Skip to main content
SpringerLink
Log in

Optimization of vibration analysis for functionally graded graphene platelets (FGGP) reinforced twisted cantilever thin shallow shell blades subjected to axial loading

  • Published:
International Journal of Mechanics and Materials in Design Aims and scope Submit manuscript

Abstract

Vibration characteristics for rotating thin shallow shell blades reinforced with functionally graded graphene platelets (FGGP) under the axial force are conducted. The blade is modeled as four twisted cantilever thin shallow shells, each with a unique shape cylindrical shallow shell panel with a straight or curved boundary as the cantilever side, spherical shallow shell panel and hyperbolic parabolic shallow shell panel. The Halpin–Tsai model, the first-order shear deformation theory and the Rayleigh–Ritz method are used to calculate the frequencies and mode shapes of the blade. The results are validated by comparing them with previous literature and ANSYS. An analysis is conducted on a range of parameters, encompassing graphene properties, rotational velocity, torsional angle, curvature radius, aspect ratio and axial forces, in order to assess their influence on the vibrational properties of the blade. The vibration behaviors of a rotating cylindrical shallow shell panel with a straight cantilever edge are found to be distinctive. The findings indicate that the blade’s stiffness is significantly higher when reinforced with FGGP-X compared to FGGP-U distribution, with FGGP-O distribution exhibiting the lowest stiffness. Furthermore, the study implies that a total layer count exceeding ten has a negligible impact on the degree of graphene distribution. Finally, the study concludes that the curvature and graphene distribution pattern significantly influence the vibration characteristics of the blade.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data availability

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

References

  • Adhikari, B., Singh, B.N.: Parametric instability analysis of laminated composite plate subject to various types of non-uniform periodic in-plane edge load. Appl. Math. Comput. 373, 125026 (2020)

    MathSciNet  Google Scholar 

  • Asha, A.V., Sahu, S.K.: Parametric instability of twisted cross-ply laminated panels. Aerosp. Sci. Technol. 15, 465–475 (2011)

    Article  Google Scholar 

  • Chandiramani, N.K., Shete, C.D., Librescu, L.I.: Vibration of higher-order-shearable pretwisted rotating composite blades. Int. J. Mech. Sci. 45, 2017–2041 (2003)

    Article  Google Scholar 

  • Chen, J., Li, Q.S.: Vibration characteristics of a rotating pre-twisted composite laminated blade. Compos. Struct. 208, 78–90 (2019)

    Article  Google Scholar 

  • Chen, Y., Ye, T., Jin, G., Li, S., Yang, C.: Vibration analysis of rotating pretwist FG sandwich blades operating in thermal environment. Int. J. Mech. Sci. 205, 106596 (2021)

    Article  Google Scholar 

  • Chen, Y., Ye, T., Jin, G., Lee, H.P., Ma, X.: A unified quasi-three-dimensional solution for vibration analysis of rotating pre-twisted laminated composite shell panels. Compos. Struct. 282, 115072 (2022a)

    Article  Google Scholar 

  • Chen, Y., Jin, G., Ye, T., Li, S., Lee, H.P.: Geometrically nonlinear vibration analysis of rotating pre-twisted shell-type blades with a high rotating speed. J. Sound Vib. 536, 117169 (2022b)

    Article  Google Scholar 

  • Cheng, H., Li, C.F., Jiang, Y.L.: Free vibration analysis of rotating pre-twisted ceramic matrix carbon nanotubes reinforced blades. Mech. Adv. Mater. Struct. 29(14), 2040–2052 (2022)

    Article  CAS  Google Scholar 

  • Dibble, R., Ondra, V., Titurus, B.: Resonance avoidance for variable speed rotor blades using an applied compressive load. Aerosp. Sci. Technol. 88, 222–232 (2019)

    Article  Google Scholar 

  • Gu, X.J., Hao, Y.X., Zhang, W., Chen, J.: Dynamic stability of rotating cantilever composite thin walled twisted plate with initial geometric imperfection under in-plane load. Thin-Walled Struct. 144, 106267 (2019)

    Article  Google Scholar 

  • Gu, X.J., Zhang, W., Zhang, Y.F.: A novel dynamic model on nonlinear vibrations of functionally graded graphene platelet reinforced rotating pretwisted composite blade considering subsonic airflow excitation and blade-casing rubbing. Compos. Struct. 315, 116936 (2023a)

