Skip to main content
SpringerLink
Log in

Flutter instability of laminated thick anisotropic plates using BEM

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

In this paper, the boundary element method (BEM) is developed for the flutter analysis of thick anisotropic plates modeled by Mindlin’s theory. Such plates describe the response of laminated plates consisting of layers of anisotropic materials, which are extensively used in various modern engineering applications. The plate is subjected to aerodynamic pressure due to supersonic air flow, a follower-type load. The governing equations are three coupled linear partial differential equations of second order subjected to three boundary conditions besides the initial conditions. The boundary value problem is solved using the analog equation method. Thus, following the principle of the analog equation, the original equations are substituted by three uncoupled Poisson’s equations under fictitious loads, which are subsequently, solved using the conventional BEM for Poisson’s equation. Various thick and thin laminated plate problems are studied using the proposed method. The obtained numerical results demonstrate the efficiency of the solution procedure, validate its accuracy and give a revealing insight into the dynamic response of the thick laminated plates under follower loads.

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

References

  1. Ziegler, H.: Die Stabilitätskriterien der Elastomechanik. Ing. Arch. 20, 49–56 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ziegler, H.: Linear elastic stability: a critical analysis of methods. Z. Angew. Math. Phys. 4, 89–121 (1953)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bolotin, V.V.: Non-conservative problems of the theory of elastic stability, Fizmatgiz (in Russian), Moscow, 1963. Pergamon, Oxford (1961)

    Google Scholar 

  4. Herrmann, G.: Stability of equilibrium of elastic systems subjected to non-conservative forces. Appl. Mech. Rev. 20, 103–108 (1967)

    Google Scholar 

  5. Dowell, E.H.: Panel flutter: A review of the aeroelastic stability of plates and shells. AIAA J. 8, 385–399 (1970)

    Article  Google Scholar 

  6. Leipholz, H., Pfendt, F.: Application of extended equations of Galerkin to stability problems of rectangular plates with free edges and subjected to uniformly distributed follower forces. Comput. Methods Appl. Mech. Eng. 37, 341–365 (1983)

    Article  MATH  Google Scholar 

  7. Adali, S.: Stability of a rectangular plate under nonconservative and conservative forces. Int. J. Solids Struct. 18, 1043–1052 (1982)

    Article  MATH  Google Scholar 

  8. Zuo, Q.H., Schreyer, H.L.: Flutter and divergence instability of nonconservative beams and plates. Int. J. Solids Struct. 33(9), 1355–1367 (1996)

    Article  MATH  Google Scholar 

  9. Kim, J.H., Kim, H.S.: A study on the dynamic stability of plates under a follower force. Comput. Struct. 74, 351–363 (2000)

    Article  Google Scholar 

  10. Sander, G., Bon, C., Geradin, M.: Finite element analysis of supersonic panel flutter. Int. J. Numer. Methods Eng. 7, 379–394 (1973)

    Article  MATH  Google Scholar 

  11. Babouskos, N., Katsikadelis, J.T.: Flutter instability of damped plates under combined conservative and nonconservative loads. Arch. Appl. Mech. 79(6–7), 541–556 (2009)

    Article  MATH  Google Scholar 

  12. Dowell, E.H.: Nonlinear oscillations of a fluttering plate. AIAA J. 4, 1267–1275 (1966)

    Article  Google Scholar 

  13. Mei, C.: A finite element approach for nonlinear panel flutter. AIAA J. 15, 1107–1110 (1977)

    Article  Google Scholar 

  14. Guo, X., Mei, C.: Using aeroelastic modes for nonlinear flutter at arbitrary supersonic yawed angle. AIAA J. 41(2), 272–279 (2003)

    Article  Google Scholar 

  15. Katsikadelis, J.T., Babouskos, N.G.: Nonlinear flutter instability of thin damped plates: a solution by the analog equation method. J. Mech. Mater. Struct. 4(7–8), 1395–1414 (2009)

    Article  Google Scholar 

  16. Rossettos, J.N., Tong, P.: Finite-element analysis of vibration and flutter of cantilever anisotropic plates. J. Appl. Mech. 41, 1075–1080 (1974)

    Article  MATH  Google Scholar 

  17. Lin, K.-J., Lu, P.-J., Tarn, J.-Q.: Flutter analysis of composite panels using high-precision finite elements. Comput. Struct. 33(2), 561–574 (1989)

    Article  MATH  Google Scholar 

  18. Liao, C.L., Lee, Z.Y.: Elastic stability of skew laminated composite plates subjected to biaxial follower forces. Int. J. Numer. Methods Eng. 36, 1825–1847 (1993)

