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Acta Mechanica

, Volume 229, Issue 6, pp 2413–2430 | Cite as

On the nonlinear dynamic responses of FG-CNTRC beams exposed to aerothermal loads using third-order piston theory

  • Hamed Asadi
  • Amin Rabiei Beheshti
Original Paper

Abstract

The purpose of this study is to analyze the nonlinear dynamic responses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams exposed to axial supersonic airflow in thermal environments. The dynamic model of the FG-CNTRC beam is developed with regard to the first-order shear deformation theory incorporating the von Kármán geometrical nonlinearity. The thermomechanical properties of the constituents are assumed to be temperature dependent. The third-order piston theory is adopted to estimate the nonlinear aerodynamic pressure induced by the supersonic airflow. Harmonic differential quadrature method is implemented to discretize the equations of motion in the spatial domain. A comprehensive parametric study is performed to expatiate on the effect of the distribution type and volume fraction of CNTs, boundary condition, slenderness ratio, and thermal environments on the aerothermoelastic responses of the FG-CNTRC beam. Simulation results indicate that the presence of the aerodynamic pressure not only increases the critical buckling temperature of the FG-CNTRC beam, but also changes the buckling mode shapes of the beam. Furthermore, the results show that aerothermoelastic characteristics of FG-CNTRC beams may be remarkably improved by the selection of a proper distribution of CNTs. Besides, it is found that FG-CNTRC beams with intermediate CNT volume fraction do not have an intermediate critical buckling temperature.

