Advances in nano research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Dynamic vibration response of functionally graded porous nanoplates in thermal and magnetic fields under moving load

  • Ismail Esen (Department of Mechanical Engineering, Karabuk University) ;
  • Mashhour A. Alazwari (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Khalid H. Almitani (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Mohamed A Eltaher (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • A. Abdelrahman (Mechanical Design & Production Department, Faculty of Engineering, Zagazig University)
  • Received : 2022.02.06
  • Accepted : 2022.10.04
  • Published : 2023.05.25
⟨ Previous Next ⟩

Abstract

In the context of nonclassical nonlocal strain gradient elasticity, this article studies the free and forced responses of functionally graded material (FGM) porous nanoplates exposed to thermal and magnetic fields under a moving load. The developed mathematical model includes shear deformation, size-scale, miscorstructure influences in the framework of higher order shear deformation theory (HSDT) and nonlocal strain gradient theory (NSGT), respectively. To explore the porosity effect, the study considers four different porosity models across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The system of quations of motion of the FGM porous nanoplate, including the effects of thermal load, Lorentz force, due to the magnetic field and moving load, are derived using the Hamilton's principle, and then solved analytically by employing the Navier method. For the free and forced responses of the nanoplate, the effects of nonlocal elasticity, strain gradient elasticity, temperature rise, magnetic field intensity, porosity volume fraction, and porosity distribution are analyzed. It is found that the forced vibrations of FGM porous nanoplates under thermal and live loads can be damped by applying a directed magnetic field.

Keywords

Acknowledgement

This research work was funded by Institutional Fund Projects (grant no. IFPIP: 206-135-1442). The authors gratefully acknowledge the technical and financial support from the Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.

References

  1. Aghababaei, R. and Reddy, J.N. (2009), "Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates", J. Sound Vib., 326, 277-289. https://doi.org/10.1016/j.jsv.2009.04.044
  2. Akavci, S.S. (2014), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Struct., 108, 667-676. https://doi.org/10.1016/j.compstruct.2013.10.019
  3. Alazwari, M.A., Esen, I., Abdelrahman, A.A., Abdraboh, A.M. and Eltaher, M.A. (2022), "Dynamic analysis of functionally graded (FG) nonlocal strain gradient nanobeams under thermo-magnetic fields and moving load", Adv. Nano Res., 12(3), 231-251. https://doi.org/10.12989/anr.2022.12.3.231
  4. Ansari, R., Ashrafi, M.A., Pourashraf, T. and Sahmani, S. (2015), "Vibration and buckling characteristics of functionally graded nanoplates subjected to thermal loading based on surface elasticity theory", Acta Astronaut., 109, 42-51. https://doi.org/https://doi.org/10.1016/j.actaastro.2014.12.015
  5. Arani, A.G. and Jalaei, M.H. (2017), "Investigation of the longitudinal magnetic field effect on dynamic response of viscoelastic graphene sheet based on sinusoidal shear deformation theory", Physica B, 506, 94-104. https://doi.org/10.1016/j.physb.2016.11.004
