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)


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.


Free vibrations Annular thin plate Eigenvalue problems Numerical solution Asymptotic approach 


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© 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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