Abstract
The theoretical modeling of a functionally graded (FG) graphene nanoplatelet (GPL)-reinforced assembled beam–plate structure resting on elastic supports is presented for the first time, and its free vibration analysis is performed. Herein, the assembled structure is modeled according to the Kirchhoff plate theory and the Rayleigh beam theory. The graphene nanoplatelets (GPLs) gradiently distribute in the beam’s radial direction and in the plate’s thickness direction, respectively. By adopting the rule of mixture and the Halpin–Tsai model, the effective material properties can be obtained. By employing the Lagrange’s equation and considering the effects of Coriolis force and centrifugal force, the coupled governing equations of the assembled structure are determined. Furthermore, the assumed modes method and substructure modal synthesis method are applied to obtain the frequencies of the assembled beam–plate structure. A comprehensive numerical investigation is carried out to discuss the influence of the structural and material parameters on the vibration behavior of the beam–plate structure.
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References
Song, O., Librescu, L.: Modeling and dynamic behavior of rotating blades carrying a tip mass and incorporating adaptive capabilities. Acta Mech. 134(3), 169–197 (1999)
Behzad, M., Bastami, A.R.: Effect of centrifugal force on natural frequency of lateral vibration of rotating shafts. J. Sound Vib. 274(3–5), 985–995 (2004)
Zhao, T.Y., Yuan, H.Q., Li, B.B., Li, Z.J., Liu, L.M.: Analytical solution for rotational rub-impact plate under thermal shock. J. Mech. 32(3), 297–311 (2016)
Jalaei, M., Civalek, O.: On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam. Int. J. Eng. Sci. 143, 14–32 (2019)
Luo, R.: Free transverse vibration of rotating blades in a bladed disk assembly. Acta Mech. 223(7), 1385–1396 (2012)
Civalek, O., Dastjerdi, S., Akbaş, S.D., Akgöz, B.: On the analysis of microbeams. Int. J. Eng. Sci. 121, 14–33 (2017)
Falsone, G., La Valle, G.: A homogenized theory for functionally graded Euler–Bernoulli and Timoshenko beams. Acta Mech. 230, 3511–3523 (2019)
Wang, Y.Q.: Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state. Acta Astronaut. 143, 263–271 (2018)
Wang, Y.Q., Huang, X.B., Li, J.: Hydroelastic dynamic analysis of axially moving plates in continuous hot-dip galvanizing process. Int. J. Mech. Sci. 110, 201–216 (2016)
Yang, F.L., Wang, Y.Q.: Free and forced vibration of beams reinforced by 3D graphene foam. Int. J. Appl. Mech. 12, 2050056 (2020)
Wang, Y., Wu, H., Yang, F., Wang, Q.: An efficient method for vibration and stability analysis of rectangular plates axially moving in fluid. Appl. Math. Mech. 42, 291–308 (2021)
Zhu, K., Chung, J.: Dynamic modeling and analysis of a spinning Rayleigh beam under deployment. Int. J. Mech. Sci. 115–116, 392–405 (2016)
Mirtalaie, S.H., Hajabasi, M.A.: Nonlinear axial–lateral–torsional free vibrations analysis of Rayleigh rotating shaft. Arch. Appl. Mech. 87(9), 1–30 (2017)
Wang, J., Li, D.X., Jiang, J.P.: Modeling and analysis for coupled flexural–torsional spinning beams with unsymmetrical cross sections. J. Theor. Appl. Mech. 55(1), 213–226 (2017)
Amine, A.M., Faouzi, L.: On mathematical modelling of linear flexural vibrations of spinning Rayleigh beams. J. Sound Vib. 430, 17–35 (2018)
Shabanlou, G., Hosseini, S.A.A., Zamanian, M.: Vibration analysis of FG spinning beam using higher-order shear deformation beam theory in thermal environment. Appl. Math. Model. 56, 325–341 (2018)
Du, C.F., Zhang, D.G., Liu, G.R.: A cell-based smoothed finite element method for free vibration analysis of a rotating plate. Int. J. Comput. Methods 16, 1840003 (2017)
Parida, S., Mohanty, S.C.: Free vibration analysis of rotating functionally graded material plate under nonlinear thermal environment using higher order shear deformation theory. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 233(6), 2056–2073 (2019)
Liu, L.T., Hao, Y.X., Zhang, W., Chen, J.: Free vibration analysis of rotating pretwisted functionally graded sandwich blades. Int. J. Aerosp. Eng. 2018, 1–18 (2018)
Babu, A.A., Vasudevan, R.: Vibration analysis of rotating delaminated non-uniform composite plates. Aerosp. Sci. Technol. 60, 172–182 (2017)
