Advances in nano research

  • 제10권2호
  • /
  • Pages.115-128
  • /
  • 2021
  • /
  • 2287-237X(pISSN)
  • /
  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Free vibration of electro-magneto-thermo sandwich Timoshenko beam made of porous core and GPLRC

  • Safari, Mohammad (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Ashrafi, Hossein (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • 투고 : 2020.03.10
  • 심사 : 2020.11.20
  • 발행 : 2021.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this article, free vibration behavior of electro-magneto-thermo sandwich Timoshenko beam made of porous core and Graphene Platelet Reinforced Composite (GPLRC) in a thermal environment is investigated. The governing equations of motion are derived by using the modified strain gradient theory for micro structures and Hamilton's principle. The magneto electro are under linear function along the thickness that contains magnetic and electric constant potentials and a cosine function. The effects of material length scale parameters, temperature change, various distributions of porous, different distributions of graphene platelets and thickness ratio on the natural frequency of Timoshenko beam are analyzed. The results show that an increase in aspect ratio, the temperature change, and the thickness of GPL leads to reduce the natural frequency; while vice versa for porous coefficient, volume fractions and length of GPL. Moreover, the effect of different size-dependent theories such as CT, MCST and MSGT on the natural frequency is investigated. It reveals that MSGT and CT have most and lowest values of natural frequency, respectively, because MSGT leads to increase the stiffness of micro Timoshenko sandwich beam by considering three material length scale parameters. It is seen that by increasing porosity coefficient, the natural frequency increases because both stiffness and mass matrices decreases, but the effect of reduction of mass matrix is more than stiffness matrix. Considering the piezo magneto-electric layers lead to enhance the stiffness of a micro beam, thus the natural frequency increases. It can be seen that with increasing of the value of WGPL, the stiffness of microbeam increases. As a result, the value of natural frequency enhances. It is shown that in hc/h = 0.7, the natural frequency for WGPL = 0.05 is 8% and 14% less than its for WGPL = 0.06 and WGPL = 0.07, respectively. The results show that with an increment in the length and width of GPLs, the natural frequency increases because the stiffness of micro structures enhances and vice versa for thickness of GPLs. It can be seen that the natural frequency for aGPL = 25 ㎛ and hc/h = 0.6 is 0.3% and 1% more than the one for aGPL = 5 ㎛ and aGPL = 1 ㎛, respectively.

키워드

과제정보

The authors would like to thank the reviewers for their valuable comments and suggestions to improve the clarity of this work. Also, they would like to acknowledgement the Iranian Nanotechnology Development Committee for supporting this research and the University of Kashan under Grant No. 8911238/25.