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References

  1. 1.
    Liew, K.M., Lei, Z.X., Zhang, L.W.: Mechanical analysis of functionally graded carbon nanotube reinforced composites: a review. Compos. Struct. 120, 90–97 (2015)CrossRefGoogle Scholar
  2. 2.
    Wuite, J., Adali, S.: Deflection and stress behavior of nanocomposite reinforced beams using a multiscale analysis. Compos. Struct. 71, 388–396 (2005)CrossRefGoogle Scholar
  3. 3.
    Yas, M.H., Samadi, N.: Free vibrations and buckling analysis of carbon nanotube reinforced composite Timoshenko beams on elastic foundation. Int. J. Press. Vessels Pip. 98, 119–128 (2012)CrossRefGoogle Scholar
  4. 4.
    Shen, H.S., Xiang, Y.: Nonlinear analysis of nanotube reinforced composite beams resting on elastic foundations in thermal environments. Eng. Struct. 56, 698–708 (2013)CrossRefGoogle Scholar
  5. 5.
    Ghorbanpour Arani, A., Maghamikia, S., Mohammadimehr, M., Arefmanesh, A.: Buckling analysis of laminated composite rectangular plates reinforced by SWNTs using analytical and finite element method. J. Mech. Sci. Technol. 25, 809–820 (2011)CrossRefGoogle Scholar
  6. 6.
    Lin, F., Xiang, Y.: Vibration of carbon nanotube reinforced composites beams based on the first and third order beam theories. Appl. Math. Model. 38, 3741–3754 (2014)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Ansari, R., Shojaei, M.F., Mohammadi, V., Gholami, R., Sadeghi, F.: Nonlinear forced vibration analysis of functionally graded carbon nanotube-reinforced composite Timoshenko beams. Compos. Struct. 113, 316–327 (2014)CrossRefGoogle Scholar
  8. 8.
    Ke, L.L., Yang, J., Kitipornchai, S.: Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams. Compos. Struct. 92, 676–683 (2010)CrossRefGoogle Scholar
  9. 9.
    Lei, Z.X., Liew, K.M., Yu, J.I.: Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method. Compos. Struct. 98, 160–168 (2013)CrossRefzbMATHGoogle Scholar
  10. 10.
    Lei, Z.X., Liew, K.M., Yu, J.I.: Large deflection analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method. Comput. Methods Appl. Mech. Eng. 256, 189–199 (2013)CrossRefzbMATHGoogle Scholar
  11. 11.
    Lei, Z.X., Zhang, L.W., Liew, K.M.: Buckling of FG-CNT reinforced composite thick skew plates resting on Pasternak foundations based on an element-free approach. Appl. Math. Comput. 266, 773–791 (2015)MathSciNetGoogle Scholar
  12. 12.
    Asadi, H., Souri, M., Wang, Q.: A numerical study on flow-induced instabilities of supersonic FG-CNT reinforced composite flat panels in thermal environments. Compos. Struct. 171, 113–125 (2017)CrossRefGoogle Scholar
  13. 13.
    Mehri, M., Asadi, H., Kouchakzadeh, M.A.: Computationally efficient model for flow-induced instability of CNT reinforced functionally graded truncated conical curved panels subjected to axial compression. Comput. Methods Appl. Mech. Eng. 318, 957–980 (2017)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Liew, K.M., Lei, Z.X., Yu, J.L., Zhang, L.W.: Postbuckling analysis of carbon nanotube reinforced functionally graded cylindrical panels under axial compression using a meshless. Comput. Methods Appl. Mech. Eng. 268, 1–17 (2014)CrossRefzbMATHGoogle Scholar
  15. 15.
    Asadi, H., Wang, Q.: Dynamic stability analysis of a pressurized FG-CNTRC cylindrical shell interacting with supersonic airflow. Compos. B 118, 15–25 (2017)CrossRefGoogle Scholar
  16. 16.
    Shen, H.S., Xiang, Y.: Thermal postbuckling of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments. Compos. Struct. 123, 383–392 (2015)CrossRefGoogle Scholar
  17. 17.
    Shen, H.S., Xiang, Y.: Nonlinear response of nanotube-reinforced composite cylindrical panels subjected to combined loadings and resting on elastic foundations. Compos. Struct. 131, 939–950 (2015)CrossRefGoogle Scholar
  18. 18.
    Shen, H.S.: Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite cylindrical shells. Compos. B 43, 1030–1038 (2012)CrossRefGoogle Scholar
  19. 19.
    Asadi, H.: Numerical simulation of the fluid-solid interaction for CNT reinforced functionally graded cylindrical shells in thermal environments. Acta Astronaut. 138, 214–224 (2017)CrossRefGoogle Scholar
  20. 20.
    Zhang, L.W., Lei, Z.X., Liew, K.M., Yu, J.L.: Large deflection geometrically nonlinear analysis of carbon nanotube reinforced functionally graded cylindrical panels. Comput. Methods Appl. Mech. Eng. 273, 1–18 (2014)CrossRefzbMATHGoogle Scholar
  21. 21.
    Zhang, L.W., Lei, Z.X., Liew, K.M., Yu, J.L.: Static and dynamic of carbon nanotube reinforced functionally graded cylindrical panels. Compos. Struct. 111, 205–212 (2014)CrossRefGoogle Scholar
  22. 22.
    Mehri, M., Asadi, H., Wang, Q.: Buckling and vibration analysis of a pressurized CNT reinforced functionally graded truncated conical shell under an axial compression using HDQ method. Comput. Methods Appl. Mech. Eng. 303, 75–100 (2016)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Ansari, R., Torabi, J.: Numerical study on the buckling and vibration of functionally graded carbon nanotube-reinforced composite conical shells under axial loading. Compos. B 95, 196–208 (2016)CrossRefGoogle Scholar
