Abstract
In this paper, thermal buckling and free/forced vibration characteristics of size-dependent composite cylindrical nanoshell reinforced with graphene platelets (GPLs) is presented. Also, the nanoshell is embedded in an elastic pasternak medium, which is obtained by adding a shear layer to the Winkler model. The present nano-resonator is based on a vibrating first order nanoscale cylindrical shell subjected to transverse pressure. The temperature-dependent material properties of piece-wise functionally graded graphene-reinforced composites (FG-GRCs) are assumed to be graded in the thickness direction of a cylindrical nanoshell and are estimated through a nanomechanical model. Also, Halpin–Tsai nanomechanical model in used to surmise the effective material properties of each layer. The size-dependent FG-GRCs nanoshell is analyzed using modified couple stress parameter. The novelty of the current study is in considering the effects of FG-GRCs and thermal in addition of size effect on resonance frequencies, thermal buckling and dynamic deflections of the FG-GRCs nanoshell. The governing equations and boundary conditions have been developed using Hamilton’s principle and have been solved with the aid of analytical method. The results show that, GPL distribution pattern, modified couple stress parameter, length to radius ratio, mode number, winkler coefficient and thermal environment have important role on resonance frequency, relative frequency change, thermal buckling and dynamic deflections of the FG-GRCs cylindrical nanoshell in thermal environments.
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Ansari, R., Gholami, R., Rouhi, H.: Vibration analysis of single-walled carbon nanotubes using different gradient elasticity theories. Compos. B Eng. 43, 2985–2989 (2012)
Asghari, M., Kahrobaiyan, M., Rahaeifard, M., Ahmadian, M.: Investigation of the size effects in Timoshenko beams based on the couple stress theory. Arch. Appl. Mech. 81, 863–874 (2011)
Atanasov, M.S., Karličić, D., Kozić, P.: Forced transverse vibrations of an elastically connected nonlocal orthotropic double-nanoplate system subjected to an in-plane magnetic field. Acta Mech. 228, 2165–2185 (2017)
Baibarac, M., Gómez-Romero, P.: Nanocomposites based on conducting polymers and carbon nanotubes: from fancy materials to functional applications. J. Nanosci. Nanotechnol. 6, 289–302 (2006)
Barati, M.R.: A general nonlocal stress-strain gradient theory for forced vibration analysis of heterogeneous porous nanoplates. Eur. J. Mech. A/Solids 67, 215–230 (2018)
Barooti, M.M., Safarpour, H., Ghadiri, M.: Critical speed and free vibration analysis of spinning 3D single-walled carbon nanotubes resting on elastic foundations. Eur. Phys. J. Plus 132, 6 (2017)
Barretta, R., Marotti de Sciarra, F.: A nonlocal model for carbon nanotubes under axial loads. Adv. Mater. Sci. Eng. 2013, 1–8 (2013)
Barretta, R., Brčić, M., Čanađija, M., Luciano, R., de Sciarra, F.M.: Application of gradient elasticity to armchair carbon nanotubes: size effects and constitutive parameters assessment. Eur. J. Mech. A/Solids 65, 1–13 (2017)
Baughman, R.H., Zakhidov, A.A., De Heer, W.A.: Carbon nanotubes—the route toward applications. Science 297, 787–792 (2002)
Čanađija, M., Barretta, R., de Sciarra, F.M.: On functionally graded Timoshenko nonisothermal nanobeams. Compos. Struct. 135, 286–296 (2016)
de Sciarra, F.M., Salerno, M.: On thermodynamic functions in thermoelasticity without energy dissipation. Eur. J. Mech. A/Solids 46, 84–95 (2014)
Eslami, M., Ziaii, A., Ghorbanpour, A.: Thermoelastic buckling of thin cylindrical shells based on improved stability equations. J. Therm. Stresses 19, 299–315 (1996)