참고문헌

  1. AkhavanAlavi, S.M., Mohammadimehr, M. and Edjtahed, S.H. (2019), "Active control of micro Reddy beam integrated with functionally graded nanocomposite sensor and actuator based on linear quadratic regulator method", Eur. J. Mech. A Solids, 74, 449-461. https://doi.org/10.1016/j.euromechsol.2018.12.008.
  2. Arefi, M. and Zenkour A.M. (2017), "Vibration and bending analysis of a sandwich microbeam with two integrated piezo-magnetic face-sheets", Compos. Struct., 159, 479-490. https://doi.org/10.1080/01495739.2016.1229146
  3. Arshid, E. and Khorshidvand, A.R. (2018), "Free vibration analysis of saturated porous FG circular plates integrated with piezoelectric actuators via differential quadrature method", Thin-Wall. Struct., 125, 220-233. https://doi.org/10.1016/j.tws.2018.01.007.
  4. Babaeeian, M. and Mohammadimehr, M. (2020), "Investigation of the time elapsed effect on residual stress measurement in a composite plate by DIC method", Opt. Lasers Eng., 128, 106002. https://doi.org/10.1016/j.optlaseng.2020.106002.
  5. Bahaadini, R. and Saidi, A.R. (2018), "Aeroelastic analysis of functionally graded rotating blades reinforced with graphene nanoplatelets in supersonic flow", Aerosp. Sci. Technol., 80, 381-391. https://doi.org/10.1016/j.ast.2018.06.035.
  6. Bamdad, M., Mohammadimehr, M. and Alambeigi, K. (2019), "Analysis of sandwich Timoshenko porous beam with temperature-dependent material properties: Magneto-electro-elastic vibration and buckling solution", J. Vib. Control, 25(23-24), 2875-2893. https://doi.org/10.1177/1077546319860314.
  7. Barati, M.R. and Shahverdi, H. (2019), "Finite element forced vibration analysis of refined shear deformable nanocomposite graphene platelet-reinforced beams", J. Braz. Soc. Mech. Sci. Eng., 42(1), 33-48. https://doi.org/10.1007/s40430-019-2118-8.
  8. Chen, D., Yang, J. and Kitipornchai S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compos. Struct., 133, 54-61. https://doi.org/10.1016/j.compstruct.2015.07.052.
  9. Chen, D., Kitipornchai, S. and Yang, J. (2016a), "Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core", Thin-Wall. Struct., 107, 39-48. https://doi.org/10.1016/j.tws.2016.05.025.
  10. Chen, D., Yang, J. and Kitipornchai, S. (2016b), "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, S., Hassanzadeh-Aghdam, M.K. and Ansari, R. (2018) , "An analytical model for elastic modulus calculation of SiC whisker-reinforced hybrid metal matrix nanocomposite containing SiC nanoparticles", J. Alloys Compd. 767, 632-641. https://doi.org/10.1016/j.jallcom.2018.07.102.
  12. Crupi, V. and Montanini, R. (2007), "Aluminium foam sandwiches collapse modes under static and dynamic three-point bending", Int. J. Impact Eng., 34(3), 509-521. https://doi.org/10.1016/j.ijimpeng.2005.10.001.
  13. Ebrahimi, F., Kokaba, M.R., Shaghaghi, G.R. and Selvamani, R. (2020), "Dynamic characteristics of hygro-magneto-thermo-electrical nanobeam with non-ideal boundary conditions", Adv. Nano Res., Int. J., 8(2), 169-182. https://doi.org/10.12989/anr.2020.8.2.169.
  14. Gao, N., Cheng, B., Hou, H. and Zhang, R. (2018), "Mesophase pitch based carbon foams as sound absorbers", Mater. Lett., 212, 243-246. https://doi.org/https://doi.org/10.1016/j.matlet.2017.10.074.
  15. Gibson, L.J. and Ashby, M.F. (1997), Introduction Cellular Solids: Structure and Properties. Cambridge University Press, USA. https://doi.org/10.1017/CBO9781139878326.003.
  16. Grygorowicz, M., Magnucki, K. and Malinowski, M. (2015), "Elastic buckling of a sandwich beam with variable mechanical properties of the core", Thin-Wall. Struct., 87, 127-132. https://doi.org/10.1016/j.tws.2014.11.014.
  17. Guo, X.Y. and Zhang, W. (2016), "Nonlinear vibrations of a reinforced composite plate with carbon nanotubes", Compos. Struct., 135, 96-108. https://doi.org/10.1016/j.compstruct.2015.08.063.
  18. Hoang, V.N.V., Minh, V.T., Ninh, D.G., Nguyen, C.T. and Huy, V.L. (2020a), "Effects of non-uniform elastic foundation on the nonlinear vibration of nanocomposite plates in thermal environment using Selvadurai methodology", Compos. Struct., 253, 112812. https://doi.org/10.1016/j.compstruct.2020.112812.
  19. Hoang, V.N.V., Tien, N.D., Ninh, D.G., Thang, V.T. and Troung, D.V. (2020b), "Nonlinear dynamics of functionally graded graphene nanoplatelet reinforced polymer doubly-curved shallow shells resting on elastic foundation using a micromechanical model", J. Sandw. Struct. Mater., 2020, 1099636220926650. https://doi.org/10.1177/1099636220926650.
