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Application of a combined Galerkin-averaging method

Part 3 Research Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 985)

Abstract

As an introduction to the combined Galerkin-averaging method we present an application. This application establishes a long-time prediction for the dynamic torsional behaviour of a thin-walled bar which has two axes of symmetry for each cross-section.

As a result we find an approximation which differs only slightly from the solution of the linearized problem.

Keywords

  • Oscillation Mode
  • Neumann Problem
  • Torsional Vibration
  • Nonlinear Partial Differential Equation
  • Free Undamped Vibration

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. BOLOTIN, W.W., Kinetische Stabilität Endlicher Verschiebungen, VEB Deutscher Verlag der Wissenschaften, Berlin, 1961.

    MATH  Google Scholar 

  2. SCHMIDT, G., Parameterregte Schwingungen, Springer Verlag, Berlin, 1974.

    Google Scholar 

  3. KAPPUS, R., Zur Elasticitätstheorie Endlicher Verschiebungen, Z. Angew. Math. Mech., 19, I. Teil 271–285, II. Teil 344–361, 1939.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. STRAUSS, W.A., On continuity of Functions with values in various Banach Spaces, Pac. J. Math., 19, 1966.

    Google Scholar 

  5. RAFEL, G.G., Asymptotic Solutions for a Class of Nonlinear Vibration Problems, Thesis Mathematisch Instituut, Rijksuniversiteit Utrecht, The Netherlands, 1982.

    Google Scholar 

  6. BESJES, I., On the Asymptotic Methods for Nonlinear Differential Equations, J. de Mécanique, 8, 1969.

    Google Scholar 

  7. KELLER, I.B. & M. MILLMAN, Perturbation theory of Nonlinear Boundary Value Problems, J. Math. Physics 10, 1969.

    Google Scholar 

  8. KELLER, I.B. & L.U. TING, Periodic Vibrations of Systems governed by Nonlinear Partial Differential Equations, Comm. Pure and Appl. Math. 12, 1966.

    Google Scholar 

  9. RAFEL, G.G., An Internal Resonance Problem for a Compressed Column, to appear in Int. J. Nonl. Mechanics.

    Google Scholar 

  10. VERHULST, F., Discrete Symmetric Dynamical Systems at the main Resonances with Applications to axi-symmetric Galaxies, Phil. Transact. Royal Soc. 290, 435–465, London, 1979.

    CrossRef  MATH  Google Scholar 

  11. VAN DER BURGH, A.H.P., Studies in the Asymptotic Theory of Nonlinear Resonance, Thesis Delft, Techn. Univ., Delft, The Netherlands, 1974; for a short account see J. Sound and Vibr. 49, 1976.

    Google Scholar 

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© 1983 Springer-Verlag

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Rafel, G.G. (1983). Application of a combined Galerkin-averaging method. In: Verhulst, F. (eds) Asymptotic Analysis II —. Lecture Notes in Mathematics, vol 985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062376

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  • DOI: https://doi.org/10.1007/BFb0062376

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12286-9

  • Online ISBN: 978-3-540-39612-3

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