Free vibration of functionally graded graphene platelet-reinforced porous beams with spinning movement via differential transformation method

Wang, Y.Q., Zhao, H.L.: Free vibration analysis of metal foam core sandwich beams on elastic foundation using Chebyshev collocation method. Arch. Appl. Mech. 89(11), 2335–2349 (2019). https://doi.org/10.1007/s00419-019-01579-0 Rabiei, A., O’Neill, A.T.: A study on processing of a composite metal foam via casting. Mater. Sci. Eng. a-Struct. Mater. Proper. Microstruct. Process. 404(1–2), 159–164 (2005). https://doi.org/10.1016/j.msea.2005.05.089 Kitipornchai, S., Chen, D., Yang, J.: Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Mater. Des. 116, 656–665 (2017). https://doi.org/10.1016/j.matdes.2016.12.061 Groven, L.J., Puszynski, J.A.: Solution combustion synthesis of carbon nanotube loaded nickel foams. Mater. Lett. 73, 126–128 (2012). https://doi.org/10.1016/j.matlet.2012.01.033 Duarte, I., Ventura, E., Olhero, S., Ferreira, J.M.F.: An effective approach to reinforced closed-cell Al-alloy foams with multiwalled carbon nanotubes. Carbon 95, 589–600 (2015). https://doi.org/10.1016/j.carbon.2015.08.065 Zhang, Z., Ding, J., Xia, X.C., Sun, X.H., Song, K.H., Zhao, W.M., Liao, B.: Fabrication and characterization of closed-cell aluminum foams with different contents of multi-walled carbon nanotubes. Mater. Des. 88, 359–365 (2015). https://doi.org/10.1016/j.matdes.2015.09.017 Garcia-Macias, E., Rodriguez-Tembleque, L., Saez, A.: Bending and free vibration analysis of functionally graded graphene vs. carbon nanotube reinforced composite plates. Compos. Struct. 186, 123–138 (2018). https://doi.org/10.1016/j.compstruct.2017.11.076 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(12), 3884–3890 (2009). https://doi.org/10.1021/nn9010472 Mao, J.-J., Zhang, W.: Linear and nonlinear free and forced vibrations of graphene reinforced piezoelectric composite plate under external voltage excitation. Compos. Struct. 203, 551–565 (2018). https://doi.org/10.1016/j.compstruct.2018.06.076 Wang, A., Chen, H., Hao, Y., Zhang, W.: Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets. Results Phys. 9, 550–559 (2018). https://doi.org/10.1016/j.rinp.2018.02.062 Zhang, W., Niu, Y., Behdinan, K.: Vibration characteristics of rotating pretwisted composite tapered blade with graphene coating layers. Aerosp. Sci. Technol. 98, 105644 (2020). https://doi.org/10.1016/j.ast.2019.105644 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). https://doi.org/10.1016/j.ijmecsci.2021.106335 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. (2021). https://doi.org/10.1016/j.apm.2020.12.025 Dong, Y., Li, X., Gao, K., Li, Y., Yang, J.: Harmonic resonances of graphene-reinforced nonlinear cylindrical shells: effects of spinning motion and thermal environment. Nonlinear Dyn. 99(2), 981–1000 (2020). https://doi.org/10.1007/s11071-019-05297-8 Dong, Y., Zhu, B., Wang, Y., He, L., Li, Y., Yang, J.: Analytical prediction of the impact response of graphene reinforced spinning cylindrical shells under axial and thermal loads. Appl. Math. Model. 71, 331–348 (2019). https://doi.org/10.1016/j.apm.2019.02.024 Dong, Y., Zhu, B., Wang, Y., Li, Y., Yang, J.: Nonlinear free vibration of graded graphene reinforced cylindrical shells: effects of spinning motion and axial load. J. Sound Vib. 437, 79–96 (2018). https://doi.org/10.1016/j.jsv.2018.08.036 Yang, Y., Chen, B., Lin, W., Li, Y., Dong, Y.: Vibration and symmetric thermal buckling of asymmetric annular sandwich plates with piezoelectric/GPLRC layers rested on foundation. Aerosp. Sci. Technol. 110, 106495 (2021). https://doi.org/10.1016/j.ast.2021.106495 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). https://doi.org/10.1016/j.tws.2021.107799 Ye, C., Wang, Y.Q.: Nonlinear forced vibration of functionally graded graphene platelet-reinforced metal foam cylindrical shells: Internal resonances. Nonlinear Dyn. 104(3), 2051–2069 (2021). https://doi.org/10.1007/s11071-021-06401-7 Yas, M.H., Rahimi, S.: Thermal vibration of functionally graded porous nanocomposite beams reinforced by graphene platelets. Appl. Math. Mech.-Engl. Edn. 41(8), 1209–1226 (2020). https://doi.org/10.1007/s10483-020-2634-6 Yang, J., Chen, D., Kitipornchai, S.: Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev–Ritz method. Compos. Struct. 193, 281–294 (2018). https://doi.org/10.1016/j.compstruct.2018.03.090 Dong, Y., He, L., Wang, L., Li, Y., Yang, J.: Buckling of spinning functionally graded graphene reinforced porous nanocomposite cylindrical shells: an analytical study. Aerosp. Sci. Technol. 