Abstract
This paper presents a study on the modelling and free vibration analysis of a rotating functionally graded (FG) porous blade-disk-shaft assembly reinforced with graphene nanoplatelets (GPLs) resting on elastic supports. The rotor is made of graphene nanoplatelet (GPL) reinforced porous foam metal matrix. Both uniform and non-uniform distributions of GPLs and pores in the rotating assembly are considered. The effective material properties are thought of as layered change along the directions of blade thickness, disk radius and shaft radius. Moreover, the material values of this functionally graded structure are determined via the open-cell scheme, the Halpin–Tsai model together with the rule of mixtures. According to the finite element (FE) method, the modelling and free vibration analysis of the nanocomposite blade-disk-shaft rotor system is conducted. To verify the present analysis, the experimental method is adopted. The FE results and experimental results have great match with each other. Special attention is paid to the effects of the rotating speed, GPL distribution pattern, GPL weight fraction, length-to-width ratio and length-to-thickness ratio of GPLs, porosity distribution, porosity coefficient and support stiffness. The obtained conclusions can give particularly important suggestions for the design of GPL reinforced porous blade-disk-shaft rotor systems to achieve advanced mechanical performance.
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References
Crawley, E.F., Ducharme, E.H., Mokadam, D.R.: Analytical and Experimental Investigation of the Coupled Bladed Disk/Shaft Whirl of a Cantilevered Turbofan. J. Eng. Gas Turbines Power 108(4), 567–575 (1986)
Zhang, H., Zhao, T., Zhang, H., Pan, H., Yuan, H.: Dynamic characteristics of mistuned bladed disk system under rub-impact force. Adv Mech Eng 12(11), 1–15 (2020)
Zhao, T.Y., Wang, Y.X., Pan, H.G., Yuan, H.Q., Yi, C.: Nonlinear forced vibration analysis of spinning shaft-disk assemblies under sliding bearing supports. Math Models Methods Appl Sci (2021). https://doi.org/10.1002/mma.7043
Chun, S.B., Lee, C.W.: Vibration analysis of shaft-bladed disk system by using substructure synthesis and assumed modes method. J. Sound Vib. 189(5), 587–608 (1996)
Loewy, R.G., Khader, N.: Structural Dynamics of Rotating Bladed-Disk Assemblies Coupled with Flexible Shaft Motions. AIAA J. 22(9), 1319–1327 (1984)
Khader, N., Loewy, R.G.: Shaft flexibility effects on the forced response of a bladed-disk assembly. J. Sound Vib. 139(3), 469–485 (1990)
Segui B and Casanova E. Application of a Reduced Order Modeling Technique for Mistuned Bladed Disk-Shaft Assemblies. Turbo Expo: Power for Land, Sea, and Air 2007; 473–483
Khader, N., Masoud, S.: Vibration of mistuned bladed disks supported by flexible continuous shafts. J. Sound Vib. 149(3), 471–488 (1991)
Mohamed, E.M., Bonello, P.: The efficient inclusion of rotation-induced inertia effects in a shaft-blisk assembly model using zero-speed modes. J. Sound Vib. 479(4), 115357 (2020)
Wang, S., Bi, C.X., Zheng, C.J.: A Reduced-Order Model for the Vibration Analysis of Mistuned Blade-Disc-Shaft Assembly. Appl. Sci. 9(22), 4762 (2019)
Irwanto B, Schmidt R, Pawandenat D and Hardtke H J. Finite Element Model Updating in the Vibration of Bladed Disk: Shaft Assemblies. Turbo Expo: Power for Land, Sea, and Air 2004; 217–225.
