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On one approach to studying free vibrations of cylindrical shells of variable thickness in the circumferential direction within a refined statement

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We used the spline collocation method for finding the frequencies of free vibrations of circular closed cylindrical shells of variable thickness in the circumferential direction. The problem was formulated within the framework of Mindlin’s refined theory. We studied the influence of change in the shell thickness on the distribution of its natural frequencies. Our calculations were carried out for different geometrical parameters of the shell and different boundary conditions. The validity of results obtained was verified by increasing the number of collocation points in our calculations and by comparing them with the results of computations according to the three-dimensional theory.

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Authors and Affiliations

  1. Timoshenko Institute of Mechanics, Ukrainian National Academy of Sciences, Kiev, Ukraine

    A. Ya. Grigorenko & T. L. Efimova

  2. Kiev National University of Construction and Architecture, Kiev, Ukraine

    L. V. Sokolova

Authors
  1. A. Ya. Grigorenko
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  2. T. L. Efimova
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  3. L. V. Sokolova
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 52, No. 3, pp. 103–115, July–September, 2009.

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Grigorenko, A.Y., Efimova, T.L. & Sokolova, L.V. On one approach to studying free vibrations of cylindrical shells of variable thickness in the circumferential direction within a refined statement. J Math Sci 171, 548–563 (2010). https://doi.org/10.1007/s10958-010-0156-y

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  • DOI: https://doi.org/10.1007/s10958-010-0156-y

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