Skip to main content
SpringerLink
Log in

Nonlinear supersonic aerothermoelastic analysis of as ymmetrically curved-fiber composite panels with nonuniform temperature distributions

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

The thermal buckle and flutter behaviors of the asymmetrically curved-fiber composite panel in supersonic air flow are studied in frequency and time domains. Based on the Mindlin thick plate theory, the Von Karman large-deformation assumption and the quasi-steady supersonic piston theory were adopted to describe deformations and supersonic loads of the composite panel, respectively. According to Hamilton variational principle, the nonlinear aerothermoelastic equations of the asymmetrically curvilinear-fiber panel were established with frequency domain characteristics obtained by the complex mode method and time domain responses obtained by the Newmark method, respectively. After verifying the correctness of the current method, the influences of temperature gradient, curvilinear-fiber orientation and incoming airflow pressure on the static large-deflection, mode coalescence, flutter-buckling boundary, time-history responses and phase-plane plots of the composite panel were discussed in detail.

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

Similar content being viewed by others

Abbreviations

T 0 :

Tangential angles of the beginning of the curved fiber

T 1 :

Tangential angles of the end of the curved fiber

θ k :

Azimuth of the curved fiber at each point

u, v, w :

Displacement components

ε 0m :

In-plane strain vector

ε 0b :

Nonlinear membrane stretching strain vector

κ :

Bending curvature vector

\(\overline {\boldsymbol{Q}} \left( x \right)\) :

Transformed material matrix

\({\overline {\boldsymbol{Q}} _s}\left( x \right)\) :

Shear material matrix

∆T :

Temperature rise

T u :

Average temperature rise

T g :

Temperature gradient

N :

Membrane force

M :

Membrane moment

F s :

Ttransverse shear force

Δp :

Aerodynamic load

δU M :

Virtual strain energy

δU T :

Temperature strain energy generated

δT :

Virtual kinetic energy

δW :

Virtual work of the aerodynamic force and damping force

M :

Mass matrix and aerodynamic damping matrix

K 0 :

Linear stiffness matrix

K ∆T :

Temperature stiffness matrix

K N1, K N2 :

Nonlinear stiffness matrices

K A0 :

Linear aerodynamic stiffness matrix

C A0 :

Linear aerodynamic damping matrix

u s :

Static deformation

u d :

Dynamic deformation

\({\boldsymbol{\ddot q}},\,\,{\boldsymbol{\dot q}},\,\,{\boldsymbol{q}}\) :

Displacement, velocity, acceleration in modal coordinates

λ :

Dimensionless dynamic pressure

References

  1. K. J. Sohn and J. H. Kim, Nonlinear thermal flutter of functionally graded panels under a supersonic flow, Composite Structures, 88(3) (2009) 380–387.

    Article  Google Scholar 

  2. D. Y. Xue and C. Mei, Finite element nonlinear panel flutter with arbitrary temperatures in supersonic flow, AIAA Journal, 31(1) (1993) 154–162.

    Article  MathSciNet  MATH  Google Scholar 

  3. R. C. Zhou, D. Y. Xue and C. Mei, Finite element time domain-modal formulation for nonlinear flutter of composite panels, AIAA Journal, 32(10) (1994) 2044–2052.

    Article  MATH  Google Scholar 

  4. L. C. Shiau, S. Y. Kuo and Y. P. Liu, Aerothermoelastic analysis of composite laminated plates, Composite Structures, 94(6) (2012) 1982–1990.

    Article  Google Scholar 

  5. A. A. Ghorbanpour, M. Eskandari and E. Haghparast, The supersonic flutter behavior of sandwich plates with an magnetorheological elastomer core and GNP-reinforced face sheets, International Journal of Applied Mechanics, 14 (9) (2022).

  6. E. Quan, M. Xu, W. Yao and X. Cheng, Analysis of the post-flutter aerothermoelastic characteristics of hypersonic skin panels using a CFD-based approach, Aerospace Science and Technology, 118 (2021) 107076.

    Article  Google Scholar 

  7. C. G. Silva, F. J. Silvestre and M. V. Donadon, A nonlinear aerothermoelastic model for slender composite beam-like wings with embedded shape memory alloys, Composite Structures, 287 (2022) 115367.

