Nonlinear vibration of functionally graded graphene plateletreinforced composite truncated conical shell using first-order shear deformation theory

doi:10.1007/s10483-021-2747-9

Abstract

Abstract: In this study, the first-order shear deformation theory (FSDT) is used to establish a nonlinear dynamic model for a conical shell truncated by a functionally graded graphene platelet-reinforced composite (FG-GPLRC). The vibration analyses of the FG-GPLRC truncated conical shell are presented. Considering the graphene platelets (GPLs) of the FG-GPLRC truncated conical shell with three different distribution patterns, the modified Halpin-Tsai model is used to calculate the effective Young’s modulus. Hamilton’s principle, the FSDT, and the von-Karman type nonlinear geometric relationships are used to derive a system of partial differential governing equations of the FG-GPLRC truncated conical shell. The Galerkin method is used to obtain the ordinary differential equations of the truncated conical shell. Then, the analytical nonlinear frequencies of the FG-GPLRC truncated conical shell are solved by the harmonic balance method. The effects of the weight fraction and distribution pattern of the GPLs, the ratio of the length to the radius as well as the ratio of the radius to the thickness of the FG-GPLRC truncated conical shell on the nonlinear natural frequency characteristics are discussed. This study culminates in the discovery of the periodic motion and chaotic motion of the FG-GPLRC truncated conical shell.

Key words: nonlinear free vibration, harmonic balance method, functionally graded graphene platelet-reinforced composite (FG-GPLRC), truncated conical shell, chaos

2010 MSC Number:

Shaowu YANG, Yuxin HAO, Wei ZHANG, Li YANG, Lingtao LIU. Nonlinear vibration of functionally graded graphene plateletreinforced composite truncated conical shell using first-order shear deformation theory. Applied Mathematics and Mechanics (English Edition), 2021, 42(7): 981-998.