    Article  Google Scholar 

  • Gu, X.J., Zhang, Y.F., Zhang, W., Bi, Q.S.: Nonlinear analysis of a rotating pre-twisted composite blade reinforced with functionally graded graphene platelets under axial and transverse excitations. Nonlinear Dyn. 111(14), 12947–12972 (2023b)

    Article  Google Scholar 

  • Guo, X., Zeng, J., Ma, H., Zhao, C., Yu, X., Wen, B.: A dynamic model for simulating rubbing between blade and flexible casing. J. Sound Vib. 466, 115036 (2020)

    Article  Google Scholar 

  • Guo, H.L., Ouyang, X., Zur, K.K., Wu, X.T., Yang, T.Z., Ferreira, A.J.M.: On the large-amplitude vibration of rotating pre-twisted graphene nanocomposite blades in a thermal environment. Compos. Struct. 282, 115129 (2022)

    Article  Google Scholar 

  • Hashemi, S.H., Farhadi, S., Carra, S.: Free vibration analysis of rotating thick plates. J. Sound Vib. 323, 366–384 (2009)

    Article  ADS  Google Scholar 

  • Hazem, K., Shaukat, M.: Piezoelectric induced bending and twisting of laminated composite shallow shells. Smart Mater. Struct. 9, 476–484 (2000)

    Article  Google Scholar 

  • Hu, X.X., Sakiyama, T., Matsuda, H., Morita, C.: Fundamental vibration of rotating cantilever blades with pre-twist. J. Sound Vib. 271, 47–66 (2004)

    Article  ADS  Google Scholar 

  • Hu, Y., Zhao, Y., Wang, N., Chen, X.: Dynamic analysis of varying speed rotating pretwisted structures using refined beam theories. Int. J. Solids Struct. 185–186, 292–310 (2020)

    Article  Google Scholar 

  • Kee, Y.J., Kim, J.H.: Vibration characteristics of initially twisted rotating shell type composite blades. Compos. Struct. 64, 151–159 (2004)

    Article  Google Scholar 

  • Lee, J.J., Yeom, C.H., Lee, I.: Vibration analysis of twisted cantilevered conical composite shells. J. Sound Vib. 255, 965–982 (2002)

    Article  ADS  Google Scholar 

  • Li, H., Hao, Y.X., Zhang, W., Liu, L.T., Yang, S.W., Cao, Y.T.: Natural vibration of an elastically supported porous truncated joined conical-conical shells using artificial spring technology and generalized differential quadrature method. Aerosp. Sci. Technol. 121, 107385 (2022)

    Article  Google Scholar 

  • Li, Z.M., Liu, T., Kang, H., Tian, J., Jing, J., Wang, D.: Theoretical and experimental investigations on steady-state responses of rotor-blade systems with varying rotating speeds based on a new nonlinear dynamic model. Mech. Syst. Signal Process. 184, 109692 (2023)

    Article  Google Scholar 

  • Lin, S.M., Wu, C.T., Lee, S.Y., et al.: Analysis of rotating nonuniform pretwisted beams with an elastically restrained root and a tip mass. Int. J. Mech. Sci. 45, 741–755 (2003)

    Article  Google Scholar 

  • Liu, Y.Y., Hao, Y.X., Zhang, W., Liu, L.T., Yang, S.W., Cao, Y.T.: Frequency veering of rotating metal porous twisted plate with cantilever boundary using shell theory. Acta Mech. Solida Sin. 35, 282–302 (2021)

    Article  Google Scholar 

  • Ma, L., Yao, M., Zhang, W., Cao, D.: Bifurcation and dynamic behavior analysis of a rotating cantilever plate in subsonic airflow. Appl. Math. Mech. Engl. Ed. 41, 1861–1880 (2020)

    Article  MathSciNet  Google Scholar 

  • Niu, Y., Yao, M., Zhang, W.: Nonlinear transient responses of rotating twisted FGM cylindrical panels. Sci. China Technol. Sci. 64, 317–330 (2020)

    Article  ADS  Google Scholar 

  • Niu, Y., Yao, M., Wu, Q.: Resonance in dangerous mode and chaotic dynamics of a rotating pre-twisted graphene reinforced composite blade with variable thickness. Compos. Struct. 288, 115422 (2022)

    Article  CAS  Google Scholar 

  • Oh, Y., Yoo, H.H.: Vibration analysis of rotating pretwisted tapered blades made of functionally graded materials. Int. J. Mech. Sci. 119, 68–79 (2016)

