NATURAL VIBRATION ANALISIS OF CLAMPED ANNULAR ISOTROPIC SECTOR SHIP HULL PLATE USING EKM

چکیده

The natural vibrations of clamped annular isotropic sector plates are analyzed using the Extended Kantorovich Method (EKM). A conformal mapping is used to transform a sector with identified geometry to a rectangular plate which the solution is available in literature and solved by Dalaei and Kerr [1] using EKM. The developed iterative scheme converges very rapidly to the final result. The obtained natural frequencies are evaluated for annular sector plate and the obtained results are compared with those published by Leissa [6] and a simulation done by the finite element method (FEM). The agreement found to be very close. As there are no exact analytical solutions for clamped annular sector plates, the generated method for the natural modes, and the corresponding natural frequencies, are very suitable for use in engineering analysis.

کلیدواژه‌ها


عنوان مقاله [English]

NATURAL VIBRATION ANALISIS OF CLAMPED ANNULAR ISOTROPIC SECTOR SHIP HULL PLATE USING EKM

چکیده [English]

The natural vibrations of clamped annular isotropic sector plates are analyzed using the Extended Kantorovich Method (EKM). A conformal mapping is used to transform a sector with identified geometry to a rectangular plate which the solution is available in literature and solved by Dalaei and Kerr [1] using EKM. The developed iterative scheme converges very rapidly to the final result. The obtained natural frequencies are evaluated for annular sector plate and the obtained results are compared with those published by Leissa [6] and a simulation done by the finite element method (FEM). The agreement found to be very close. As there are no exact analytical solutions for clamped annular sector plates, the generated method for the natural modes, and the corresponding natural frequencies, are very suitable for use in engineering analysis.

کلیدواژه‌ها [English]

  • Annual Sector
  • Natural frequencies
  • EKM
  • Complex Mapping
 [1]         M. Dalaei, A. D Kerr, Natural vibration Analysis of Clamped rectangular Orthotropic Plates, Journal of Sound and Vibration (1996),189(3), 399-406

 [2]         R. Jones , B.J. Milne ,Application of the extended Kantorovich method to the vibration of clamped rectangular plates. Journal of Sound and Vibration 45 (1976), 309-316.

 [3]         A.D. Kerr, An extention of the Kantorovich method, Proc. 5th U.S.National Congress of Applied Mechanics 290, 1996.

 [4]         A. D. Keer, An Extension of the Kantorovich method, Quarterly of Applied Mathematic 26, 1968, pp. 219-229.

 [5]         A. D. Kerr, An Extended Kantorovich Method for the Solution of  Eigenvalue Problems, International Journal of Solids and Structures 5, 1969, pp. 559-572.

 [6]         A. W. Leissa, Vibration of Plates, National Aeronautics and Administration, 1969

 [7]         S. G. Lekhnitskkii, 1968 Anisotropic Plates.New York: Gorden and Breach.

 [8]         Brown, James Ward, Complex Variables and Applications, 7th Ed., McGraw-Hill Higher Edu., 2004.