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Numerical and Asymptotic Modeling of Annular Plate Vibrations

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Book cover Numerical Analysis and Its Applications (NAA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8236))

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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.

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References

  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)

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  2. Ascher, U.M., Mattheij, R., Russell, R.: Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, 2nd edn. SIAM, Philadelphia (1995)

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  3. Filippov, S.B.: Optimal design of stiffened cylindrical shells based on an asymptotic approach. Technische Mechanik 24, 221–230 (2004)

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Author information

Authors and Affiliations

  1. Mathematics and Mechanics Faculty, St. Petersburg State University, Universitetsky Prospekt, 28, 198504, St. Petersburg, Russia

    Sergei Filippov & Mikhail Kolyada

Authors
  1. Sergei Filippov
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  2. Mikhail Kolyada
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Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technlogies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl25A, 1113, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Pázm\’{a}ny P\’{e}ter s\’{e}t\’{a}ny 1/C,, Eötvös Loránd University, 1117, Budapest, Hungary

    István Faragó

  3. University of Rousse, 8 Studentska Str.,, 7017, Rousse, Bulgaria

    Lubin Vulkov

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Filippov, S., Kolyada, M. (2013). Numerical and Asymptotic Modeling of Annular Plate Vibrations. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_32

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  • DOI: https://doi.org/10.1007/978-3-642-41515-9_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41514-2

  • Online ISBN: 978-3-642-41515-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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