Nonlinear Oscillations

, Volume 8, Issue 3, pp 414–429 | Cite as

Solution of a Problem of Free Vibrations of a Nonclosed Shell of Revolution under Conditions of its Singular Perturbation

  • V. A. Trotsenko
  • Yu. V. Trotsenko


We develop a variational method for solving the spectral problem of free vibrations of a shell of revolution nonclosed in the meridional direction. This method is equally efficient for both medium and small values of the relative thickness of the shell. Coordinate systems of functions are constructed with regard for the structure of formal asymptotic expansions of a fundamental system of solutions of the initial equations. As an example, we calculate frequencies and forms of vibrations of a circular cylindrical shell and show that the algorithm proposed for solving the considered problem guarantees the uniform convergence of solutions and their first three derivatives in the entire region of integration of the equations.


Differential Equation Coordinate System Partial Differential Equation Ordinary Differential Equation Functional Equation 
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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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • V. A. Trotsenko
    • 1
  • Yu. V. Trotsenko
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKievUkraine

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