  6. Askari, M., Brusa, E. and Delprete, C. (2021), "On the vibration analysis of coupled transverse and shear piezoelectric functionally graded porous beams with higher-order theories", J. Strain Anal. Eng., 56, 29-49. https://doi.org/10.1177/0309324720922085
  7. Azartash, P., Khorsandijou, S.M. and Khorshidvand, A.R. (2021), "Enhanced geometrically-nonlinear poro-FG shear-deformable beams under moving load in discrete state-space", Austral. J. Mech. Eng., 1-28. https://doi.org/10.1080/14484846.2021.1914389
  8. Bendaho, B., Belabed, Z., Bourada, M., Benatta, M.A., Bourada, F. and Tounsi, A. (2019), "Assessment of new 2D and quasi-3D Nonlocal theories for free vibration analysis of size-dependent functionally graded (FG) nanoplates", Adv. Nano Res., 7(4), 277-292. https://doi.org/10.12989/anr.2019.7.4.277
  9. Boggarapu, V., Gujjala, R., Ojha, S., Acharya, S., Chowdary, S. and Kumar Gara, D. (2021), "State of the art in functionally graded materials", Compos. Struct., 262, 113596. https://doi.org/10.1016/j.compstruct.2021.113596
  10. Chen, D., Yang, J. and Kitipornchai, S. (2016), "Free and forced vibrations of shear deformable functionally graded porous beams", Int. J. Mech. Sci., 108-109, 14-22. https://doi.org/10.1016/j.ijmecsci.2016.01.025
  11. Chen, D., Zheng, S., Wang, Y., Yang, L. and Li, Z. (2020), "Nonlinear free vibration analysis of a rotating two-dimensional functionally graded porous micro-beam using isogeometric analysis", Eur. J. Mech. A Solids, 84, 104083. https://doi.org/10.1016/j.euromechsol.2020.104083
  12. Chinh, T.H., Tu, T.M., Duc, D.M. and Hung, T.Q. (2021), "Static flexural analysis of sandwich beam with functionally graded face sheets and porous core via point interpolation meshfree method based on polynomial basic function", Arch. Appl. Mech., 91, 933-947. https://doi.org/10.1007/s00419-020-01797-x
  13. Dang, V.H. and Do, Q.C. (2021), "Nonlinear vibration and stability of functionally graded porous microbeam under electrostatic actuation", Arch. Appl. Mech., 91, 2301-2329. https://doi.org/10.1007/s00419-021-01884-7
  14. Derikvand, M., Farhatnia, F. and Hodges, D.H. (2021), "Functionally graded thick sandwich beams with porous core: Buckling analysis via differential transform method", Mech. Based Des. Struct. Mach., 1-28. https://doi.org/10.1080/15397734.2021.1931309
  15. Doan, T.L., Le, P.B., Tran, T.T., Trai, V.K. and Pham, Q.H. (2021), "Free vibration analysis of functionally graded porous nanoplates with different shapes resting on elastic foundation", J. Appl. Comput. Mech., 7, 1593-1605. https://doi.org/10.22055/jacm.2021.36181.2807
  16. Ebrahimi, F., Dabbagh, A. and Taheri, M. (2021), "Vibration analysis of porous metal foam plates rested on viscoelastic substrate", Eng. Comput., 37(4), 3727-3739. https://doi.org/10.1007/s00366-020-01031-w.
  17. Ebrahimi, F., Ghasemi, F. and Salari, E. (2016), "Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities", Meccanica, 51, 223-249. https://doi.org/10.1007/s11012-015-0208-y
  18. Ebrahimi, F. and Jafari, A. (2016), "A higher-order thermo-mechanical vibration analysis of temperature-dependent FGM beams with porosities", J. Eng., 2016, 20. https://doi.org/10.1155/2016/9561504
  19. Eltaher, M.A., Abdelrahman, A.A., Al-Nabawy, A., Khater, M. and Mansour, A. (2014), "Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position", Appl. Math. Comput., 235, 512-529. https://doi.org/10.1016/j.amc.2014.03.028.