Rostami, H., Rahbar Ranji, A., Bakhtiarinejad, F.: Free in-plane vibration analysis of rotating rectangular orthotropic cantilever plates. Int. J. Mech. Sci. 115, 438–456 (2016)
Li, L., Zhang, D.G.: Free vibration analysis of rotating functionally graded rectangular plates. Compos. Struct. 136, 493–504 (2016)
Rafiee, M.A., Rafiee, J., Wang, Z., Song, H.H., Yu, Z.Z., Koratkar, N.: Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano 3, 3884–3890 (2009)
Ansari, R., Faraji Oskouie, M., Roghani, M., Rouhi, H.: Nonlinear analysis of laminated FG-GPLRC beams resting on an elastic foundation based on the two-phase stress-driven nonlocal model. Acta Mech. 232, 2183–2199 (2021)
Civalek, O., Dastjerdi, S., Akbaş, S.D., Akgöz, B.: Vibration analysis of carbon nanotube-reinforced composite microbeams. Math. Methods Appl. Sci. (2021). https://doi.org/10.1002/mma.7069
Wang, Y.Q., Ye, C., Zu, J.W.: Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets. Aerosp. Sci. Technol. 85, 359–370 (2019)
Teng, M.W., Wang, Y.Q.: Nonlinear forced vibration of simply supported functionally graded porous nanocomposite thin plates reinforced with graphene platelets. Thin-Walled Struct. 164, 107799 (2021)
Ye, C., Wang, Y.Q.: Nonlinear forced vibration of functionally graded graphene platelet-reinforced metal foam cylindrical shells: internal resonances. Nonlinear Dyn. 104, 2051–2069 (2021)
Zhao, T.Y., Ma, Y., Zhang, H.Y., Pan, H.G., Cai, Y.: Free vibration analysis of a rotating graphene nanoplatelet reinforced pre-twist blade-disk assembly with a setting angle. Appl. Math. Model. 93, 578 (2021)
Zhao, T.Y., Jiang, L.P., Pan, H.G., Yang, J., Kitipornchai, S.: Coupled free vibration of a functionally graded pre-twisted blade-shaft system reinforced with graphene nanoplatelets. Compos. Struct. 262, 113362 (2021)
Zhao, T.Y., Cui, Y.S., Wang, Y.Q., Pan, H.G.: Vibration characteristics of graphene nanoplatelet reinforced disk-shaft rotor with eccentric mass. Mech. Adv. Mater. Struct. (2021). https://doi.org/10.1080/15376494.2021.1904525
Zhao, T.Y., Liu, Z.F., Pan, H.G., Zhang, H.Y., Yuan, H.Q.: Vibration characteristics of functionally graded porous nanocomposite blade-diskshaft rotor system reinforced with graphene nanoplatelets. Appl. Compos. Mater. 28, 717–731 (2021)
Zhao, T., Ma, Y., Zhang, H., Yang, J.: Coupled free vibration of spinning functionally graded porous double-bladed disk systems reinforced with graphene nanoplatelets. Materials 13, 5610 (2020)
Feng, C., Kitipornchai, S., Yang, J.: Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLs). Eng. Struct. 140, 110–119 (2017)
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)
Ebrahimi, F., Nouraei, M., Dabbagh, A.: Thermal vibration analysis of embedded graphene oxide powder-reinforced nanocomposite plates. Eng. Comput. 36(3), 879–895 (2019)
Niu, Y., Zhang, W., Guo, X.Y.: Free vibration of rotating pretwisted functionally graded composite cylindrical panel reinforced with graphene platelets. Eur. J. Mech./A Solids 77, 103798 (2019)
Wang, Y., Feng, C., Wang, X., Zhao, Z., Yang, J.: Nonlinear free vibration of graphene platelets (GPLs)/polymer dielectric beam. Smart Mater. Struct. 28(5), 055013 (2019)
Wu, H., Kitipornchai, S., Yang, J.: Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates. Mater. Des. 132, 430–441 (2017)
Zhao, T.Y., Cui, Y.S., Pan, H.G., Yuan, H.Q., Yang, J.: Free vibration analysis of a functionally graded graphene nanoplatelet reinforced disk-shaft assembly with whirl motion. Int. J. Mech. Sci. 197, 106335 (2021)
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This project is supported by the National Science Foundation of China (No. 51805076, No. U1708255, No. 51775093 and No. 11922205) and the Natural Science Foundation of Hebei Province (No. B2019501073).
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Zhao, T.Y., Wang, Y.X., Yu, Y.X. et al. Modeling and vibration analysis of a spinning assembled beam–plate structure reinforced by graphene nanoplatelets. Acta Mech 232, 3863–3879 (2021). https://doi.org/10.1007/s00707-021-03039-9
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DOI: https://doi.org/10.1007/s00707-021-03039-9