Feng, C., Kitipornchai, S., Yang, J.: Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs). Compos. B Eng. 110, 132–140 (2017)
Fu, Y., Du, H., Huang, W., Zhang, S., Hu, M.: TiNi-based thin films in MEMS applications: a review. Sens. Actuators A Phys. 112, 395–408 (2004)
Ghadiri, M., Safarpour, H.: Free vibration analysis of embedded magneto-electro-thermo-elastic cylindrical nanoshell based on the modified couple stress theory. Appl. Phys. A 122, 833 (2016)
Huang, H., Han, Q.: Buckling of imperfect functionally graded cylindrical shells under axial compression. Eur. J. Mech. A/Solids 27, 1026–1036 (2008)
Khanade, K., Sasangohar, F., Sadeghi, M., Sutherland, S., Alexander, K.: Deriving information requirements for a smart nursing system for intensive care units. In: Proceedings of the Human Factors and Ergonomics Society Annual Meeting, pp. 653–654 (2017)
Kolter, W.: Couple stresses in the theory of elasticity. Proc. Koninklijke Nederl. Akaad. van Wetensch 67, 20 (1964)
Kothurkar, N.K.: Solid State, Transparent, Cadmium Sulfide-Polymer Nanocomposites. University of Florida, Gainesville (2004)
Lee, Z., Ophus, C., Fischer, L., Nelson-Fitzpatrick, N., Westra, K., Evoy, S., et al.: Metallic NEMS components fabricated from nanocomposite Al–Mo films. Nanotechnology 17, 3063 (2006)
Li, M., Liu, J., Zhang, X., Tian, Y., Jiang, K.: Fabrication of graphene/nickel composite microcomponents using electroforming. Int. J. Adv. Manuf. Technol. 96, 3191–3196 (2018)
Mescher, M.J., Houston, K., Bernstein, J.J., Kirkos, G., Cheng, J., Cross, L.E.: Novel MEMS microshell transducer arrays for high-resolution underwater acoustic imaging applications. In: Sensors, 2002. Proceedings of IEEE, pp. 541–546 (2002)
Miandoab, E.M., Pishkenari, H.N., Yousefi-Koma, A., Hoorzad, H.: Polysilicon nano-beam model based on modified couple stress and Eringen’s nonlocal elasticity theories. Physica E 63, 223–228 (2014)
Mindlin, R.D.: Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51–78 (1964)
Mirzavand, B., Eslami, M.: Thermal buckling of imperfect functionally graded cylindrical shells based on the Wan-Donnell model. J. Therm. Stresses 29, 37–55 (2006)
Mirzavand, B., Eslami, M.R., Shahsiah, R.: Effect of imperfections on thermal buckling of functionally graded cylindrical shells. AIAA J 43, 2073–2076 (2005)
Moniruzzaman, M., Winey, K.I.: Polymer nanocomposites containing carbon nanotubes. Macromolecules 39, 5194–5205 (2006)
Montazeri, A., Rafii-Tabar, H.: Multiscale modeling of graphene-and nanotube-based reinforced polymer nanocomposites. Phys. Lett. A 375, 4034–4040 (2011)
Mortazavi, B., Benzerara, O., Meyer, H., Bardon, J., Ahzi, S.: Combined molecular dynamics-finite element multiscale modeling of thermal conduction in graphene epoxy nanocomposites. Carbon 60, 356–365 (2013)
Park, S., Gao, X.: Bernoulli–Euler beam model based on a modified couple stress theory. J. Micromech. Microeng. 16, 2355 (2006)
Potts, J.R., Dreyer, D.R., Bielawski, C.W., Ruoff, R.S.: Graphene-based polymer nanocomposites. Polymer 52, 5–25 (2011)
Radhamoman, S., Enkataramana, J.: Thermal buckling of orthotropic cylindrical shells. AIAA J 13, 397–399 (1975)
Rafiee, M.A., Rafiee, J., Wang, Z., Song, H., Yu, Z.-Z., Koratkar, N.: Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano 3, 3884–3890 (2009a)
Rafiee, M., Rafiee, J., Yu, Z.-Z., Koratkar, N.: Buckling resistant graphene nanocomposites. Appl. Phys. Lett. 95, 223103 (2009b)
Rafiee, M.A., Rafiee, J., Srivastava, I., Wang, Z., Song, H., Yu, Z.Z., et al.: Fracture and fatigue in graphene nanocomposites. Small 6, 179–183 (2010)
Rahaeifard, M., Kahrobaiyan, M., Ahmadian, M.: Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials. In: ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 539–544 (2009)
