Free vibration of laminated composite skew plates with central cutouts

  • Lee, Sang-Youl ;
  • Park, Taehyo
  • Received : 2008.01.08
  • Accepted : 2009.02.26
  • Published : 2009.03.30


We performed a free vibration analysis of skew composite laminates with or without cutout based on the high-order shear deformation plate theory (HSDT). The effects of skew angles and ply orientations on the natural frequencies for various boundary conditions are studied using a nonlinear high-order finite element program developed for this study. The numerical results are in good agreement with those reported by other investigators for simple test cases, and the new results reported in this paper show the interactions between the skew angle, layup sequence and cutout size on the free vibration of the laminate. The findings highlight the importance of skew angles when analyzing laminated composite skew plates with cutout or without cutout.


composite laminates;skew plates;finite element analysis;high-order shear deformation plate theory;free vibration;skew angles;cutout ratios


  1. ABAQUS (2007), ABAQUS/CAE User’s Manual, Version 6.7, Hibbitt, Karlsson and Sorensen Inc., USA
  2. Anlas, G. and Göoker, G. (2001), 'Vibration analysis of skew fibre-reinforced composite laminated plates', J. Sound Vib., 242, 265-276
  3. Bardell, N.S. (1992), 'The free vibration of skew plates using the hierarchical finite element method', Comput. Struct., 45, 841-874
  4. Bathe, K.J. (1996), 'The finite element procedures in engineering analysis', Prentice Hall, New Jersey
  5. Bhimaraddi, A. and Stevens, L.K. (1984), 'A high order theory for free vibration of orthotropic, homogeneous and laminated rectangular plates', J. Appl. Mech., 51, 195-198
  6. Han, W. and Dickinson, S.M. (1997), 'Free vibration of symmetrically laminated skew plates', J. Sound Vib., 208, 367-390
  7. Hosokawa, K., Terada, Y. and Sakata, T. (1996), 'Free vibrations of clamped symmetrically laminated skew plates', J. Sound Vib., 189, 525-533
  8. Kant, T., Varaiya, J.H. and Arora, C.P. (1990), 'Finite element transient analysis of composite and sandwich plates based on a refined theory and implicit time integration schemes', Comput. Struct., 36, 401-420
  9. Kennedy, J.B. and Huggins, M.V. (1964), 'Series solution of skewed stiffened plates', Proc. ASCE, J. Eng. Mech. Div., 90, 1-22
  10. Kennedy, J.B. and Tamberg, K.G. (1969), 'Programs of skew in concrete bridge design', Department of Highways, Downsview, Ontario, Canada, Report No. RR144
  11. Khdeir, A.A. and Reddy, J.N. (1991), 'Analytical solutions of refined plate theories of cross-ply composite laminates', J. Pressure Vessel Tech., 113, 570-578
  12. Kim, K.D. and Park, T. (2002), 'An 8-node assumed strain element with explicit integration for isotropic and laminated composite shells', Struct. Eng. Mech., 13, 387-410
  13. Kumar, A. and Shrivastava, R.P. (2005), 'Free vibration of square laminates with delamination around a central cutout using HSDT', Comput. Struct., 70, 317-333
  14. Lee, S.Y. and Wooh, S.C. (2004), 'Finite element vibration analysis of composite box structures using the high order plate theory', J. Sound Vib., 277, 801-814
  15. Lee, S.Y. and Yhim, S.S. (2004), 'Dynamic analysis of composite plates subjected to multi-moving loads based on a third order theory', Int. J. Solids Struct., 41, 4457-4472
  16. Mizusawa, T., Kajita, T. and Naruoka, M. (1979), 'Vibration of skew plates by using b-spline function', J. Sound Vib., 62, 301-308
  17. Murthy, M.V.V. (1981),'An improved transverse shear deformation theory for laminated anisotropic plates', NASA Technical Paper. 1903, 1-37
  18. Park, T., Lee, S.Y., Seo, J.W. and Voyiadjis, G.Z. (2008), 'Structural dynamic behavior of skew sandwich plates with laminated composite faces', Compos. Part B, 39, 316-326
  19. Reddy, A.R.K. and Palaninathan, R. (1999), 'Free vibration of skew laminates', Comput. Struct., 70, 415-423
  20. Reddy, J.N. (2004), 'Mechanics of laminated composite plates and shells : Theory and analysis', CRC press, New York
  21. Reddy, J.N. and Phan, N.D. (1985), 'Stability and vibration of isotropic, orthotropic, and laminated plates according to a higher-order shear deformation theory', J. Sound Vib., 98, 157-170
  22. Reddy, J.N. and Krishnan, S. (2001), 'Vibration control of laminated plates using embedded smart layers', Struct. Eng. Mech., 12, 135-156
  23. Singha, M.K. and Ganapathi, M. (2004), 'Large amplitude free flexural vibrations of laminated composite skew plates', Int. J. Non-linear Mech., 38, 1709-1720
  24. Sivakumar, K., Iyengar, N.G.R. and Deb, K. (1999), 'Free vibrations of laminated composite plates with cutout', J. Sound Vib., 221, 443-470
  25. Szilard, R. (1974), 'Theory and analysis of plates : Classical and numerical methods', Prentice-hall, New Jersey
  26. Wang, C.M., Ang, K.K., Yang, L. and Watanabe, E. (2000), 'Free vibration of skew sandwich plates with laminated facings', J. Sound Vib., 235, 317-340
  27. Wang, S. (1997), 'Free vibration analysis of skew fibre-reinforced composite laminates based on first-order shear deformation plate theory', Comput. Struct., 63, 525-538

Cited by

  1. Finite element dynamic stability analysis of laminated composite skew plates containing cutouts based on HSDT vol.70, pp.8, 2010,
  2. Control of geometrically nonlinear vibrations of skew laminated composite plates using skew or rectangular 1–3 piezoelectric patches vol.9, pp.4, 2013,
  3. Dynamic instability of delaminated composite skew plates subjected to combined static and dynamic loads based on HSDT vol.58, 2014,
  4. Effects of geometrical and material parameters on free vibration analysis of fiber metal laminated plates vol.14, pp.4, 2013,