  20. Hosseini, M. and Jamalpoor, A. (2015), "Analytical solution for thermomechanical vibration of double-viscoelastic nanoplate-systems made of functionally graded materials", J. Therm. Stresses, 38(12), 1428-1456. https://doi.org/10.1080/01495739.2015.1073986.
  21. Ma, H.M., Gao, X.L. and Reddy, J.N. (2008), "A microstructure-dependent Timoshenko beam model based on a modified couple stress theory", J. Mech. Phys. Solids, 56(12), 3379-3391. https://doi.org/10.1016/j.jmps.2008.09.007.
  22. Magnuca-Blandzi E. (2011), "Mathematical modelling of a rectangular sandwich plate with a metal foam core", J. Theor. Appl. Mech., 49(2), 439-455.
  23. Mohammadimehr, M. and Mostafavifar M. (2016), "Free vibration analysis of sandwich plate with a transversely flexible core and FG-CNTs reinforced nanocomposite face sheets subjected to magnetic field and temperature-dependent material properties using SGT", Compos. Part B Eng. 94, 253-270. https://doi.org/10.1016/j.compositesb.2016.03.030.
  24. Mohammadimehr, M. and Meskini, M. (2020), "Analysis of porous micro sandwich plate: Free and forced vibration under magneto-electro-elastic loadings", Adv. Nano Res., Int. J., 8(1), 69-82. https://doi.org/10.12989/anr.2020.8.1.069.
  25. Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2015a), "Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method", Compos. Struct., 131, 654-671. https://doi.org/10.1016/j.compstruct.2015.05.077.
  26. Mohammadimehr, M., Rostami, R. and Arefi, M. (2015b), "Electro-elastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT", Steel Compos. Struct., Int. J., 20(3), 513-543. https://doi.org/10.12989/scs.2016.20.3.513.
  27. Mohammadimehr, M., Salemi, M. and Rousta Navi, B. (2016), "Bending, buckling, and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperature-dependent material properties under hydro-thermo-mechanical loadings using DQM", Compos. Struct., 138, 361-380. https://doi.org/10.1016/j.compstruct.2015.11.055.
  28. Mohammadimehr, M., Mohammadi-Dehabadi, A.A., Akhavan Alavi, S.M., Alambeigi, K., Bamdad, M., Yazdani, R. and Hanifehlou, S. (2018), "Bending, buckling, and free vibration analyses of carbon nanotube reinforced composite beams and experimental tensile test to obtain the mechanical properties of nanocomposite", Steel Compos. Struct., Int. J., 29(3), 405-422. https://doi.org/10.12989/scs.2018.29.3.405.
  29. Mohammadimehr, M., Monajemi, A.A. and Afshari, H. (2020), "Free and forced vibration analysis of viscoelastic damped FG-CNT reinforced micro composite beams", Microsyst. Technol., 26, 3085-3099. https://doi.org/10.1007/s00542-017-3682-4.
  30. Nejadi, M.M. and Mohammadimehr, M. (2020), "Buckling analysis of nano composite sandwich Euler-Bernoulli beam considering porosity distribution on elastic foundation using DQM", Adv. Nano Res., Int. J., 8(1), 59-68. https://doi.org/10.12989/anr.2020.8.1.059.
  31. Ninh, D.G. (2018), "Nonlinear thermal torsional post-buckling of carbon nanotube-reinforced composite cylindrical shell with piezoelectric actuator layers surrounded by elastic medium", Thin-Wall. Struct., 123, 528-538. https://doi.org/10.1016/j.tws.2017.11.027.
  32. Ninh, D.G. and Bich, D.H. (2018), "Characteristics of nonlinear vibration of nanocomposite cylindrical shells with piezoelectric actuators under thermo-mechanical loads", Aerosp. Sci. Technol., 77, 595-609. https://doi.org/10.1016/j.ast.2018.04.008.
  33. Ninh, D.G. and Tien, N.D. (2019), "Investigation for electro-thermo-mechanical vibration of nanocomposite cylindrical shells with an internal fluid flow", Aerosp. Sci. Technol., 92, 501-519. https://doi.org/10.1016/j.ast.2019.06.023.
  34. Ninh, D.G., Tien, N.D. and Hoang, V.N.V. (2019), "Analyses of nonlinear dynamics of imperfect nanocomposite circular cylindrical shells with swirling annular and internal fluid flow using higher order shear deformation shell theory", Eng. Struct., 198, 109502. https://doi.org/10.1016/j.engstruct.2019.109502.
  35. Noroozi, R., Barati, A., Kazemi, A., Norouzi, S. and Hadi, A. (2020), "Torsional vibration analysis of bi-directional FG nano-cone with arbitrary cross-section based on nonlocal strain gradient elasticity", Adv. Nano Res., Int. J., 8(1), 13-24. https://doi.org/10.12989/anr.2020.8.1.013.
  36. Qin, Q.H. and Wang, T.J. (2009), "An analytical solution for the large deflections of a slender sandwich beam with a metallic foam core under transverse loading by a flat punch", Compos. Struct., 88, 509-518. https://doi.org/10.1016/j.compstruct.2008.05.012.