  24. 24.
    Mehri, M., Asadi, H., Wang, Q.: On dynamic instability of a pressurized functionally graded carbon nanotube reinforced truncated conical shell subjected to yawed supersonic airflow. Compos. Struct. 153, 938–951 (2016)CrossRefGoogle Scholar
  25. 25.
    Zhang, L.W., Song, Z.G., Liew, K.M.: Computation of aerothermoelastic properties and active flutter control of CNT reinforced functionally graded composite panels in supersonic airflow. Comput. Methods Appl. Mech. Eng. 300, 427–441 (2016)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Wu, H., Kitipornchai, S., Yang, J.: Thermal buckling and postbuckling analysis of functionally graded carbon nanotube-reinforced composite beams. Appl. Mech. Mater. 846, 182–187 (2016)CrossRefGoogle Scholar
  27. 27.
    Asadi, H., Wang, Q.: An investigation on the aeroelastic flutter characteristics of FG-CNTRC beams in the supersonic flow. Compos. B 116, 486–499 (2017)CrossRefGoogle Scholar
  28. 28.
    Zhang, L.W., Song, Z.G., Qiao, P., Liew, K.M.: Modeling of dynamic responses of CNT-reinforced composite cylindrical shells under impact loads. Comput. Methods Appl. Mech. Eng. (2016).  https://doi.org/10.1016/j.cma.2016.10.020
  29. 29.
    Mohammadzadeh-Keleshteri, M., Asadi, H., Aghdam, M.M.: Geometrical nonlinear free vibration responses of FG-CNT reinforced composite annular sector plates integrated with piezoelectric layers. Compos. Struct. 171, 100–112 (2017)CrossRefGoogle Scholar
  30. 30.
    Mohammadzadeh-Keleshteri, M., Asadi, H., Wang, Q.: Postbuckling analysis of smart FG-CNTRC annular sector plates with surface-bonded piezoelectric layers using generalized differential quadrature method. Comput. Methods Appl. Mech. Eng. 325, 689–710 (2017)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Keleshteri, M.M., Asadi, H., Wang, Q.: On the snap-through instability of post-buckled FG-CNTRC rectangular plates with integrated piezoelectric layers. Comput. Methods Appl. Mech. Eng. 331, 53–71 (2018)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Keleshteri, M.M., Asadi, H., Wang, Q.: Large amplitude vibration of FG-CNT reinforced composite annular plates with integrated piezoelectric layers on elastic foundation. Thin-Walled Struct. 120, 203–214 (2017)CrossRefGoogle Scholar
  33. 33.
    Dowell, E.H.: A Modern Course in Aeroelasticity, 5th edn. Springer, Berlin (2015)zbMATHGoogle Scholar
  34. 34.
    Dowell, E.H., Ilgamov, M.: Studies in Nonlinear Aeroelasticity. Springer, Berlin (1988)CrossRefzbMATHGoogle Scholar
  35. 35.
    Bisplinghoff, R.L., Ashley, H.: Principles of Aeroelasticity. Wiley, New York (1962)zbMATHGoogle Scholar
  36. 36.
    Amabili, M., Pellicano, F.: Multimode approach to nonlinear supersonic flutter of imperfect circular cylindrical shells. J. Appl. Mech. 69, 117–129 (2012)CrossRefzbMATHGoogle Scholar
  37. 37.
    Gray, C.E., Mei, C., Shore, C.P.: Finite element method for large-amplitude two-dimensional panel flutter at hypersonic speeds. AIAA J. 29(2), 290–298 (1991)CrossRefGoogle Scholar
  38. 38.
    Bellman, R.E., Kashef, B.G., Casti, J.: Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. J. Comput. Phys. 10, 40–52 (1972)MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Bellman, R.E., Casti, J.: Differential quadrature and long-term integration. J. Math. Anal. Appl. 34, 235–238 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Asadi, H., Aghdam, M.M., Shakeri, M.: Vibration analysis of axially moving line supported functionally graded plates with temperature dependent properties. Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 228(6), 953–969 (2014)CrossRefGoogle Scholar
  41. 41.
    Asadi, H., Kiani, Y., Aghdam, M.M., Shakeri, M.: Enhanced thermal buckling of laminated composite cylindrical shells with shape memory alloy. J. Compos. Mater. 50(2), 243–256 (2016)CrossRefGoogle Scholar
  42. 42.
    Shu, C., Du, H.: A general approach for implementing general boundary conditions in the GDQ free vibration analysis of plates. Int. J. Solids Struct. 34(7), 837–846 (1997)CrossRefzbMATHGoogle Scholar
  43. 43.
    Samadpour, M., Asadi, H., Wang, Q.: Nonlinear aero-thermal flutter postponement of supersonic laminated composite beams with shape memory alloys. Eur. J. Mech. A. Solids 57, 18–28 (2016)MathSciNetCrossRefGoogle Scholar
  44. 44.
    Prabhakara, M.K., Chia, C.Y.: Nonlinear flexural vibrations of orthotropic rectangular plates. J. Sound Vib. 52(4), 511–518 (1977)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of AlbertaEdmontonCanada
  2. 2.Department of Mechanical EngineeringAmirkabir University of TechnologyTehranIran
  3. 3.Department of Aerospace EngineeringSharif University of TechnologyTehranIran

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