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On The Application Of Constant Deflection Contour Method To Non-Linear Vibration Analysis Of Elastic Plates And Shells

  • M. M. Banerjee*Email author
Chapter
Part of the Springer Proceedings in Physics book series (SPPHY, volume 126)

The present paper aims at establishing the validity of the constant deflection contour (CDC) method to the nonlinear analysis of plates of arbitrary shapes vibrating at large amplitude. It begins with a review of the basic ideas developed earlier by the present author. The deduction of the governing differential equations have been established. The author has made an attempt here to develop the concept of constant deflection contour method and specifically to make its introduction into the nonlinear analysis of plates. A combination of the constant deflection contour method and the Galerkin procedure has been employed for solution. The numerical results obtained for the illustrative problems are in excellent agreement with those of available studies. Application of the present analysis to structures with complicated geometry has also been attempted in this paper. It has been demonstrated that this method provides a powerful tool to tackle problems involving structures with uncommon boundaries. The comparison of the present results with others strongly supports this. The analysis carried out in this paper may readily be applied to other geometrical structures and as a byproduct the static deflection is also obtainable.

Keywords

constant deflection contours iso-deflection curves contour integration and Green's function 

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References

  1. 1.
    G. Herrmann, 1955. Influence of the large amplitude on flexural motion of elastic plates, NASA Tech. Note 3578.Google Scholar
  2. 2.
    H. N. Chu and G. Herrmann, 1956. Influence of large amplitude on free flexural vibrations of rectangular elastic plates, J. Appl. Mech. 23, 532– 540.zbMATHMathSciNetGoogle Scholar
  3. 3.
    N. Yamaki, 1961. Influence of large amplitude on flexural vibrations of elastic plates, ZAMM, 41, 501– 510.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    H. M. Berger, 1955. A new approach to the analysis of large deflections of plates, J. Appl. Mech., 22, 465– 472.zbMATHMathSciNetGoogle Scholar
  5. 5.
    G. C. Sinharay and B. Banerjee, 1985. Large amplitude free vibrations of shallow spherical shell and cylindrical shell A new approach, Intl. J. Nonlinear Mech., 20, 69– 78.zbMATHCrossRefGoogle Scholar
  6. 6.
    J. Nowinski and H. Ohanabe, 1972. On certain inconsistencies in Berger equations for large deflections of plastic plates, Intl. J. Mech. Sci., 14, 165– 170.zbMATHCrossRefGoogle Scholar
  7. 7.
    M. M. Banerjee, P. Biswas and S. Sikder, 1993. Temperature effect on the dynamic response of spherical shells, SMIRT-12 Trans., Vol. B, Paper No. B06/3, 159– 163.Google Scholar
  8. 8.
    M. M. Banerjee, 1997. A new approach to the nonlinear vibration analysis of plates and shells, Trans. 14th Intl. Conf. On Struc. Mech. In Reactor Tech., (SMIRT-13), (Lyon, France) Divn. B, Paper No. 247.Google Scholar
  9. 9.
    J. Mazumdar, 1970. A method for solving problems of elastic plates of arbitrary shapes, J. Aust. Math. Soc., 11, 95– 112.zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    J. Mazumdar, 1971. Buckling of elastic plates by the method of constant deflection lines, J. Aust. Math. Soc., 13, 91– 103.CrossRefGoogle Scholar
  11. 11.
    R. Jones and J. Mazumdar, 1997. Transverse vibration of shallow shells by the method of constant deflection contours, J. Accoust. Soc. Am., 56, 1487– 1492.CrossRefGoogle Scholar
  12. 12.
    D. Bucco and J. Mazumdar, 1979. Vibration analysis of plates of arbitrary shape A new approach, J. Sound Vib., 67, 253– 262.zbMATHCrossRefADSGoogle Scholar
  13. 13.
    J. Mazumdar and D. Bucco, 1978. Transverse vibrations of visco-elastic shallow shells, J. Sound Vib., 57, 323– 331.zbMATHCrossRefADSGoogle Scholar
  14. 14.
    M. M. Banerjee and G. A. Rogerson, 2002. An application of the constant contour deflection method to non-linear vibration. Archive of Applied Mechanics. 72, 279– 292.zbMATHCrossRefGoogle Scholar
  15. 15.
    S. P. Timoshenko and S. Woinowisky-Krieger, 1959. Theory of plates and shells, 2nd Edn., McGraw-Hill, New York.Google Scholar
  16. 16.
    S. Way, 1934. Bending of circular plates with large deflection, Trans. ASME, 56, 627– 636.Google Scholar
  17. 17.
    G. Anderson, B. M. Irons and O. C. Zienkiwicz, 1978. Vibration and stability of plates using finite elements, Intl. J. Solids and Struc., 4, 1031– 1055.CrossRefGoogle Scholar
  18. 18.
    M. M. Banerjee, S. Chanda, J. Mazundar and B. Pincombe, 2000. On the free vibration of elastic-plastic shells, Proc. Fourth Biennial Engg. Maths. and Applications Conf. RMIT University, Melbourne, Australia, 10– 13 September, 59– 62.Google Scholar
  19. 19.
    J. Mazumdar and R. K. Jain, 1989. Elastic-plastic analysis of plates of arbitrary shape—A new approach, Int. Jl. of Plasticity, 5, 463– 475.zbMATHCrossRefGoogle Scholar
  20. 20.
    R. Jones and J. Mazumdar, 1974. Transverse vibration of elastic plates by the method of Constant Deflection Line, Journal of the Acoustical Society of America, 56, 1487– 1492.zbMATHCrossRefADSGoogle Scholar

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