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Numerical and Asymptotic Modeling of Annular Plate Vibrations

  • Sergei Filippov
  • Mikhail Kolyada
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8236)

Abstract

Free axisymmetric flexural vibrations of an annular elastic thin plate are studied. Numerical solutions of eigenvalue problem for various boundary conditions are obtained. The plate can be used as a model of the supporting frame of a shell. In this connection the boundary conditions corresponding the attaching of the plate to a cylindrical shell are also considered. The plate is called narrow if the ratio of its width to the radius of the inner edge is small. For the vibrations analysis of a narrow plate new asymptotic methods are elaborated. Comparison asymptotic and numerical results shows, that the error of the approximate formulae quickly decreases with reduction of the plate width.

Keywords

Free vibrations Annular thin plate Eigenvalue problems Numerical solution Asymptotic approach 

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References

  1. 1.
    Wang, C.Y., Wang, C.M., Chen, W.Q.: Exact closed form solutions for free vibration of non-uniform annular plates. The IES Journal Part A: Civil & Structural Engineering 24, 50–55 (2012)CrossRefGoogle Scholar
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    Ascher, U.M., Mattheij, R., Russell, R.: Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, 2nd edn. SIAM, Philadelphia (1995)CrossRefzbMATHGoogle Scholar
  3. 3.
    Filippov, S.B.: Optimal design of stiffened cylindrical shells based on an asymptotic approach. Technische Mechanik 24, 221–230 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sergei Filippov
    • 1
  • Mikhail Kolyada
    • 1
  1. 1.Mathematics and Mechanics FacultySt. Petersburg State UniversitySt. PetersburgRussia

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