Skip to main content
SpringerLink
Log in

Transient response of laminated plates with arbitrary laminations and boundary conditions under general dynamic loadings

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

The dynamic analysis of laminated plates with various loading and boundary conditions is presented employing generalized differential quadrature (GDQ) method. The first-order shear deformation theory is considered to model the transient response of the plate. The GDQ technique together with Newmark integration scheme is employed to solve the system of transient equations governing dynamics of the plate. Different symmetric and asymmetric lamination sequences together with various combinations of clamped, simply supported, and free boundary conditions are considered. Particular interest of this study regards to asymmetric orthotropic plates having free edge and mixed boundary conditions. It is shown that the method provides reasonably accurate results with relatively small number of grid points. Comparison of the results with those of other methods demonstrates a very good agreement. It is also revealed that the present method offers similar order of accuracy for all variables including displacements and stress resultants.

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. Wang Y.Y., Lam K.Y., Liu G.R.: A strip element method for the transient analysis of symmetric laminated plates. Int. J. Solids Struct. 38, 241–259 (2001)

    Article  MATH  Google Scholar 

  2. Lee Y., Reismann H.: Dynamics of rectangular plates. Int. J. Eng. Sci. 7, 93–113 (1969)

    Article  MATH  Google Scholar 

  3. Mallikarjuna M., Kant T.: Dynamics of laminated composite plates with a higher order theory and finite element discretization. J. Sound Vib. 126, 463–475 (1988)

    Article  Google Scholar 

  4. Noor A.K., Burton W.S., Bert C.W.: Computational models for sandwich panels and shells. Appl. Mech. Rev. 49(3), 155–199 (1996)

    Article  Google Scholar 

  5. Mallikarjuna M., Kant T.: A critical review and some results of recently developed refined theories of fiber reinforced laminated composites and sandwiches. Compos. Struct. 23, 293–312 (1993)

    Article  Google Scholar 

  6. Bhimaraddi A.: Static and transient response of rectangular plates. Thin Walled Struct. 5, 125–143 (1987)

    Article  Google Scholar 

  7. Khdeir A.A.: Transient response of refined cross-ply laminated plates for various boundary conditions. J. Acous Soc. Am. 97, 1664–1669 (1995)

    Article  Google Scholar 

  8. Reddy J.N.: Mechanics of Laminated Composite Plates and Shells Theory and Analysis. 2nd edn. CRC Press, London (2004)

    Google Scholar 

  9. Reddy J.N.: Dynamic (transient) analysis of layered anisotropic composite-material plates. Int. J. Numer. Meth. Eng. 19, 237–255 (1983)

    Article  MATH  Google Scholar 

  10. Reddy J.N.: Geometrically nonlinear transient analysis of laminated composite plates. AIAA J. 21(4), 621–629 (1983)

    Article  MATH  Google Scholar 

  11. Reddy J.N.: A note on symmetry considerations in the transient response of unsymmetrically laminated anisotropic plates. Int. J. Numer. Meth. Eng. 20, 175–181 (1984)

    Article  MATH  Google Scholar 

  12. Reddy J.N.: On the solutions to forced motions of rectangular composite plates. J. Appl. Mech. 49, 403–408 (1982)

    Article  MATH  Google Scholar 

  13. Khdeir A.A., Reddy J.N.: Exact solutions for the transient response of symmetric cross-ply laminates using a higher-order plate theory. Compos. Sci. Tech. 34, 205–224 (1989)

    Article  Google Scholar 

  14. Khdeir A.A., Reddy J.N.: On the forced motions of antisymmetric cross-ply laminated plates. Int. J. Mech. Sci. 31, 499–510 (1989)

    Article  MATH  Google Scholar 

  15. Ray M.C., Bhattacharya R., Samanta B.: Exact solution for dynamic analysis of composite plates with distributed piezoelectric layers. Comput. Struct. 66, 737–743 (1998)

    Article  MATH  Google Scholar 

  16. Shen H.S., Zheng J.J., Huang X.L.: Dynamic response of shear deformable laminated plates under thermomechanical loading and resting on elastic foundations. Compos. Struct. 60, 57–66 (2003)

    Article  Google Scholar 

  17. Yanga Y., Liub J.K., Huang P.Y.: Exact convergence studies on static and dynamic analyses of plates by using the double U-transformation and the finite-element method. J. Sound Vib. 305, 85–96 (2007)

    Article  Google Scholar 

  18. Rossi R.E., Gutiérrez R.H., Laura P.A.A.: Forced vibrations of rectangular plates subjected to harmonic loading distributed over a rectangular subdomain. Ocean Eng. 28, 1575–1584 (2001)