  20. Eltaher, M.A., Almalki, T.A., Ahmed, K.I. and Almitani, K.H. (2019), "Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach", Adv. Nano Res., 7(1), 39. https://doi.org/10.12989/anr.2019.7.1.039
  21. Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano Res., 4(1), 51. https://doi.org/10.12989/anr.2016.4.1.051
  22. Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazil. Soc. Mech. Sci. Eng., 40, 1-10. https://doi.org/10.1007/s40430-018-1065-0
  23. 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
  24. Eringen, A.C. and Suhubi, E.S. (1964), "Nonlinear theory of simple micro-elastic solids-I", Int. J. Eng. Sci., 2, 189-203. https://doi.org/https://doi.org/10.1016/0020-7225(64)90004-7
  25. Esmaeilzadeh, M., Esmaeil Golmakani, M., Kadkhodayan, M., Amoozgar, M. and Bodaghi, M. (2021), "Geometrically nonlinear thermo-mechanical analysis of graphene-reinforced moving polymer nanoplates", Adv. Nano Res., 10(2), 151-163. https://doi.org/10.12989/anr.2021.10.2.151
  26. 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. Modell., 80, 169-190. https://doi.org/10.1016/j.apm.2019.11.040
  27. Fryba, L. (1999), Vibration of Solids and Structures under Moving Loads, Thomas Telford Publishing. https://doi.org/10.1680/vosasuml.35393
  28. Gayen, D. (2022), "Analysis of temperature, displacement, and stress in shafts made of functionally graded materials with various grading laws", Adv. Eng. Mater., 24(5), 2101328. https://doi.org/10.1002/adem.202101328
  29. Gayen, D., Tiwari, R. and Chakraborty, D. (2019), "Static and dynamic analyses of cracked functionally graded structural components: A review", Compos. Part B Eng., 173, 106982. https://doi.org/10.1016/j.compositesb.2019.106982
  30. Gayen, D., Tiwari, R. and Chakraborty, D. (2021), "Thermo-Mechanical Analysis of a Rotor-Bearing System Having a Functionally Graded Shaft with Transverse Breathing Cracks", In Proceedings of the 6th National Symposium on Rotor Dynamics. Springer, Singapore. https://doi.org/10.1007/978-981-15-5701-98
  31. Ghandourah, E.E., Ahmed, H.M., Eltaher, M.A., Attia, M.A. and Abdraboh, A.M. (2021), "Free vibration of porous FG nonlocal modified couple nanobeams via a modified porosity model", Adv. Nano Res., 11(4), 405-422. https://doi.org/10.12989/anr.2021.11.4.405
  32. Ghandourah, E.E. and Abdraboh, A.M. (2020), "Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models", Steel Compos. Struct., 36, 293-305. https://doi.org/10.12989/scs.2020.36.3.293
  33. Giannopoulos, G.I., Kakavas, P.A. and Anifantis, N.K. (2008), "Evaluation of the effective mechanical properties of single walled carbon nanotubes using a spring based finite element approach", Comput. Mater. Sci., 41, 561-569. https://doi.org/https://doi.org/10.1016/j.commatsci.2007.05.016
  34. Huang, X.L. and Shen, H.S. (2004), "Nonlinear vibration and dynamic response of functionally graded plates in thermal environments", Int. J. Solids Struct., 41, 2403-2427. https://doi.org/10.1016/j.ijsolstr.2003.11.012
  35. Jalaei, M.H. and Arani, A.G. (2018), "Analytical solution for static and dynamic analysis of magnetically affected viscoelastic orthotropic double-layered graphene sheets resting on viscoelastic foundation", Physica B, 530, 222-235. https://doi.org/10.1016/j.physb.2017.11.049
  36. 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
  37. Jalaei, M.H. and Thai, H.T. (2019), "Dynamic stability of viscoelastic porous FG nanoplate under longitudinal magnetic field via a nonlocal strain gradient quasi-3D theory", Compos. Part B Eng., 175, 107164. https://doi.org/10.1016/j.compositesb.2019.107164
  38. Jankowski, P., Zur, K.K., Kim, J., Lim, C.W. and Reddy, J.N. (2021), "On the piezoelectric effect on stability of symmetric FGM porous nanobeams", Compos. Struct., 267. https://doi.org/10.1016/j.compstruct.2021.113880
  39. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2012), "Nonlinear free vibration of size-dependent functionally graded microbeams", Int. J. Eng. Sci., 50, 256-267. https://doi.org/10.1016/J.IJENGSCI.2010.12.008
  40. Kiani, Y. (2017), "Thermal post-buckling of FG-CNT reinforced composite plates", Compos. Struct., 159, 299-306. https://doi.org/10.1016/j.compstruct.2016.09.084.
  41. Kim, J., Zur, K.K. and Reddy, J.N. (2019), "Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates", Compos. Struct., 209, 879-888. https://doi.org/10.1016/j.compstruct.2018.11.023.
