With the use of the 3D theory of elasticity, we investigate the problem of free torsional vibrations of an anisotropic hollow cylinder with different boundary conditions at its end faces. We have proposed a numerical-analytic approach for the solution of this problem. The original partial differential equations of the theory of elasticity with the use of spline approximation and collocation are reduced to an eigenvalue problem for a system of ordinary differential equations of high order in the radial coordinate. This system is solved by the stable numerical method of discrete orthogonalization together with the method of step-by-step search. We also present numerical results for the case of orthotropic and inhomogeneous material of the cylinder for some kinds of boundary conditions.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 52, No. 1, pp. 92–100, January–March, 2009.
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Efimova, T.L. Solution of problems of free torsional vibrations of thick-walled orthotropic inhomogeneous cylinders. J Math Sci 168, 613–623 (2010). https://doi.org/10.1007/s10958-010-0012-0
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DOI: https://doi.org/10.1007/s10958-010-0012-0