    Article  Google Scholar 

  8. H. Akhavan, P. Ribeiro and M. D. Moura, Large deflection and stresses in variable stiffness composite laminates with curvilinear fibres, International Journal of Applied Mechanics, 73 (2013) 14–26.

    Article  Google Scholar 

  9. S. Honda and Y. Narita, Natural frequencies and vibration modes of laminated composite plates reinforced with arbitrary curvilinear fiber shape paths, Journal of Sound and Vibration, 331 (2012) 180–191.

    Article  Google Scholar 

  10. Z. Gürdal and R. Olmedo, In-plane response of laminates with spatially varying fiber orientations: variable stiffness concept, AIAA Journal, 31(4) (1993) 751–758.

    Article  MATH  Google Scholar 

  11. K. A. Hasim and A. Kefal, Isogeometric static analysis of laminated plates with curvilinear fibers based on refined zigzag theory, Composite Structures, 256 (2021) 113097.

    Article  Google Scholar 

  12. S. D. Akbas, Hygrothermal post-buckling analysis of laminated composite beams, International Journal of Applied Mechanics, 11(6) (2019) 1950009.

    Article  Google Scholar 

  13. M. Ganapathi, B. Anirudh, D. A. Narayan, C. Anant and B. Pradyumna, Thermal buckling behaviour of variable stiffness laminated composite plates, Materials Today Communications, 16 (2018) 142–151.

    Article  Google Scholar 

  14. G. M. Günay and T. Timarci, Stresses in thin-walled composite laminated box-beams with curvilinear fibers: antisymmetric and symmetric fiber paths, Thin-Walled Structures, 138 (2019) 170–182.

    Article  Google Scholar 

  15. H. Akhavan and P. Ribeiro, Aeroelasticity of composite plates with curvilinear fibers in supersonic flow, Composite Structures, 194 (2018) 335–344.

    Article  Google Scholar 

  16. S. Y. Kuo, Flutter of thermally buckled angle-ply laminates with variable fiber spacing, Composites Part B, 95 (2016) 240–251.

    Article  Google Scholar 

  17. T. Farsadi, D. Asadi and H. Kurtaran, Flutter improvement of a thin walled wing-engine system by applying curvilinear fiber path, Aerospace Science and Technology, 93 (2019) 105353.

    Article  Google Scholar 

  18. V. Khalafi and J. Fazilati, Supersonic panel flutter of variable stiffness composite laminated skew panels subjected to yawed flow by using NURBS-based isogeometric approach, Journal of Fluids and Structures, 82 (2018) 198–214.

    Article  Google Scholar 

  19. T. A. M. Guimarães, S. G. P. Castro, C. E. S. Cesnik and D. A. Rade, Supersonic flutter and buckling optimization of tow-steered composite plates, AIAA Journal, 57(1) (2019) 397–407.

    Article  Google Scholar 

  20. X. Chen and G. Nie, Nonlinear thermal flutter analysis of variable angle tow composite curved panels in supersonic air flow, Composite Structures, 277 (2021) 114610.

    Article  Google Scholar 

  21. H. Haddadpour and Z. Zamani, Curvilinear fiber optimization tools for aeroelastic design of composite wings, Journal of Fluids and Structures, 33 (2012) 180–190.

    Article  Google Scholar 

  22. W. Xia and H. Feng, Aeroelastic flutter of thermal overscaling functional gradient siding, Acta Mechanica Sinica, 48(3) (2016) 609–614.

    MathSciNet  Google Scholar 

  23. P. Camacho, H. Akhavan and P. Ribeiro, Linear aeroelastic analysis of cantilever hybrid composite laminated plates with curvilinear fibres and carbon nanotubes, Composite Structures, 266(13) (2021) 113765.

    Article  Google Scholar 

  24. M. Wu, W. Zhang and Y. Niu, Experimental and numerical studies on nonlinear vibrations and dynamic snap-through phenomena of bistable asymmetric composite laminated shallow shell under center foundation excitation, European Journal of Mechanics/A Solids, 89 (2021) 104303.

    Article  MathSciNet  MATH  Google Scholar 

  25. T. Liu, W. Zhang, M. Wu, Y. Zheng and Y. Zhang, Metastable nonlinear vibrations: third chaos of bistable asymmetric composite laminated square shallow shell under foundation excitation, Composite Structures, 255 (2021) 112966.