    Article  MATH  Google Scholar 

  19. Kumar, L.R., Datta, P.K., Prabhakara, D.L.: Dynamic instability characteristics of laminated plates subjected to partial follower edge load with damping. Int. J. Mech. Sci. 45, 1429–1448 (2003)

    Article  MATH  Google Scholar 

  20. Kouchakzadeh, M.A., Rasekh, M., Haddadpour, H.: Panel flutter analysis of general laminated composite plates. Compos. Struct. 92, 2906–2915 (2010)

    Article  Google Scholar 

  21. Li, J., Narit, Y.: Analysis and optimal design for supersonic composite laminated plate. Compos. Struct. 101, 35–46 (2013)

    Article  Google Scholar 

  22. Pai, P.: A new look at shear correction factors and warping functions of anisotropic laminates. Int. J. Solids Struct. 32(16), 2295–2313 (1995)

    Article  MATH  Google Scholar 

  23. Srinivansan, R.S., Babu, B.J.C.: Free vibration and flutter of laminated quadrilateral plates. Comput. Struct. 27(2), 297–304 (1987)

    Article  MATH  Google Scholar 

  24. Lee, I., Cho, M.H.: Finite element analysis of composite panel flutter. Comput. Struct. 39(1/2), 165–172 (1991)

    Article  MATH  Google Scholar 

  25. Chowdary, T.V.R., Parthan, S., Sinha, P.K.: Finite element flutter analysis of laminated composite panels. Comput. Struct. 53(2), 245–251 (1994)

    Article  MATH  Google Scholar 

  26. Fazelzadeh, S.A., Marzocca, P., Mazidi, A., Rashidi, E.: Divergence and flutter of shear deformable aircraft swept wings subjected to roll angular velocity. Acta Mech. 212, 151–165 (2010)

    Article  Google Scholar 

  27. Grover, N., Singh, B.N., Maiti, D.K.: An inverse trigonometric shear deformation theory for supersonic flutter characteristics of multilayered composite plates. Aerosp. Sci. Technol. 52, 41–51 (2016)

    Article  Google Scholar 

  28. Birman, V., Librescu, L.: Supersonic flutter of shear deformable laminated composite flat panels. J. Sound Vib. 139(2), 265–275 (1990)

    Article  Google Scholar 

  29. Song, Z.G., Zhang, L.W., Liew, K.M.: Aeroelastic analysis of CNT reinforced functionally graded composite panels in supersonic airflow using a higher-order shear deformation theory. Compos. Struct. 141, 79–90 (2016)

    Article  Google Scholar 

  30. Li, F.-M., Song, Z.-G.: Aeroelastic flutter analysis for 2d Kirchhoff and Mindlin panels with different boundary conditions in supersonic airflow. Acta Mech. 225, 3339–3351 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  31. Dowell, E.H.: Aeroelsticity of Plates and Shells. Noordhoff International Publishing, Leyden (1975)

    MATH  Google Scholar 

  32. Mindlin, R.D.: Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. ASME J. Appl. Mech. 18, 31–38 (1951)

    MATH  Google Scholar 

  33. Katsikadelis, J.T.: The Boundary Element Method for Plate Analysis. Academic Press, Elsevier (2014)

    MATH  Google Scholar 

  34. Katsikadelis, J.T.: The Boundary Element Method for Engineer and Scientists. Academic Press, Elsevier (2016)

    Google Scholar 

  35. Katsikadelis, J.T., Kounadis, A.N.: Flutter loads of a Timoshenko beam-column under a follower force governed by two variants of equations of motion. Acta Mech. 48, 209–217 (1983)

    Article  MATH  Google Scholar 

  36. Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press, Florida (2003)

    Google Scholar 

  37. Kounadis, A.N., Katsiakdelis, J.T.: On the discontinuity of the flutter load for various types of cantilevers. Int. J. Solids Struct. 16, 375–383 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  38. Seyranian, A.P., Mailybaev, A.A.: Multiparameter Stability Theory with Mechanical Applications. World Scientific, Singapore (2004)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil Engineering, National Technical University of Athens, Zografou Campus, 15773, Athens, Greece

    John T. Katsikadelis & Nick G. Babouskos

Authors
  1. John T. Katsikadelis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nick G. Babouskos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to John T. Katsikadelis.

Additional information

This paper is dedicated to the memory of Franz Ziegler

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Katsikadelis, J.T., Babouskos, N.G. Flutter instability of laminated thick anisotropic plates using BEM. Acta Mech 229, 613–628 (2018). https://doi.org/10.1007/s00707-017-1988-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-017-1988-z

Search

Navigation