  42. Kong, S., Zhou, S., Nie, Z. and Wang, K. (2008), "The size-dependent natural frequency of Bernoulli-Euler micro-beams", Int. J. Eng. Sci., 46, 427-437. https://doi.org/10.1016/j.ijengsci.2007.10.002
  43. Kraus, J. (1992), Electromagnetics, McGraw-Hill.
  44. Li, L. and Hu, Y. (2015), "Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory", Int. J. Eng. Sci., 97, 84-94. https://doi.org/10.1016/j.ijengsci.2015.08.013
  45. Li, L. and Hu, Y. (2016), "Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 107. https://doi.org/10.1016/j.ijengsci.2016.07.011
  46. Li, L., Pratihar, D.K., Chakrabarty, S. and Mishra, P.C. (2020), Advances in Materials and Manufacturing Engineering, 119(125), Springer. https://doi.org/10.1007/978-981-15-1307-7
  47. Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001
  48. Liu, H., Liu, H. and Yang, J. (2018), "Vibration of FG magneto-electro-viscoelastic porous nanobeams on visco-Pasternak foundation", Compos. Part B Eng., 155, 244-256. https://doi.org/10.1016/j.compositesb.2018.08.042
  49. Merzouki, T., Ahmed, H.M.S., Bessaim, A., Haboussi, M., Dimitri, R. and Tornabene, F. (2021), "Bending analysis of functionally graded porous nanocomposite beams based on a non-local strain gradient theory", Math. Mech. Solids, 27(1), 66-92. https://doi.org/10.1177/10812865211011759
  50. Najafi, F., Shojaeefard, M.H. and Googarchin, H.S. (2017), "Nonlinear dynamic response of FGM beams with Winkler-Pasternak foundation subject to noncentral low velocity impact in thermal field", Compos. Struct., 167, 132-143. https://doi.org/https://doi.org/10.1016/j.compstruct.2017.01.063.
  51. Nikrad, S.F., Kanellopoulos, A., Bodaghi, M., Chen, Z.T. and Pourasghar, A. (2021), "Large deformation behavior of functionally graded porous curved beams in thermal environment", Arch. Appl. Mech., 91, 2255-2278. https://doi.org/10.1007/s00419-021-01882-9
  52. Oguamanam, D.C.D., Hansen, J.S. and Heppler, G.R. (1998), "Dynamic response of an overhead crane system", J. Sound Vib., 213, 889-906. https://doi.org/https://doi.org/10.1006/jsvi.1998.1564
  53. Pandey, S. and Pradyumna, S. (2015), "Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory", Eur. J. Mech. A Solids, 51, 55-66. https://doi.org/10.1016/j.euromechsol.2014.12.001
  54. Penna, R., Feo, L. and Lovisi, G. (2021a), "Hygro-thermal bending behavior of porous FG nano-beams via local/nonlocal strain and stress gradient theories of elasticity", Compos. Struct., 263, 113627. https://doi.org/10.1016/j.compstruct.2021.113627
  55. Penna, R., Feo, L., Lovisi, G. and Fabbrocino, F. (2021b), "Hygro-thermal vibration of porous fg nano-beams based on local/ nonlocal stress gradient theory of elasticity", Nanomaterials, 11, 1-16. https://doi.org/10.3390/nano11040910
  56. Rahmani, A., Faroughi, S. and Friswell, M.I. (2020a), "The vibration of two-dimensional imperfect functionally graded (2D-FG) porous rotating nanobeams based on general nonlocal theory", Mech. Syst. Signal Pr., 144, 106854. https://doi.org/10.1016/j.ymssp.2020.106854
  57. Rahmani, F., Kamgar, R. and Rahgozar, R. (2020b), "Finite element analysis of functionally graded beams using different beam theories", Civil Eng. J., 6, 2086-2102. https://doi.org/10.28991/cej-2020-03091604
  58. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719
  59. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45, 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  60. Reddy, J.N. and Chin, C.D. (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21, 593-626. https://doi.org/10.1080/01495739808956165
  61. Salari, E., Sadough Vanini, S.A., Ashoori, A.R. and Akbarzadeh, A.H. (2020), "Nonlinear thermal behavior of shear deformable FG porous nanobeams with geometrical imperfection: Snap-through and postbuckling analysis", Int. J. Mech. Sci., 178, 105615. https://doi.org/10.1016/j.ijmecsci.2020.105615