Heydari, H., Khorram, A., Afzalipour, L.: The Influences of Stagger and Pretwist Angles of Blades on Coupling Vibration in Shaft-Disk-Blade Systems. J. Vib. Acoust. 142(1), 011007 (2020)
Li, Z., Zhao, T., Kou, H., Zhang, H., Yuan, H.: Vibration Characteristics of Multi-Stage Blade-Disk-Shaft Integrated Structure with Three-Dimensional Crack. Journal of Vibration Engineering and Technologies (2020). https://doi.org/10.1007/s42417-020-00251-0
Liu, D., Kitipornchai, S., Chen, W., Yang, J.: Three-dimensional buckling and free vibration analyses of initially stressed functionally graded graphene reinforced composite cylindrical shell. Compos. Struct. 189(1), 560–569 (2018)
Guo, H., Cao, S., Yang, T., Chen, Y.: Vibration of laminated composite quadrilateral plates reinforced with graphene nanoplatelets using the element-free IMLS-Ritz method. Int. J. Mech. Sci. 142–143, 610–621 (2018)
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. (2020). https://doi.org/10.1016/j.compstruct.2020.113362
Zhao, T.Y., Jiang, Z.Y., Zhao, Z., Xie, L.Y., Yuan, H.Q.: Modeling and free vibration analysis of rotating hub-blade assemblies reinforced with graphene nanoplatelets. J Strain Anal Eng Des (2021). https://doi.org/10.1177/0309324720986904
Wang, Y., Feng, C., Zhao, Z., Lu, F., Yang, J.: Torsional buckling of graphene platelets (GPLs) reinforced functionally graded cylindrical shell with cutout. Compos. Struct. 197(1), 72–79 (2018)
Zhao, Z., Feng, C., Wang, Y., Yang, J.: Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs). Compos. Struct. 180(15), 799–808 (2017)
Reddy, R.M.R., Karunasena, W., Lokuge, W.: Free vibration of functionally graded-GPL reinforced composite plates with different boundary conditions. Aerosp. Sci. Technol. 78, 147–156 (2018)
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, 578–596 (2021)
Feng, C., Kitipornchai, S., Yang, J.: Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLs). Eng. Struct. 140(1), 110–119 (2017)
Shahverdi, H., Barati, M.R.: Vibration analysis of porous functionally graded nanoplates. Int. J. Eng. Sci. 120, 82–99 (2017)
Wang, Y.Q.: Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state. Acta Astronaut. 143, 263–271 (2018)
Di, W., Liu, A., Huang, Y., Huang, Y., Pi, Y., Gao, W.: Dynamic analysis of functionally graded porous structures through finite element analysis. Eng. Struct. 165, 287–301 (2018)
Pourjabari, A., Hajilak, Z.E., Mohammadi, A., Habibi, M., Safarpour, H.: Effect of Porosity on free and forced vibration characteristics of the GPL reinforcement composite nanostructures. Comput. Math. Appl. 77(10), 2608–2626 (2019)
Zhao, T.Y., Ma, Y., Zhang, H.Y., Yang, J.: Coupled Free Vibration of Spinning Functionally Graded Porous Double-Bladed Disk Systems Reinforced with Graphene Nanoplatelets. Materials 13(24), 5610 (2020)
Li, Q., Wu, D., Chen, X., Liu, L., Yu, Y., Gao, W.: Nonlinear vibration and dynamic buckling analyses of sandwich functionally graded porous plate with graphene platelet reinforcement resting on Winkler-Pasternak elastic foundation. Int. J. Mech. Sci. 148, 596–610 (2018)
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)
Li, K., Wu, D., Chen, X., Cheng, J., Liu, Z., Gao, W., Liu, M.: Isogeometric analysis of functionally graded porous plates reinforced by graphene platelets. Compos. Struct. 204, 114–130 (2018)
Liu, Z., Yang, C., Gao, W., Wu, D., Li, G.: Nonlinear behavior and stability of functionally graded porous arches with graphene platelets reinforcements. Int. J. Eng. Sci. 137, 37–56 (2019)
Zhao TY, Yang YF, Pan HG Zhang HY and Yuan HQ. Free vibration analysis of a spinning porous nanocomposite blade reinforced with graphene nanoplatelets. J Strain Anal Eng Des 2021; https://doi.org/10.1177/0309324720985758.
Kitipornchai, S., Chen, D., Yang, J.: Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Mater. Des. 116(15), 656–665 (2017)
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)
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. B Eng. 145, 1–13 (2018)
Yang, J., Dong, J., Kitipornchai, S.: Unilateral and bilateral buckling of functionally graded corrugated thin plates reinforced with graphene nanoplatelets. Compos. Struct. 209, 789–801 (2019)
Funding
This project is supported by the National Science Foundation of China (No. 51805076, No. U1708255 and No. 51775093), the Doctorate Start Foundation of Liaoning Province (No. 20180540077) and the Natural Science Foundation of Hebei Province, China (No. B2019501073).
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Zhao, T.Y., Liu, Z.F., Pan, H.G. et al. Vibration Characteristics of Functionally Graded Porous Nanocomposite Blade-disk-shaft Rotor System Reinforced with Graphene Nanoplatelets. Appl Compos Mater 28, 717–731 (2021). https://doi.org/10.1007/s10443-021-09880-4
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DOI: https://doi.org/10.1007/s10443-021-09880-4