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Free vibration of symmetric angle-ply laminated cylindrical shells of variable thickness

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Abstract

In this paper, free vibrations of symmetric angle-ply laminated cylindrical shells are presented under different thickness variations. The thickness variations of the shells are linear, exponential, and sinusoidal. Spline function techniques are adopted to approximate the displacement functions, and the point collocation method is used to obtain the generalized eigenvalue problem with appropriate boundary conditions. The effects of the geometric parameters, thickness parameters, and material parameters on the frequencies of symmetric angle-ply laminated cylindrical shells with two kinds of material properties under different boundary conditions are analyzed.

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References

  1. Greenberg J.B., Stavsky Y.: Buckling and vibration of orthotropic composite cylindrical shells. Acta Mech. 36, 15–29 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alam N., Asnani N.T.: Vibration and damping of multilayered cylindrical shells, part II: numerical results. AIAA J. 22, 975–981 (1984)

    Article  MATH  Google Scholar 

  3. Sharma C.B., Darvizeh M.: Free vibration of specially orthotropic, multilayered, thin cylindrical shells with various end conditions. Compos. Struct. 7, 123–138 (1987)

    Article  Google Scholar 

  4. Alam N., Asnani N.T.: Vibration and damping analysis of a fiber reinforced composite material cylindrical shell. J. Compos. Mater. 21, 348–361 (1987)

    Article  Google Scholar 

  5. Viswanathan K.K., Kim K.S., Lee J.H., Koh H.S., Lee J.B.: Free vibration of multi-layered circular cylindrical shell with cross-ply walls, including shear deformation by using spline function method. J. Mech. Sci. Technol. 22, 2062–2075 (2008)

    Article  Google Scholar 

  6. Khdeir A.A.: Thermally induced vibrations of cross-ply laminated shallow shells. Acta Mech. 151, 135–147 (2001)

    Article  MATH  Google Scholar 

  7. Raouf R.A.: Tailoring the dynamic characteristics of composite panels using fiber orientation. Compos. Struct. 29, 259–267 (1994)

    Article  Google Scholar 

  8. Abrate S.: Optimal design of laminated plates and shells. Compos. Struct. 29, 269–286 (1994)

    Article  Google Scholar 

  9. Viswanathan K.K., Navaneethakrishnan P.V.: Free vibration of layered truncated conical shell frusta if differently varying thickness by the method of collocation with cubic and quintic splines. Int. J. Solids Struct. 42, 1129–1150 (2005)

    Article  MATH  Google Scholar 

  10. Loy C.T., Lam K.Y., Hua L., Liu G.R.: Vibration of antisymmetric angle-ply laminated cylindrical panels with different boundary conditions. Q. J. Mech. Appl. Math. 52, 55–71 (1999)

    Article  MATH  Google Scholar 

  11. Andrianov A.A., Awejcewicz J.: Edge-localized effects in buckling and vibrations of a shell with free in circumferential direction ends. Acta Mech. 173, 41–47 (2004)

    Article  MATH  Google Scholar 

  12. Lam K.Y., Qian W.: Free vibration of symmetric angle-ply thick laminated composite cylindrical shells. Compos. B Eng. 31, 345–354 (2000)

    Article  Google Scholar 

  13. Iqbal Z., Naeem M.N., Sultana N.: Vibration characteristics of FGM circular cylindrical shells using wave propagation approach. Acta Mech. 208, 237–248 (2009)

    Article  MATH  Google Scholar 

  14. Shah A.G., Mahmood T., Naeen M.N., Z Z., Arshad S.H.: Vibrations of functionally graded cylindrical shells based on elastic foundation. Acta Mech. 211, 293–307 (2010)

    Article  MATH  Google Scholar 

  15. Tmarchi T., Soldatos K.P.: Vibrations of angle-ply laminated circular cylindrical shells subjected to different sets of edge boundary conditions. J. Eng. Math. 37, 211–230 (2000)

    Article  Google Scholar 

  16. Nazargah M.L., Shariyat M., Behesti-Aval S.B.: A refined high-order global-local theory for finite element bending and vibration analyses of laminated composite beams. Acta Mech. 217, 219–242 (2011)

    Article  MATH  Google Scholar 

  17. Topal U., Uzman U.: Thermal buckling load optimization of angle-ply laminated cylindrical shells. Mater. Design 30, 532–536 (2009)

    Article  Google Scholar 

  18. Viswanathan K.K., Navaneethakrishnan P.V.: Free vibration study of layered cylindrical shells by collocation with splines. J. Sound Vib. 260, 807–827 (2003)

    Article  Google Scholar 

  19. Viswanathan K.K., Kim K.S., Lee J.H., Lee C.H., Lee J.B.: Axisymmetric vibrations of layered cylindrical shells of variable thickness using spline function approximation. Struct. Eng. Mech. 28, 749–765 (2008)

    Google Scholar 

  20. Viswanathan K.K., Lee S.K.: Free vibration of laminated cross-ply plates including shear deformation by spline method. Int. J. Mech. Sci. 49, 352–363 (2007)

    Article  Google Scholar 

  21. Viswanathan K.K., Kim K.S.: Free vibration of anti symmetric angle-ply laminated plates including shear deformation: spline method. Int. J. Mech. Sci. 50, 1476–1485 (2008)

    Article  Google Scholar 

  22. Takahashi S., Suzuki K., Kosawada T., Anzai E.: Vibration of cylindrical shells with variable thickness. Bull. Jpn. Soc. Mech. Eng. 24, 1826–1836 (1981)

    Google Scholar 

  23. Sivadas K.R., Ganesan N.: Free vibration of circular cylindrical shells with axially varying thickness. J. Sound Vib. 147, 73–85 (1991)

    Article  Google Scholar 

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Author notes

  1. K. K. Viswanathan

    Present address: Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia

Authors and Affiliations

  1. Department of Naval Architecture and Ocean Engineering, Inha University, #253, Yonghyun dong, Nam ku, Inchon, 402-751, South Korea

    K. K. Viswanathan & Jang Hyun Lee

  2. Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia

    Zainal Abdul Aziz

  3. Department of Physics, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia

    I. Hossain

Authors
  1. K. K. Viswanathan
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  2. Jang Hyun Lee
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  3. Zainal Abdul Aziz
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  4. I. Hossain
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Correspondence to K. K. Viswanathan.

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Viswanathan, K.K., Lee, J.H., Aziz, Z.A. et al. Free vibration of symmetric angle-ply laminated cylindrical shells of variable thickness. Acta Mech 221, 309–319 (2011). https://doi.org/10.1007/s00707-011-0505-z

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  • DOI: https://doi.org/10.1007/s00707-011-0505-z

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