    Article  Google Scholar 

  • Pan, Z., Liew, K.M.: Predicting vibration characteristics of rotating composite blades containing CNT-reinforced composite laminae and damaged fiber-reinforced composite laminae. Compos. Struct. 250, 112580 (2020)

    Article  Google Scholar 

  • Pan, Z.Z., Chen, X., Zhang, L.W.: Modeling large amplitude vibration of pretwisted hybrid composite blades containing CNTRC layers and matrix cracked FRC layers. Appl. Math. Model. 83, 640–659 (2020)

    Article  MathSciNet  Google Scholar 

  • Qatu, M.S.: Vibration of laminated shells and plates. Elsevier, New York (2004)

    Google Scholar 

  • Qatu, M.S., Asadi, E.: Vibration of doubly curved shallow shells with arbitrary boundaries. Appl. Acoust. 73(1), 21–27 (2012)

    Article  Google Scholar 

  • Qatu, M.S., Leissa, A.W.: Vibration studies for laminated composite twisted cantilever plates. Int. J. Mech. Sci. 33, 927–940 (1991)

    Article  Google Scholar 

  • Ramesh, M.N.V., Rao, N.M.: Free vibration analysis of pre-twisted rotating FGM beams. Int. J. Mech. Mater. Des. 9(4), 367–383 (2013)

    Article  Google Scholar 

  • Rout, M., Karmakar, A.: Free vibration of rotating pretwisted CNTs-reinforced shallow shells in thermal environment. Mech. Adv. Mater. Struct. 26, 1808–1820 (2019)

    Article  CAS  Google Scholar 

  • Rout, M., Bandyopadhyay, T., Karmakar, A.: Free vibration analysis of pretwisted delaminated composite stiffened shallow shells: a finite element approach. J. Reinf. Plast. Compos. 36, 619–636 (2017)

    Article  CAS  Google Scholar 

  • Roy, P.A., Hu, Y., Meguid, S.A., et al.: Dynamic behaviour of pretwisted metal matrix composite blades. Compos. Struct. 268, 113947 (2021)

    Article  CAS  Google Scholar 

  • Sakar, G., Sabuncu, M.: Dynamic stability of a rotating asymmetric cross-section blade subjected to an axial periodic force. Int. J. Mech. Sci. 45(9), 1467–1482 (2003)

    Article  Google Scholar 

  • Sakar, G., Sabuncu, M.: Buckling and dynamic stability of a rotating pretwisted asymmetric cross-section blade subjected to an axial periodic force. Finite Elem. Anal. Des. 40, 1399–1415 (2004)

    Article  Google Scholar 

  • Sina, S.A., Haddadpour, H.: Axial-torsional vibrations of rotating pretwisted thin walled composite beams. Int. J. Mech. Sci. 80, 93–101 (2014)

    Article  Google Scholar 

  • Sinha, S.K.: Combined torsional-bending-axial dynamics of a twisted rotating cantilever Timoshenko beam with contact-impact loads at the free end. J. Appl. Mech. 74(3), 505–522 (2006)

    Article  Google Scholar 

  • Sinha, S.K., Turner, K.E.: Natural frequencies of a pre-twisted blade in a centrifugal force field. J. Sound Vib. 330, 2655–2681 (2011)

    Article  ADS  Google Scholar 

  • Sun, J., Kari, L., Arteaga, I.L., et al.: A dynamic rotating blade model at an arbitrary stagger angle based on classical plate theory and the Hamilton’s principle. J. Sound Vib. 332, 1355–1371 (2013a)

    Article  ADS  Google Scholar 

  • Sun, J., Arteaga, I.L., Kari, L.: General shell model for a rotating pretwisted blade. J. Sound Vib. 332(22), 5804–5820 (2013b)

    Article  ADS  Google Scholar 

  • Wang, Y., Chen, J.: Nonlinear free vibration of rotating functionally graded graphene platelets reinforced blades with variable cross-sections. Eng. Anal. Bound. Elem. 144, 262–278 (2022)

    Article  MathSciNet  Google Scholar 

  • Wang, A., Chen, H., Hao, Y., Zhang, W.: Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets. Result Phys. 9, 550–559 (2018)

    Article  ADS  Google Scholar 

  • Wang, L., Su, Z., Wang, L.: Flutter analysis of rotating beams with elastic restraints. Appl. Math. Mech. Engl. Ed. 43, 761–776 (2022)

    Article  MathSciNet  CAS  Google Scholar 

  • Wen, C.L., Lu, C.C.: Vibration and stability of cracked thick rotating blades. Comput. Struct. 28, 67–74 (1988)