  37. Rafiee, M., Yang, J. and Kitipornchai, S. (2013), "Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers", Compos. Struct., 96, 716-725. https://doi.org/10.1016/j.compstruct.2012.10.005.
  38. Rajabi, J. and Mohammadimehr, M. (2019), "Hydro-thermo-mechanical biaxial buckling analysis of sandwich micro-plate with isotropic/orthotropic cores and piezoelectric/polymeric nanocomposite face sheets based on FSDT on elastic foundations", Steel Compos. Struct., Int. J., 33(4), 509-523. https://doi.org/10.12989/scs.2019.33.4.509.
  39. Shahdin, A., Mezeix, L., Bouvet, C., Morlier, J. and Gourinat, Y. (2009), "Fabrication and mechanical testing of glass fiber entangled sandwich beams: A comparison with honeycomb and foam sandwich beams", Compos. Struct., 90(4), 404-412. https://doi.org/10.1016/j.compstruct.2009.04.003.
  40. Shen, H.S., Lin, F. and Xiang, Y. (2017), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated beams resting on elastic foundations in thermal environments", Nonlin. Dyn. 90(2), 899-914. https://doi.org/10.1007/s11071-017-3701-0.
  41. 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., Int. J., 8(2), 135-148. https://doi.org/10.12989/anr.2020.8.2.135.
  42. Tagarielli, V.L., Deshpande, V.S. and Fleck, N.A. (2007), "The dynamic response of composite sandwich beams to transverse impact", Int. J. Solids Struct. 44(7), 2442-2457. https://doi.org/10.1016/j.ijsolstr.2006.07.015.
  43. Tien, N.D., Hoang, V.N.V., Ninh, D.G., Huy, V.L. and Hung, N.C. (2020), "Nonlinear dynamics and chaos of a nanocomposite plate subjected to electro-thermo-mechanical loads using Flugge-Lur'e-Bryrne theory", J. Vib. Control, 2020, 1077546320938185. https://doi.org/10.1177/1077546320938185.
  44. Wadley, H.N.G., Fleck, N.A. and Evans, A.G. (2003), "Fabrication and structural performance of periodic cellular metal sandwich structures", Compos. Sci. Technol., 63(16), 2331-2343. https://doi.org/10.1016/S0266-3538(03)00266-5.
  45. Wang, M., Guo, Y., Wang, B., Luo, H., Zhang, X., Wang, Q., Zhang, Y., Wu, H., Liu, H. and Dou, S. (2020), "An engineered self-supported electrocatalytic cathode and dendrite-free composite anode based on 3D double-carbon hosts for advanced Li-SeS2 batteries", J. Mater. Chem. A, 8(6), 2969-2983. https://doi.org/10.1039/C9TA11124G.
  46. Wu, H., Kitipornchai, S. and Yang, J. (2015), "Free vibration and buckling analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets", Int. J. Struct. Stab. Dyn., 15(7), 1540011. https://doi.org/10.1142/S0219455415400118.
  47. Wu, H., Yang, J. and Kitipornchai, S. (2017), "Dynamic instability of functionally graded multilayer graphene nanocomposite beams in thermal environment", Compos. Struct., 162, 244-254. https://doi.org/10.1016/j.compstruct.2016.12.001.
  48. Zenkour, A.M. and Arefi, M. (2017), "Nonlocal transient electrothermomechanical vibration and bending analysis of a functionally graded piezoelectric single-layered nanosheet rest on visco-Pasternak foundation", J. Therm. Stresses, 40(2), 1-18. https://doi.org/10.1080/01495739.2016.1229146.
  49. Zeverdejani, M.K. and Beni, Y.T. (2020), "Effect of laminate configuration on the free vibration/buckling of FG Graphene/PMMA composites", Adv. Nano Res., Int. J., 8(2), 103-114. https://doi.org/10.12989/anr.2020.8.2.103.
  50. Zhang, L.W., Lei, Z.X. and Liew, K.M. (2015), "Free vibration analysis of FG-CNT reinforced composite straight-sided quadrilateral plates resting on elastic foundations using the IMLS-Ritz method", J. Vib. Control, 23(6), 1026-1043. https://doi.org/10.1177/1077546315587804.
  51. Zhao, H., Li, Y., Song, Q., Liu, S., Ma, Q., Ma, L. and Shu, X. (2019), "Catalytic reforming of volatiles from co-pyrolysis of lignite blended with corn straw over three different structures of iron ores", J. Anal. Appl. Pyrolysis, 144, 104714. https://doi.org/10.1016/j.jaap.2019.104714
  52. Zhao, H., Li, Y., Song, Q., Ma, Q., Ma, L., Liu, S. and Shu, X. (2020), "The rate-limiting step in the integrated coal tar decomposition and upgrading-iron ore reduction reaction determined by kinetic analysis", J. Anal. Appl. Pyrolysis, 147, 104808. https://doi.org/10.1016/j.jaap.2020.104808.
  53. Zhou, H.W., Mishnaevsky, L., Yi, H.Y., Liu, Y.Q., Hu, X., Warrier, A. and Dai, G.M. (2016), "Carbon fiber/carbon nanotube reinforced hierarchical composites: Effect of CNT distribution on shearing strength", Compos. Part B Eng., 88, 201-211. https://doi.org/10.2514/1.11780.