using higher-order theory", Eng. Comput., 35(2), 467-485. https://doi.org/10.1007/s00366-018-0609-3
  43. Khanik, H.B. (2018), "On vibrations of nanobeam systems", Int. J. Eng. Sci., 124, 85-103. https://doi.org/10.1016/j.ijengsci.2017.12.010
  44. Kiani, Y. and Eslami, M.R. (2013), "An exact solution for thermal buckling of annular FGM plates on an elastic medium", Compos. Part B: Eng., 45(1), 101-110. https://doi.org/10.1016/j.compositesb.2012.09.034
  45. Kolahchi, R., Safari, M. and Esmailpour, M. (2016), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023
  46. Lal, A., Jagtap, K.R. and Singh, B.N. (2017), "Thermomechanically induced finite element based nonlinear static response of elastically supported functionally graded plate with random system properties", Adv. Computat. Des., Int. J, 2(3), 165-194. https://doi.org/10.12989/acd.2017.2.3.165
  47. Li, D.H., Guo, Q.R., Xu, D. and Yang, X. (2017), "Threedimensional micromechanical analysis models of fiber reinforced composite plates with damage", Comput. Struct., 191, 100-114. https://doi.org/10.1016/j.compstruc.2017.06.005
  48. Mohamed, N., Eltaher, M.A., Mohamed, S.A. and Seddek, L.F. (2019), "Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation", Struct. Eng. Mech., Int. J., 70(6), 737-750. https://doi.org/10.12989/sem.2019.70.6.737
  49. Na, K.S. and Kim, J.H. (2004), "Three-dimensional thermal buckling analysis of functionally graded materials", Compos. B Eng., 35(5), 429-437. https://doi.org/10.1016/j.compositesb.2003.11.013
  50. Narwariya, M., Choudhury, A. and Sharma, A.K. (2018), "Harmonic analysis of moderately thick symmetric cross-ply laminated composite plate using FEM", Adv. Computat. Des., Int. J., 3(2), 113-132. https://doi.org/10.12989/acd.2018.3.2.113
  51. Othman, M.I.A., Abouelregal, A.E. and Said, S.M. (2019), "The effect of variable thermal conductivity on an infinite fiberreinforced thick plate under initial stress", J. Mech. Mater. Struct., 14(2), 277-293. https://doi.org/10.2140/jomms.2019.14.277
  52. Panjehpour, M., Loh, E.W.K. and Deepak, T.J. (2018), "Structural Insulated Panels: State-of-the-Art", Trends Civil Eng. Architect., 3(1), 336-340. https://doi.org/10.32474/TCEIA.2018.03.000151
  53. Pascon, J.P. (2018), "Large deformation analysis of functionally graded visco-hyperelastic materials", Comput. Struct., 206, 90-108. https://doi.org/10.1016/j.compstruc.2018.06.001
  54. Rajabi, J. and Mohammadimehr, M. (2019), "Bending analysis of a micro sandwich skew plate using extended Kantorovich method based on Eshelby-Mori-Tanaka approach", Comput. Concrete, Int. J., 23(5), 361-376. https://doi.org/10.12989/cac.2019.23.5.361
  55. Rezaiee-Pajand, M., Masoodi, A.R. and Mokhtari, M. (2018), "Static analysis of functionally graded non-prismatic sandwich beams", Adv. Computat. Des., Int. J., 3(2), 165-190. https://doi.org/10.12989/acd.2018.3.2.165
  56. Romano, G., Barretta, R. and Diaco, M. (2017), "On nonlocal integral models for elastic nano-beams", Int. J. Mech. Sci., 131-132, 490-499. https://doi.org/10.1016/j.ijmecsci.2017.07.013
  57. Safa, A., Hadji, L., Bourada, M. and Zouatnia, N. (2019), "Thermal vibration analysis of FGM beams using an efficient shear deformation beam theory", Earthq. Struct., Int. J., 17(3), 329-336. https://doi.org/10.12989/eas.2019.17.3.329