TrendMD

References

[1] MAO, J. J. and ZHANG, W. Linear and nonlinear free and forced vibrations of graphene reinforced piezoelectric composite plate under external voltage excitation. Composite Structures, 203, 551–565(2018)
[2] SINGH, V., JOUNG, D., ZHAI, L., DAS, S., KHONDAKER, S. I., and SEAL, S. Graphene based materials: past, present and future. Progress in Materials Science, 56, 1178–1271(2011)
[3] MENSAH, B., GUPTA, K. C., KIM, H., WANG, W., JEONG, K., and NAH, C. Graphene-reinforced elastomeric nanocomposites: a review. Polymer Testing, 68, 160–184(2018)
[4] RAFIEE, M. A., RAFIEE, J., YU, Z. Z., and KORATKAR, N. Buckling resistant graphene nanocomposites. Applied Physics Letters, 95, 223103(2009)
[5] YANG, S. W., HAO, Y. X., ZHANG, W., and LI, S. B. Nonlinear dynamic behavior of functionally graded truncated conical shell under complex loads. International Journal of Bifurcation and Chaos, 25(2), 1550025(2015)
[6] YANG, S. W., ZHANG, W., HAO, Y. X., and NIU, Y. Nonlinear vibrations of FGM truncated conical shell under aerodynamics and in-plane force along meridian near internal resonances. Thin-Walled Structures, 142, 369–391(2019)
[7] YANG, J., WU, H., and KITIPORNCHAI, S. Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams. Composite Structures, 161, 111–118(2017)
[8] FENG, C., KITIPORNCHAI, S., and YANG, J. Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs). Composites Part B: Engineering, 110, 132–140(2017)
[9] SONG, M., YANG, J., and KITIPORNCHAI, S. Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets. Composites Part B: Engineering, 134, 106–113(2018)
[10] WU, H., KITIPORNCHAI, S., and YANG, J. Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates. Materials & Design, 132, 431–441(2017)
[11] SONG, M., LI, X., KITIPORNCHAI, S., BI, Q., and YANG, J. Low-velocity impact response of geometrically nonlinear functionally graded graphene platelet-reinforced nanocomposite plates. Nonlinear Dynamics, 95(3), 2333–2352(2019)
[12] ZHAO, S., ZHAO, Z., YANG, Z., KE, L. L., KITIPORNCHAI, S., and YANG, J. Functionally graded graphene reinforced composite structures: a review. Engineering Structures, 210, 110339(2020)
[13] SHEN, H. S., XIANG, Y., FAN, L., and HUI, D. Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical panels resting on elastic foundations in thermal environments. Composites Part B: Engineering, 136, 177–186(2018)
[14] SHEN, H. S., XIANG, Y., and FAN, L. Postbuckling of functionally graded graphene-reinforced composite laminated cylindrical panels under axial compression in thermal environments. International Journal of Mechanical Sciences, 135, 398–409(2018)
[15] LU, L., SHE, G. L., and GUO, X. Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection. International Journal of Mechanical Sciences, 199, 106428(2021)
[16] YAS, M. H. and RAHIMI, S. Thermal vibration of functionally graded porous nanocomposite beams reinforced by graphene platelets. Applied Mathematics and Mechanics (English Edition), 41(8), 1209–1226(2020) https://doi.org/10.1007/s10483-020-2634-6
[17] BLOORIYAN, S., ANSARI, R., DARVIZEH, A., GHOLAMI, R., and ROUHI, H. Post-buckling analysis of functionally graded graphene platelet-reinforced polymer composite cylindrical shells using an analytical solution approach. Applied Mathematics and Mechanics (English Edition), 40(7), 1001–1016(2019) https://doi.org/10.1007/s10483-019-2498-8
[18] NGUYEN, N. V., LEE, J., and NGUYEN-XUAN, H. Active vibration control of GPLs-reinforced FG metal foam plates with piezoelectric sensor and actuator layers. Composites Part B: Engineering, 172, 769–784(2019)
[19] GAO, W. L., QIN, Z. Y., and CHU, F. L. Wave propagation in functionally graded porous plates reinforced with graphene platelets. Aerospace Science and Technology, 102, 105860(2020)
[20] WANG, Y. Q., YE, C., and ZU, J. W. Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets. Aerospace Science and Technology, 85, 359–370(2019)
[21] LIU, J., DENG, X., WANG, Q., ZHONG, R., XIONG, R., and ZHAO, J. A unified modeling method for dynamic analysis of GPL-reinforced FGP plate resting on Winkler-Pasternak foundation with elastic boundary conditions. Composite Structures, 244, 112217(2020)
[22] SOFIYEV. A. H. Review of research on the vibration and buckling of the FGM conical shells. Composite Structures, 211, 301–317(2019)
[23] SONG, Z. Y., CAO, Q. J., and DAI, Q. Y. Free vibration of truncated conical shells with elastic boundary constraints and added mass. International Journal of Mechanical Sciences, 155, 286–294(2019)
[24] AKBARI, M., KIANI, Y., and ESLAMI, M. R. Thermal buckling of temperature-dependent FGM conical shells with arbitrary edge supports. Acta Mechanica, 226, 897–915(2015)
[25] ANSARI, R., HASRATI, E., and TORABI, J. Nonlinear vibration response of higher-order shear deformable FG-CNTRC conical shells. Composite Structures, 222, 110906(2019)
[26] CHAN, D. Q., ANH, V. T. T., and DUC, N. D. Vibration and nonlinear dynamic response of eccentrically stiffened functionally graded composite truncated conical shells surrounded by an elastic medium in thermal environments. Acta Mechanica, 230, 157–178(2019)
[27] CHAN, D. Q., QUAN, T. Q., and KIM, S. E. Nonlinear dynamic response and vibration of shear deformable piezoelectric functionally graded truncated conical panel in thermal environments. European Journal of Mechanics-A/Solids, 77, 103795(2019)