    Article  Google Scholar 

  • Wu, Z.Y., Yan, H., Zhao, L.C., Yan, G., Yang, Z.B., Hu, H.F., Zhang, W.M.: Axial-bending coupling vibration characteristics of a rotating blade with breathing crack. Mech. Syst. Signal Process. 182, 109547 (2023)

    Article  Google Scholar 

  • Xiang, R., Pan, Z.Z., Ouyang, H., Zhang, L.W.: A study of the vibration and lay-up optimization of rotating cross-ply laminated nanocomposite blades. Compos. Struct. 235, 111775 (2020)

    Article  Google Scholar 

  • Yang, X., Wang, S., Zhang, W., Qin, Z., Yang, T.: Dynamic analysis of a rotating tapered cantilever Timoshenko beam based on the power series method. Appl. Math. Mech. Engl. Ed. 38, 1425–1438 (2017)

    Article  MathSciNet  Google Scholar 

  • Yao, M.H., Chen, Y.P., Zhang, W.: Nonlinear vibrations of blade with varying rotating speed. Nonlinear Dyn. 68, 487–504 (2011)

    Article  MathSciNet  Google Scholar 

  • Zhang, B., Zhang, Y.-L., Yang, X.-D., Chen, L.-Q.: Saturation and stability in internal resonance of a rotating blade under thermal gradient. J. Sound Vib. 440, 34–50 (2019a)

    Article  ADS  Google Scholar 

  • Zhang, B., Ding, H., Chen, L.Q.: Super-harmonic resonances of a rotating pre-deformed blade subjected to gas pressure. Nonlinear Dyn. 98, 2531–2549 (2019b)

    Article  Google Scholar 

  • Zhang, B., Ding, H., Chen, L.-Q.: Three to one internal resonances of a pre-deformed rotating beam with quadratic and cubic nonlinearities. Int. J. Non-Linear Mech. 126, 103552 (2020a)

    Article  ADS  Google Scholar 

  • Zhang, B., Ding, H., Chen, L.Q.: Subharmonic and combination resonance of rotating pre-deformed blades subjected to high gas pressure. Acta Mech. Solida Sin. 33, 635–649 (2020b)

    Article  Google Scholar 

  • Zhang, Y.F., Niu, Y., Zhang, W.: Nonlinear vibrations and internal resonance of pretwisted rotating cantilever rectangular plate with varying cross-section and aerodynamic force. Eng. Struct. 225, 111259 (2020c)

    Article  Google Scholar 

  • Zhang, L.W., Pan, Z.Z., Chen, X.: Vibration characteristics of matrix cracked pretwisted hybrid composite blades containing CNTRC layers. J. Sound Vib. 473, 115242 (2020d)

    Article  Google Scholar 

  • 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 (2021a)

    Article  MathSciNet  Google Scholar 

  • 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 (2021b)

    Article  CAS  Google Scholar 

  • 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 (2021c)

    Article  Google Scholar 

  • Zhao, T.Y., Yan, K., Li, H.W., Wang, X.: Study on theoretical modeling and vibration performance of an assembled cylindrical shell-plate structure with whirl motion. Appl. Math. Model. 110, 618–632 (2022)

    Article  MathSciNet  Google Scholar 

  • Zhao, T.Y., Yan, K., Chen, L., Wang, X.: Vibration analysis of spinning porous cylindrical shell coupled with multiple plates assembly structures reinforced by graphene nanoplatelets. Thin-Walled Struct. 184, 110498 (2023)

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the support of National Natural Science Foundation of China (NNSFC) through Grant Nos. 11832002, 12072201 and 11427801, Inner Mongolia Autonomous Region Science and Technology Plan Project (2022JBGS0041).

Author information

Authors and Affiliations

  1. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, 212013, People’s Republic of China

    X. J. Gu, Q. S. Bi & X. J. Han

  2. Department of Mechanics, GuangXi University, GuangXi, 530004, People’s Republic of China

    W. Zhang & Y. F. Zhang

Authors
  1. X. J. Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Q. S. Bi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Y. F. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. X. J. Han
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to X. J. Gu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gu, X.J., Bi, Q.S., Zhang, W. et al. Optimization of vibration analysis for functionally graded graphene platelets (FGGP) reinforced twisted cantilever thin shallow shell blades subjected to axial loading. Int J Mech Mater Des (2024). https://doi.org/10.1007/s10999-023-09706-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10999-023-09706-0

Keywords

Search

Navigation