  58. Sahouane, A., Hadji, L. and Bourada, M. (2019), "Numerical analysis for free vibration of functionally graded beams using an original HSDBT", Earthq. Struct., Int. J., 17(1), 31-37. https://doi.org/10.12989/eas.2019.17.1.031
  59. Salamat, D. and Sedighi, H.M. (2017), "The effect of small scale on the vibrational behavior of single-walled carbon nanotubes with a moving nanoparticle", J. Appl. Computat. Mech., 3, 208-217. https://doi.org/10.22055/JACM.2017.12740
  60. Sedighi, H.M. (2014), "Size-dependent dynamic pull-in instability of vibrating electrically actuated microbeams based on the strain gradient elasticity theory", Acta Astronautica, 95(1), 111-123. https://doi.org/10.1016/j.actaastro.2013.10.020
  61. Sedighi, H.M. and Bozorgmehri, A. (2014), "Dynamic instability analysis of doubly clamped cylindrical nanowires in the presence of Casimir attraction and surface effects using modified couple stress theory", Acta Mechanica, 227(6), 1575-1591. https://doi.org/10.1007/s00707-016-1562-0
  62. Sedighi, H.M. and Sheikhanzadeh, A. (2017), "Static and dynamic pull-in instability of nano-beams resting on elastic foundation based on the nonlocal elasticity theory", Chin. J. Mech. Eng., 30, 385-397. https://doi.org/10.1007/s10033-017-0079-3
  63. Selmi, A. (2019), "Effectiveness of SWNT in reducing the crack effect on the dynamic behavior of aluminium alloy", Adv. Nano Res., Int. J., 7(5), 365-377. https://doi.org/10.12989/anr.2019.7.5.365
  64. Selmi, A. and Bisharat, A. (2018), "Free vibration of functionally graded SWNT reinforced aluminum alloy beam", J. Vibroeng., 20(5), 2151-2164. https://doi.org/10.21595/jve.2018.19445
  65. Shahadat, M.R.B., Alam, M.F., Mandal, M.N.A. and Ali, M.M. (2018), "Thermal transportation behaviour prediction of defective graphene sheet at various temperature: A Molecular Dynamics Study", Am. J. Nanomater., 6(1), 34-40. https://doi.org/10.12691/ajn-6-1-4
  66. Shahsavari, D., Karami, B. and Mansouri, S. (2018), "Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories", Eur. J. Mech. A, Solids, 67, 200-214. https://doi.org/10.1016/j.euromechsol.2017.09.004
  67. Sharma, J.N., Chand, R. and Othman, M.I.A. (2009), "On the propagation of Lamb waves in viscothermoelastic plates under fluid loadings", Int. J. Eng. Sci., 47(3), 391-404. https://doi.org/10.1016/j.ijengsci.2008.10.008
  68. Shodja, H.M., Ahmadpoor, F. and Tehranchi, A. (2012), "Calculation of the additional constants for fcc materials in second strain gradient elasticity: Behavior of a nano-size Bernoulli-Euler beam with surface effects", J. Appl. Mech. - Transact. ASME, 79, 021008:1-8. https://doi.org/10.1115/1.4005535
  69. Sobhy, M. (2017), "Hygro-thermo-mechanical vibration and buckling of exponentially graded nanoplates resting on elastic foundations via nonlocal elasticity theory", Struct. Eng. Mech., Int. J., 63(3), 401-415. http://dx.doi.org/10.12989/sem.2017.63.3.401
  70. Yuksela, Y.Z. and Akbas, S.D. (2018), "Free Vibration Analysis of a Cross-Ply Laminated Plate in Thermal Environment", Int. J. Eng. Appl. Sci. (IJEAS), 10(3), 176-189. http://dx.doi.org/10.24107/ijeas.456755
  71. Yuksela, Y.Z. and Akbas, S.D. (2019), "Buckling Analysis of a Fiber Reinforced Laminated Composite Plate with Porosity", J. Computat. Appl. Mech., 50(2), 375-380. https://doi.org/10.22059/jcamech.2019.291967.448

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