Abstract
We consider a mechanical system consisting of a circular cylindrical shell and an absolutely rigid body attached to one of the ends of the shell. Using the principle of possible displacements, we construct a mathematical model for the equilibrium state of the considered system under loads of general form. Using this model, we formulate an eigenvalue boundary-value problem that describes the free vibrations of the “shell-body” system and propose its approximate solution. In the case where the shell is replaced by an equivalent Timoshenko beam, we construct an exact solution of the problem under consideration. We also give an estimate for the effect of the rigid body on the vibrations of the system and investigate the accuracy of the beam approximation of flexural vibrations of the shell.
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Translated from Neliniini Kolyvannya, Vol. 7, No. 2, pp. 263–285, April–June, 2004.
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Trotsenko, V.A., Trotsenko, Y.V. Methods for calculation of free vibrations of a cylindrical shell with attached rigid body. Nonlinear Oscill 7, 262–284 (2004). https://doi.org/10.1007/s11072-005-0011-0
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DOI: https://doi.org/10.1007/s11072-005-0011-0