82, 466–478 (2018). https://doi.org/10.1016/j.ast.2018.09.037 Dong, Y.H., Li, Y.H., Chen, D., Yang, J.: Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion. Compos. Part B-Eng. 145, 1–13 (2018). https://doi.org/10.1016/j.compositesb.2018.03.009 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). https://doi.org/10.1016/j.ast.2018.12.022 Banerjee, J.R.: Free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method. J. Sound Vib. 233(5), 857–875 (2000). https://doi.org/10.1006/jsvi.1999.2855 Chung, J., Yoo, H.H.: Dynamic analysis of a rotating cantilever beam by using the finite element method. J. Sound Vib. 249(1), 147–164 (2002). https://doi.org/10.1006/jsvi.2001.3856 Huang, C.L., Lin, W.Y., Hsiao, K.M.: Free vibration analysis of rotating Euler beams at high angular velocity. Comput. Struct. 88(17–18), 991–1001 (2010). https://doi.org/10.1016/j.compstruc.2010.06.001 Shahba, A., Attarnejad, R., Zarrinzadeh, H.: Free vibration analysis of centrifugally stiffened tapered functionally graded beams. Mech. Adv. Mater. Struct. 20(5), 331–338 (2013). https://doi.org/10.1080/15376494.2011.627634 Aksencer, T., Aydogdu, M.: Flapwise vibration of rotating composite beams. Compos. Struct. 134, 672–679 (2015). https://doi.org/10.1016/j.compstruct.2015.08.130 Adair, D., Jaeger, M.: Vibration analysis of a uniform pre-twisted rotating Euler–Bernoulli beam using the modified Adomian decomposition method. Math. Mech. Solids 23(9), 1345–1363 (2018). https://doi.org/10.1177/1081286517720843 Dong, S.P., Li, L., Zhang, D.G.: Vibration analysis of rotating functionally graded tapered beams with hollow circular cross-section. Aerosp. Sci. Technol. 95, 105476 (2019). https://doi.org/10.1016/j.ast.2019.105476 Zhou, J.: Differential Transformation and Its Applications for Electrical Circuits. Huazhong University Press, Wuhan (1986) Özdemir, Ö., Kaya, M.: Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli-Euler beam by differential transform method. J. Sound Vib. 289(1–2), 413–420 (2006). https://doi.org/10.1016/j.jsv.2005.01.055 Arvin, H.: The flapwise bending free vibration analysis of micro-rotating timoshenko beams using the differential transform method. J. Vib. Control 24(20), 4868–4884 (2018). https://doi.org/10.1177/1077546317736706 Tjong, S.C.: Recent progress in the development and properties of novel metal matrix nanocomposites reinforced with carbon nanotubes and graphene nanosheets. Mater. Sci. Eng. R-Rep. 74(10), 281–350 (2013). https://doi.org/10.1016/j.mser.2013.08.001 De Villoria, R.G., Miravete, A.: Mechanical model to evaluate the effect of the dispersion in nanocomposites. Acta Mater. 55(9), 3025–3031 (2007). https://doi.org/10.1016/j.actamat.2007.01.007 Affdl, J.H., Kardos, J.: The Halpin-Tsai equations: a review. Polym. Eng. Sci. 16(5), 344–352 (1976). https://doi.org/10.1002/pen.760160512 Gibson, I., Ashby, M.F.: The mechanics of three-dimensional cellular materials. Proc. R. Soc. Lond. A Math. Phys. Sci. 382(1782), 43–59 (1982). https://doi.org/10.1098/rspa.1982.0088 Kane, T., Ryan, R., Banerjeer, A.: Dynamics of a cantilever beam attached to a moving base. J. Guid. Control. Dyn. 10(2), 139–151 (1987). https://doi.org/10.2514/3.20195 Eisenhart, L.P.: Introduction to Differential Geometry. Princeton University Press, Princeton (2015) Gorman, D.J.: Free Vibration Analysis of Beams and Shafts(Book). Research Supported by the National Research Council of Canada. Wiley-Interscience, New York (1975) Banerjee, J.R., Kennedy, D.: Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects. J. Sound Vib. 333(26), 7299–7312 (2014). https://doi.org/10.1016/j.jsv.2014.08.019 Cheng, J.L., Xu, H., Yan, A.Z.: Frequency analysis of a rotating cantilever beam using assumed mode method with coupling effect. Mech. Based Des. Struct. Mach. 34(1), 25–47 (2006). https://doi.org/10.1080/15367730500501587 Yang, J., Jiang, L., Chen, D.C.: Dynamic modelling and control of a rotating Euler–Bernoulli beam. J. Sound Vib. 274(3–5), 863–875 (2004). https://doi.org/10.1016/S0022-460X(03)00611-4 Yoo, H.H., Shin, S.H.: Vibration analysis of rotating cantilever beams. J. Sound Vib. 212(5), 807–828 (1998). https://doi.org/10.1006/jsvi.1997.1469 Keskin, Y., Oturanc, G.: Reduced differential transform method for partial differential equations. Int. J. Nonlinear Sci. Numer. Simul. 10(6), 741–749 (2009). https://doi.org/10.1515/IJNSNS.2009.10.6.741 Wright, A., Smith, C., Thresher, R., Wang, J.: Vibration modes of centrifugally stiffened beams. J. Appl. Mech. 49, 197–202 (1982). https://doi.org/10.1115/1.3161966