    Article  Google Scholar 

  19. Faria A.R., Oguamanam D.C.D.: Finite element analysis of the dynamic response of plates under traversing loads using adaptive meshes. Thin-Walled Struct. 42, 1481–1493 (2004)

    Article  Google Scholar 

  20. Nayak A.K., Shenoi R.A., Moy S.S.J.: Transient response of composite sandwich plates. Compos. Struct. 64, 249–267 (2004)

    Article  Google Scholar 

  21. Lowrey M.J.: Elasticity/strip solutions for orthotropic plate systems: static and dynamic case studies. Thin-Walled Struct. 15, 65–79 (1993)

    Article  Google Scholar 

  22. Aghdam M.M., Mohammadi M., Erfanian V.: Bending analysis of thin annular sector plates using extended Kantorovich method. Thin-Walled Struct. 45, 983–990 (2007)

    Article  Google Scholar 

  23. Abouhamza M., Aghdam M.M., Alijani F.: Bending analysis of symmetrically laminated cylindrical panels using the extended Kantorovich method. Mech. Adv. Mat. Struct. 14, 523–530 (2007)

    Article  Google Scholar 

  24. Sladek J., Sladek V., Krivacek J., Wen P.H., Zhang C.: Meshless local Petrov–Galerkin (MLPG) method for Reissner–Mindlin plates under dynamic load. Comput. Meth. Appl. Mech. Eng. 196, 2681–2691 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Liew K.M., Teo T.M., Han J.B.: Comparative accuracy of DQ and HDQ methods for three-dimensional vibration analysis of rectangular plates. Int. J. Numer. Meth. Eng. 45, 1831–1848 (1999)

    Article  MATH  Google Scholar 

  26. Liew K.M., Han J.B., Xiao Z.M.: Vibration analysis of circular Mindlin plates using the differential quadrature method. J. Sound Vib. 205, 617–630 (1997)

    Article  Google Scholar 

  27. Lam K.Y., Li H.: Generalized differential quadrature for frequency of rotating multilayered conical shell. ASCE J. Eng. Mech. 126, 1156–1162 (2000)

    Article  Google Scholar 

  28. Wu T.Y., Liu G.R.: A generalized differential quadrature rule for initial-value differential equations. J. Sound Vib. 233, 195–213 (2000)

    Article  Google Scholar 

  29. Shu, C.: Generalized differential-integral quadrature and application to the simulation of incompressible viscous flow including parallel computation. Ph.D. Thesis, University of Glasgow, UK (1991)

  30. Bellman R., 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)

    Article  MathSciNet  MATH  Google Scholar 

  31. Shu C., Richards B.E.: Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations. Int. J. Numer. Meth. Fluids 15, 791–798 (1992)

    Article  MATH  Google Scholar 

  32. Andakhshideh A., Maleki S., Aghdam M.M.: Non-linear bending analysis of laminated sector plates using generalized differential quadrature. Compos. Struct. 92, 2258–2264 (2010)

    Article  Google Scholar 

  33. Aghdam M.M., Farahani M.R., Dashty M., Rezaei niya S.M.: Application of GDQ method to the bending of thick laminated plates with various boundary conditions. Appl. Mech. Mater. 5–6, 407–414 (2006)

    Article  Google Scholar 

  34. Hong C.C., Jane K.C.: Shear deformation in thermal bending analysis of laminated plates by the GDQ method. Mech. Res. Comm. 30, 175–186 (2003)

    Article  MATH  Google Scholar 

  35. Shu C., Wang C.M.: Treatment of mixed and nonuniform boundary conditions in GDQ vibration analysis of rectangular plates. Eng. Struct. 21, 125–134 (1999)

    Article  Google Scholar 

  36. Shu C., Chew Y.T.: On the equivalence of generalized differential quadrature and highest order finite difference scheme. Comput. Meth. Appl. Mech. Eng. 15, 249–260 (1998)

    Article  MathSciNet  Google Scholar 

  37. Lu, C.: Computational modeling of composite structures and low-velocity impact. Ph.D. Thesis, National University of Singapore (1996)

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, P.O.Box 91775-1111, Mashhad, Iran

    S. Maleki, M. Tahani & A. Andakhshideh

Authors
  1. S. Maleki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Tahani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Andakhshideh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Tahani.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maleki, S., Tahani, M. & Andakhshideh, A. Transient response of laminated plates with arbitrary laminations and boundary conditions under general dynamic loadings. Arch Appl Mech 82, 615–630 (2012). https://doi.org/10.1007/s00419-011-0577-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-011-0577-1

Keywords

Search

Navigation