[28] DAI, Q. Y., CAO, Q. J., and CHEN, Y. S. Frequency analysis of rotating truncated conical shells using the Haar wavelet method. Applied Mathematical Modelling, 57, 603–613(2018)
[29] RAHMANI, M., MOHAMMADI, Y., and KAKAVAND, F. Vibration analysis of sandwich truncated conical shells with porous FG face sheets in various thermal surroundings. Steel and Composite Structures, 32, 239–252(2019)
[30] HAO, Y. X., YANG, S. W., ZHANG, W., YAO, M. H., and WANG, A. W. Flutter of high-dimension nonlinear system for an FGM truncated conical shell. Mechanics of Advanced Materials and Structures, 25, 47–61(2018)
[31] HAO, Y. X., NIU, Y., ZHANG, W., LI, S. B., YAO, M. H., and WANG, A. W. Supersonic flutter analysis of FGM shallow conical panel accounting for thermal effects. Meccanica, 53, 95–109(2018)
[32] DENIZ, A. and SOFIYEV, A. H. The nonlinear dynamic buckling response of functionally graded truncated conical shells. Journal of Sound and Vibration, 332, 978–992(2013)
[33] SOFIYEV, A. H., ZERIN, Z., ALLAHVERDIEV, B. P., HUI, D., TURAN, F., and ERDEM, H. The dynamic instability of FG orthotropic conical shells within the SDT. Steel and Composite Structures, 25, 581–591(2017)
[34] HOA, L. K., HOAI, B. T. T., and CHAN, D. Q. Nonlinear thermomechanical postbuckling analysis of ES-FGM truncated conical shells resting on elastic foundations. Mechanics of Advanced Materials and Structures, 26, 1089–1103(2019)
[35] CHAN, D. Q., NGUYEN, P. D., and QUANG, V. D. Nonlinear buckling and post-buckling of functionally graded CNTs reinforced composite truncated conical shells subjected to axial load. Steel and Composite Structures, 31, 243–259(2019)
[36] CHAN, D. Q., LONG, V. D., and DUC, N. D. Nonlinear buckling and postbuckling of FGM shear-deformable truncated conical shells reinforced by FGM stiffeners. Mechanics of Composite Materials, 54, 745–764(2019)
[37] KIANI, Y. Buckling of functionally graded graphene reinforced conical shells under external pressure in thermal environment. Composites Part B: Engineering, 156, 128–137(2019)
[38] JIAO, P., CHEN, Z. P., and LI, Y. Dynamic buckling analyses of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) cylindrical shell under axial power-law time-varying displacement load. Composite Structures, 220, 784–797(2019)
[39] DUNG, D. V., HOA, L. K., THUYET, B. T., and NGA, N. T. Buckling analysis of functionally graded material (FGM) sandwich truncated conical shells reinforced by FGM stiffeners filled inside by elastic foundations. Applied Mathematics and Mechanics (English Edition), 37(7), 879–902(2016) https://doi.org/10.1007/s10483-016-2097-9
[40] BICH, D. H., PHUONG, N. T., and TUNG, H. V. Buckling of functionally graded conical panels under mechanical loads. Composite Structures, 94, 1379–1384(2012)
[41] SAFARPOUR, M., GHABUSSI, A., EBRAHIMI, F., HABIBI, M., and SAFARPOUR, H. Frequency characteristics of FG-GPLRC viscoelastic thick annular plate with the aid of GDQM. Thin-Walled Structures, 150, 106683(2020)
[42] SHOKRIEH, M. M., GHOREISHI, S. M., and ESMKHANI, M. Toughening mechanisms of nanoparticle-reinforced polymers. Woodhead Publishing Series in Composites Science and Engineering, 2015, 295–320(2015)
[43] MAO, J. J. and ZHANG, W. Buckling and post-buckling analyses of functionally graded graphene reinforced piezoelectric plate subjected to electric potential and axial forces. Composite Structures, 216, 332–405(2019)
[44] NIU, Y., ZHANG, W., and GUO, X. Y. Free vibration of rotating pretwisted functionally graded composite cylindrical panel reinforced with graphene platelets. European Journal of Mechanics-A/Solids, 77, 103798(2019)
[45] MOJIRI, H. R. and JEDARI-SALAMI, S. Free vibration and dynamic transient response of functionally graded composite beams reinforced with graphene nanoplatelets (GPLs) resting on elastic foundation in thermal environment. Mechanics Based Design of Structures and Machines (2020) https://doi.org/10.1080/15397734.2020.1766492
[46] DONG, Y., LI, X., GAO, K., LI, Y., and YANG, J. Harmonic resonances of graphene-reinforced nonlinear cylindrical shells: effects of spinning motion and thermal environment. Nonlinear Dynamics, 99(2), 981–1000(2020)
[47] REDDY, J. N. Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, New York (2004)
[48] NOSEIR, A. and REDDY, J. N. A study of non-linear dynamic equations of higher-order deformation plate theories. International Journal of Non-Linear Mechanics, 26(2), 233–249(1991)
[49] TENG, M. W. and WANG, Y. Q. Nonlinear free vibration of rectangular plates reinforced with 3D graphene foam: approximate analytical solution. Results in Physics, 17, 103147(2020)
[50] NAJAFOV, A. M. and SOFIYEV, A. H. The non-linear dynamics of FGM truncated conical shells surrounded by an elastic medium. International Journal of Mechanical Sciences, 66, 33–44(2013)
[51] KERBOUA, Y., LAKIS, A. A., and HMILA, M. Vibration analysis of truncated conical shells subjected to flowing fluid. Applied Mathematical Modelling, 34(3), 791–809(2010)
[52] LIEW, K. M., NG, T. Y., and ZHAO, X. Free vibration analysis of conical shells via the element-free kp-Ritz method. Journal of Sound and Vibration, 281, 627–645(2005)
[53] TENG, M. W. and WANG, Y. Q. Nonlinear free vibration of rectangular plates reinforced with 3D graphene foam: approximate analytical solution. Results in Physics, 17, 103147(2020)
[54] CHEN, C. S., CHENG, W. S., CHIEN, R. D., and DONG, J. L. Large amplitude vibration of an initially stressed cross ply laminated plates. Applied Acoustic, 63, 939–956(2002)