  62. Saleh, B., Jiang, J., Fathi, R., Al-hababi, T., Xu, Q., Wang, L., Song, D. and Ma, A. (2020), "30 Years of functionally graded materials: An overview of manufacturing methods, applications and future challenges", Compos. Part B Eng., 201, 108376. https://doi.org/10.1016/j.compositesb.2020.108376
  63. Shafiei, N. and Kazemi, M. (2017), "Nonlinear buckling of functionally graded nano-/micro-scaled porous beams", Compos. Struct., 178, 483-492. https://doi.org/10.1016/j.compstruct.2017.07.045
  64. She, G.L., Ren, Y.R. and Yan, K.M. (2019), "On snap-buckling of porous FG curved nanobeams", Acta Astronaut., 161, 475-484. https://doi.org/10.1016/j.actaastro.2019.04.010
  65. Sobhy, M. (2015), "Hygrothermal deformation of orthotropic nanoplates based on the state-space concept", Compos. Part B Eng., 79, 224-235. https://doi.org/10.1016/j.compositesb.2015.04.042
  66. Srinivas, S. and Rao, A.K. (1970), "Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates", Int. J. Solid Struct., 6, 1463-1481. https://doi.org/https://doi.org/10.1016/0020-7683(70)90076-4
  67. Talebizadehsardari, P., Salehipour, H., Shahgholian-Ghahfarokhi, D., Shahsavar, A. and Karimi, M. (2020), "Free vibration analysis of the macro-micro-nano plates and shells made of a material with functionally graded porosity: A closed-form solution", Mech. Based Des. Struct. Mach., 1-27. https://doi.org/10.1080/15397734.2020.1744002
  68. Touloukian, Y.S. (1967), Thermophysical Properties of High Temperature Solid Materials, Macmillan, New York, U.S.A.
  69. Wang, Y., Xie, K. and Fu, T. (2018), "Vibration analysis of functionally graded porous shear deformable tubes excited by moving distributed loads", Acta Astronaut., 151, 603-613. https://doi.org/https://doi.org/10.1016/j.actaastro.2018.06.003
  70. 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
  71. Xu, X., Karami, B. and Shahsavari, D. (2021), "Time-dependent behavior of porous curved nanobeam", Int. J. Eng. Sci., 160. https://doi.org/10.1016/j.ijengsci.2021.103455
  72. Yayli, M.O. (2015), "Buckling analysis of a rotationally restrained single walled carbon nanotube", Acta Phys. Pol. A, 127(3), 678-683. https/doi.org/10.12693/APhysPolA.127.678
  73. Yayli, M.O. (2016), "Buckling analysis of a microbeam embedded in an elastic medium with deformable boundary conditions", Micro Nano Lett., 11(11), 741-745. https://doi.org/10.1049/mnl.2016.0257
  74. Yayli, M.O . (2018a), "Free longitudinal vibration of a nanorod with elastic spring boundary conditions made of functionally graded material", Micro Nano Lett., 13(7), 1031-1035. https://doi.org/10.1049/mnl.2018.0181
  75. Yayli, M.O. (2018b), "Free vibration analysis of a single-walled carbon nanotube embedded in an elastic matrix under rotational restraints", Micro Nano Lett., 13(2), 202-206. https://doi.org/10.1049/mnl.2017.0463
  76. Yayli, M.O. (2018c), "Torsional vibration analysis of nanorods with elastic torsional restraints using non-local elasticity theory", Micro Nano Lett., 13(5), 595-599. https://doi.org/10.1049/mnl.2017.0751
  77. Yayli, M.O. (2019a), "Effects of rotational restraints on the thermal buckling of carbon nanotube", Micro Nano Lett., 14(2), 158-162. https://doi.org/10.1049/mnl.2018.5428
  78. Yayli, M.O. (2019b), "Free vibration analysis of a rotationally restrained (FG) nanotube", Microsyst. Technol., 25(10), 3723-3734. https://doi.org/10.1007/s00542-019-04307-4
  79. Yayli, M.O . (2020), "Axial vibration analysis of a Rayleigh nanorod with deformable boundaries", Microsyst. Technol., 26(8), 2661-2671. https://doi.org/10.1007/s00542-020-04808-7