Reddy, J.: Microstructure-dependent couple stress theories of functionally graded beams. J. Mech. Phys. Solids 59, 2382–2399 (2011)
Sadeghi, M., Thomassie, R., Sasangohar, F.: Objective assessment of functional information requirements for patient portals. In: Proceedings of the Human Factors and Ergonomics Society Annual Meeting, pp. 1788–1792 (2017)
Sahmani, S., Aghdam, M.: A nonlocal strain gradient hyperbolic shear deformable shell model for radial postbuckling analysis of functionally graded multilayer GPLRC nanoshells. Compos. Struct. 178, 97–109 (2017a)
Sahmani, S., Aghdam, M.: Nonlinear instability of axially loaded functionally graded multilayer graphene platelet-reinforced nanoshells based on nonlocal strain gradient elasticity theory. Int. J. Mech. Sci. 131, 95–106 (2017b)
Sandler, J., Kirk, J., Kinloch, I., Shaffer, M., Windle, A.: Ultra-low electrical percolation threshold in carbon-nanotube–epoxy composites. Polymer 44, 5893–5899 (2003)
Shaat, M., Mahmoud, F., Gao, X.-L., Faheem, A.F.: Size-dependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects. Int. J. Mech. Sci. 79, 31–37 (2014)
Shahsiah, R., Eslami, M.: Thermal buckling of functionally graded cylindrical shell. J. Therm. Stresses 26, 277–294 (2003)
Shojaeian, M., Beni, Y.T.: Size-dependent electromechanical buckling of functionally graded electrostatic nano-bridges. Sens. Actuators A Phys. 112, 395–408 (2015)
Soltani, P., Saberian, J., Bahramian, R.: Nonlinear vibration analysis of single-walled carbon nanotube with shell model based on the nonlocal elasticity theory. J. Comput. Nonlinear Dyn. 11, 011002 (2016)
Song, M., Kitipornchai, S., Yang, J.: Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets. Compos. Struct. 159, 579–588 (2017)
Tadi Beni, Y., Mehralian, F., Zeighampour, H.: The modified couple stress functionally graded cylindrical thin shell formulation. Mech. Adv. Mater. Struct. 23, 791–801 (2016)
Thangaratnam, R.K., Palaninathan, R., Ramachandran, J.: Thermal buckling of laminated composite shells. AIAA J 28, 859–860 (1990)
Toupin, R.A.: Elastic materials with couple-stresses. Arch. Ration. Mech. Anal. 11, 385–414 (1962)
Vafamehr, A., Khodayar, M.E., Abdelghany, K.: Oligopolistic competition among cloud providers in electricity and data networks. IEEE Trans. Smart Grid (2017). https://doi.org/10.1109/TSG.2017.2778027
Vafamehr, A., Khodayar, M.E.: Energy-aware cloud computing. Electr. J. 31, 40–49 (2018)
Vafamehr, A., Khodayar, M.E., Manshadi, S.D., Ahmad, I., Lin, J.: A framework for expansion planning of data centers in electricity and data networks under uncertainty. IEEE Trans. Smart Grid 6, 2283–2393 (2017)
Wang, Y., Yu, J., Dai, W., Song, Y., Wang, D., Zeng, L., et al.: Enhanced thermal and electrical properties of epoxy composites reinforced with graphene nanoplatelets. Polym. Compos. 36, 556–565 (2015)
Witvrouw, A., Mehta, A.: The use of functionally graded poly-SiGe layers for MEMS applications. Mater. Sci. Forum 492, 255–260 (2005)
Wu, H., Kitipornchai, S., Yang, J.: Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates. Mater. Des. 132, 430–441 (2017)
Yang, F., Chong, A., Lam, D., Tong, P.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39, 2731–2743 (2002)
Yang, J., Wu, H., Kitipornchai, S.: Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams. Compos. Struct. 161, 111–118 (2017)
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Safarpour, H., Esmailpoor Hajilak, Z. & Habibi, M. A size-dependent exact theory for thermal buckling, free and forced vibration analysis of temperature dependent FG multilayer GPLRC composite nanostructures restring on elastic foundation. Int J Mech Mater Des 15, 569–583 (2019). https://doi.org/10.1007/s10999-018-9431-8
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DOI: https://doi.org/10.1007/s10999-018-9431-8