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Free vibration of composite shells containing embedded delaminations based on the third-order shear deformation theory

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Abstract

The finite element vibration analysis of laminated spherical shell panels with rectangular embedded delamination is carried out based on the third-order shear deformation theory of Sanders. In the finite element formulation for the embedded delamination, the seven degrees of freedom per each node are used with transformations in order to fit the displacement continuity conditions at the delamination region. The numerical results obtained for plates and shells with delaminations are in good agreement with those of other preceding investigations. The new results for composite shell structures in this study mainly show the significant effect of the interactions between the radius-length ratio and other various parameters, for example, embedded delamination size, fiber angles, the number of layer and location of delamination in the layer direction.

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References

  • Bhimaraddi, A. and Stevens, L. K. (1984). “A high order theory for free vibration of orthotropic, homogeneous and laminated rectangular plates.” Journal of Applied Mechanics, Vol. 51, pp. 195–198.

    Article  Google Scholar 

  • Ferreira, A. J. M., Roque, C. M. C., and Jorge, R. M. N. (2006). “Static and free vibration analysis of composite shells by radial basis functions.” Engineering Analysis with Boundary Elements, Vol. 30, pp. 719–733.

    Article  MATH  Google Scholar 

  • Ganapathi, M., Patel, B. P., and Pawargi, D. S. (2002). “Dynamic analysis of laminated cross-ply composite non-circular thick cylindrical shells using higher-order theory.” International Journal of Solids and Structures, Vol. 39, pp. 5945–5962.

    Article  MATH  Google Scholar 

  • 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.” Computers and Structures, Vol. 36, No. 3, pp. 401–420.

    Article  MATH  Google Scholar 

  • Karmakar, A., Roy, H., and Kishimoto, K. (2005). “Free vibration analysis of delaminated composite pretwisted shells.” Aircraft Engineering and Aerospace Technology: An International Journal, Vol. 77, No. 6, pp. 486–490.

    Article  Google Scholar 

  • Kumar, A. and Shrivastava, R. P. (2005). “Free vibration of square laminates with delamination around a central cutout using HSDT.” Composite Structure, Vol. 70, No. 3, pp. 317–333.

    Article  Google Scholar 

  • Lee, S. Y. and Chang, S. Y. (2010). “Dynamic instability of delaminated composite structures with various geometrical shapes.” Journal of the Korean Society for Advanced Composite Structures, Vol. 1, pp. 1–8.

    Google Scholar 

  • Lee, S. J. and Reddy, J. N. (2004). “Vibration suppression of laminated shell structures investigated using higher order shear deformation theory.” Smart Materials and Structures, Vol. 13, pp. 1176–1194.

    Article  Google Scholar 

  • Lee, S.Y. and Wooh, S. C. (2004). “Finite element vibration analysis of composite box structures using the high order plate theory.” Journal of Sound and Vibration, Vol. 277, pp. 801–814.

    Article  Google Scholar 

  • Lee, S. Y., Wooh, S. C., and Yhim, S. S. (2004). “Dynamic behavior of folded composite plates analyzed by the third order plate theory.” International Journal of Solids and Structures, Vol. 41, pp. 1879–1892.

    Article  MATH  Google Scholar 

  • Messina, A. and Soldatos, K. P. (1999). “Vibration of completely free composite plates and cylindrical shell panels by a higher-order theory.” International Journal of Mechanical Sciences, Vol. 41, pp. 891–918.

    Article  MATH  Google Scholar 

  • Murthy, M. V. V. (1981). “An improved transverse shear deformation theory for laminated anisotropic plates.” NASA Technical paper 1903, pp. 1–37.

    Google Scholar 

  • Parthi, P. K., Bhattacharyya, S. K., and Sinha, P. K. (2001). “Hydrothermal effects on the dynamic behavior of multiple delaminated composite plates and shells.” Journal of Sound and Vibration, Vol. 248, No. 2, pp. 195–214.

    Article  Google Scholar 

  • Reddy, J. N. (2004). Mechanics of laminated composite plates and shells: Theory and analysis, CRC Press, New York.

    MATH  Google Scholar 

  • Reddy, J. N. and Liu, C. F. (1985). “A higher-order shear deformation theory for laminated elastic shells.” International Journal of Engineering Science, Vol. 23, pp. 319–330.

    Article  MATH  Google Scholar 

  • Sanders, J. L. Jr. (1959). An improved first approximation theory of thin shells, NASA TR-R24.

  • Sanders, J. L. Jr. (1963) “Nonlinear theories for thin shells.” Applied Mathematics, Vol. 21, pp. 21–36.

    Google Scholar 

  • Zukas, J. A. and Vinson, J. R. (1971). “Laminated transversely isotropic cylindrical shells.” Journal of Applied Mechanics, Vol. 38, pp. 400–407.

    Article  Google Scholar 

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Correspondence to Sang-Youl Lee.

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Noh, MH., Lee, SY. Free vibration of composite shells containing embedded delaminations based on the third-order shear deformation theory. KSCE J Civ Eng 16, 1193–1201 (2012). https://doi.org/10.1007/s12205-012-0931-z

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  • DOI: https://doi.org/10.1007/s12205-012-0931-z

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