    Article  Google Scholar 

  26. S. Mahmoudkhani and K. S. Laghaie, Flutter analysis of sandwich panel with the constrained viscoelastic layer considering the effects of the imperfection and the core thickness deformation, Thin-Walled Structures, 173 (2022) 108980.

    Article  Google Scholar 

  27. S. Kaneko and S. Yoshimura, Fluid-structure-control interaction simulation of flutter control problems, Finite Elements in Analysis and Design, 203 (2022) 103722.

    Article  MathSciNet  Google Scholar 

  28. W. Tian, T. Zhao and Z. Yang, Theoretical modelling and design of metamaterial stiffened plate for vibration suppression and supersonic flutter, Composite Structures, 282 (2021) 115010.

    Article  Google Scholar 

  29. M. Rahmanian, T. Farsadi and H. Kurtaran, Nonlinear flutter of tapered and skewed cantilevered plates with curvilinear fiber paths, Journal of Sound and Vibration, 500 (2021) 116021.

    Article  Google Scholar 

  30. H. Akhavan and P. Ribeiro, Nonlinear flutter of composite laminates with curvilinear fibres using a full linearized aerodynamic theory, Journal of Fluids and Structures, 115 (2022) 103756.

    Article  Google Scholar 

  31. D. Kumar, K. K. Singh and M. T. A. Ansari, Effect of ply lay up sequence on interlaminar shear strength of symmetric and asymmetric GFRP composite, Materials Today: Proceedings, 22 (2020) 2041–2046.

    Google Scholar 

  32. C. B. York, On tapered warp-free laminates with single-ply Terminations, Composites: Part A, 72 (2015) 127–138.

    Article  Google Scholar 

  33. D. Cui and D. Li, The effect of importing extension-bending coupling into asymmetric composite structures, Mechanics of Composite Materials, 56(6) (2021) 779–788.

    Article  Google Scholar 

  34. K. Falkowicz, H. Debski, P. Wysmulski and P. Rozylo, The behaviour of compressed plate with a central cut-out, made of composite in an asymmetrical arrangement of layers, Composite Structures, 214 (2019) 406–413.

    Article  Google Scholar 

  35. J. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd Ed., CRC Press (2004).

  36. H. Li, H. Lv, Z. Zou, Z. Luo, H. Ma and Q. Han, Nonlinear vibration analysis and verification of fiber-reinforced cylindrical shell in thermal environment, Acta Aeronautica et Astronautica Sinica (2021) http://kns.cnki.net/kcms/detail/11.1929.v.20210521.1019.004.html.

  37. X. Ouyang and Y. Liu, Panel flutter of variable stiffness composite laminates in supersonic flow, Acta Aeronautica et Astronautica Sinica, 39(3) (2018) 116–126.

    Google Scholar 

Download references

Acknowledgments

This work was supported by the Open Fund for Key Laboratory of Airworthiness Certification Technology of Civil Aviation Aircraft (Grant No. SH2020112705), China, the Natural Science Foundation of China (Grant No.11702325), China and the Key Research and Development Projects in Hebei Province (Grant No.21350401D), China.

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Yating Liu, Jingbo Duan & Buqing Xu

  2. Hebei Key Laboratory of Mechanics of Intelligent Materials and Structures, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Jingbo Duan & Buqing Xu

  3. College of Electronic Science and Engineering, National University of Defense Technology, Changsha, 410073, China

    Yihang Gao

  4. Beijing Institute of Astronautical Systems Engineering, Beijing, 100076, China

    Yihang Gao

Authors
  1. Yating Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jingbo Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yihang Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Buqing Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jingbo Duan.

Additional information

Jingbo Duan is an Associate Professor of the Department of Engineering Mechanics, Shijiazhuang Tiedao University. He received his Ph.D. in Solid Mechanics from National University of Defence Technology. His research interests include aeroelastic flutter stability of composite panels and numerical calculation method in mechanics and engineering.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Duan, J., Gao, Y. et al. Nonlinear supersonic aerothermoelastic analysis of as ymmetrically curved-fiber composite panels with nonuniform temperature distributions. J Mech Sci Technol 37, 1325–1337 (2023). https://doi.org/10.1007/s12206-023-0219-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-023-0219-x

Keywords

Search

Navigation