The problem of free vibrations of a solid cylinder with different boundary conditions is solved using the three-dimensional theory of elasticity and a numerical analytic approach. The spline-approximation and collocation methods are used to reduce the partial differential equations of elasticity to systems of ordinary differential equations of high order with respect to the radial coordinate. These equations are solved by stable numerical discrete orthogonalization and incremental search. Calculated results are presented for transversely isotropic and inhomogeneous materials of the cylinder and for several types of boundary conditions at its ends
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Translated from Prikladnaya Mekhanika, Vol. 46, No. 5, pp. 10–20, May 2010.
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Grigorenko, A.Y., Efimova, T.L. Free axisymmetric vibrations of solid cylinders: numerical problem solving. Int Appl Mech 46, 499–508 (2010). https://doi.org/10.1007/s10778-010-0334-0
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DOI: https://doi.org/10.1007/s10778-010-0334-0