Vol. 3, No. 7, 2008

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Vibrations of highly inhomogeneous shells of revolution under static loading

Elena Bespalova and Galina Urusova

Vol. 3 (2008), No. 7, 1299–1313

An approach to determining natural frequencies of middle-thickness inhomogeneous shells of revolution acted upon by static axisymmetrical loads is proposed. The approach is based on application of the nonclassic shell model that takes into account transverse shears and reduction across the wall thickness. In solving the problem posed, decomposition into two interconnected problems is used. The first problem is related to determination of the initial stress-strain state of shells under static axisymmetrical loads. The second problem is related to determination of natural frequencies of shells relative to this state that appears in the form of parametric terms. To solve the problems, the numerical-analytical technique developed by the authors is used. The efficiency of allowance for reduction across the wall thickness is illustrated on the example of an inhomogeneous middle-thickness cylindrical shell under local loads. Analysis of natural frequencies of the shell having the form of a pneumatic tire is presented depending on the value of internal pressure.

shells of revolution, inhomogeneity, preliminary stresses, natural frequencies, nonclassic model, numerical-analytical technique
Received: 4 February 2008
Revised: 11 July 2008
Accepted: 12 July 2008
Published: 1 September 2008
Elena Bespalova
Timoshenko Institute of Mechanics
National Academy of Sciences
3, Nesterov str.
Kiev 03057
Galina Urusova
Timoshenko Institute of Mechanics
National Academy of Sciences
3, Nesterov str.
Kiev 03057