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A comparative study on free vibration analysis of delaminated torsion stiff and bending stiff composite shells

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Abstract

This paper presents a finite element method to compare the effects of delamination on free vibration of graphite-epoxy bending stiff and torsion stiff composite pretwisted shallow conical shells. The generalized dynamic equilibrium equation is derived from Lagrange’s equation of motion neglecting the Coriolis effect for moderate rotational speeds. An eight noded isoparametric plate bending element is employed incorporating rotary inertia and effects of transverse shear deformation based on Mindlin’s theory. The multipoint constraint algorithm is utilized to ensure the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front. The standard eigen value problem is solved by applying the QR iteration algorithm. Mode shapes for typical configurations are also depicted. Numerical results obtained are the first known non-dimensional frequencies which could serve as reference solutions for the future investigators.

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References

  1. E. F. Crawley, The natural modes of graphite/epoxy cantilever plates and shells, Composite Materials, 13 (1979) 195–205.

    Article  Google Scholar 

  2. J. T. S. Wang, D. Shaw and O. Mahrenholtz, Vibration of rotating rectangular plates, J. Sound and Vibration, 112(3) (1987) 455–468.

    Article  Google Scholar 

  3. D. Shaw, K. Y. Shen and J. T. S. Wang, Flexural vibration of rotating rectangular plates of variable thickness, J. Sound and Vibration, 126(3) (1988) 373–385.

    Article  Google Scholar 

  4. M. S. Qatu and A. W. Leissa, Vibration studies for laminated composite twisted cantilever plates, I. J. Mechanical Sciences, 33 (1991) 927–940.

    Article  Google Scholar 

  5. K. M. Liew, C. M. Lim and L. S. Ong, Vibration of pret-wisted cantilever shallow conical shells, I. J. Solids Structures, 31 (1994) 2463–74.

    Article  MATH  Google Scholar 

  6. O. G. McGee and H. R. Chu, Three-dimensional vibration analysis of rotating laminated composite blades, J. Engg. for Gas Turbines and Power, ASME, 116 (1994) 663–671.

    Article  Google Scholar 

  7. M. H. H. Shen and J. E. Grady, Free vibrations of delaminated beams, AIAA, 30 (1992) 1361–1370.

    Article  Google Scholar 

  8. M. Krawczuk, W. Ostachowicz and A. Zak, Dynamics of cracked composite material structures, Computational Mechanics, 20 (1997) 79–83.

    Article  MATH  Google Scholar 

  9. P. K. Parhi, S. K. Bhattacharyya and P. K. Sinha, Failure analysis of multiple delaminated due to bending and impact, Bull. Mater. Sci., 24 (2001) 143–149.

    Article  Google Scholar 

  10. Y. Kee, and J. Kim, Vibration characteristics of initially twisted rotating shell type composite blades, Composite Structures, 64(2) (2004) 151–159.

    Article  Google Scholar 

  11. M. G. Andrews, R. Massabò, A. Cavicchi and B. N. Cox, Dynamic interaction effects of multiple delaminations in plates subject to cylindrical bending, I. J. Solids and Structures, 46(9) (2009) 1815–1833.

    Article  MATH  Google Scholar 

  12. F. Aymerich, F. Dore and P. Priolo, Simulation of multiple delaminations in impacted cross-ply laminates using a finite element model based on cohesive interface elements, Composites Science and Technology, 69(11–12) (2009) 1699–1709.

    Article  Google Scholar 

  13. C. K. Gim, Plate finite element modelling of laminated plates, Composite Structures, 52 (1994) 157–168.

    Article  MATH  Google Scholar 

  14. K. J. Bathe, Finite element procedures in engineering analysis, PHI, New Delhi, India (1990).

    Google Scholar 

  15. A. W. Leissa, J. K. Lee and A. J. Wang, Vibrations of twisted rotating blades, J. Vibration, Acoustics, Stress and Reliability in Design, Trans., ASME, 106 (1984) 251–257.

    Article  Google Scholar 

  16. A. Karmakar, A. and P. K. Sinha, Failure analysis of laminated composite pretwisted rotating plates, J. Reinforced Plastics and Composites, 20 (2001) 1326–1357.

    Article  Google Scholar 

  17. S. Sreenivasamurthy and V. Ramamurti, Coriolis effect on the vibration of flat rotating low aspect ratio cantilever plates, J. Strain Analysis, 16 (1981) 97–106.

    Article  Google Scholar 

  18. R. M. Jones, Mechanics of composite materials, Hemisphere, p.147–156, New York, USA (1975).

    Google Scholar 

  19. M. S. Qatu and A. W. Leissa, Natural frequencies for cantilevered doubly-curved laminated composite shallow shells, Composite Structures, 17 (1991) 227–255.

    Article  Google Scholar 

  20. S. Dey, T. Bandopadhyay, A. Karmakar and K. Kishimoto, Free vibration of delaminated composite shallow conical shells, Journal of Solid Mechanics and Materials Engineering (JSME Series A), 5(11) (2011) 610–626.

    Article  Google Scholar 

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Authors and Affiliations

  1. Mechanical Engineering Department, Jadavpur University, Kolkata, 700 032, India

    Sudip Dey & Amit Karmakar

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  1. Sudip Dey
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  2. Amit Karmakar
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Correspondence to Sudip Dey.

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Recommended by Associate Editor Jun-Sik Kim

Sudip Dey is a research scholar in Mechanical Engineering Department, Jadavpur University, Kolkata, India. His basic research interests are mechanics of composites, structural health monitoring, computational mechanics and modelling, functionally graded materials and impact mechanics. He has more than 10 years industry and research experience. He is also actively engaged in various industrial and research projects. He has published several papers in reputed international journals.

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Dey, S., Karmakar, A. A comparative study on free vibration analysis of delaminated torsion stiff and bending stiff composite shells. J Mech Sci Technol 27, 963–972 (2013). https://doi.org/10.1007/s12206-013-0208-6

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  • DOI: https://doi.org/10.1007/s12206-013-0208-6

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