Григоренко А.Я., Ефимова Т.Л. «Об одном подходе к решению задачи о свободных колебаниях сплошного неоднородного цилиндра конечной длины» Доповiдi нацiональноi академii наук Украiни, № 9, с. 67-72 (2009)

A problem on natural vibrations of a solid cylinder under various boundary conditions of its end-faces is considered on the basis of 3D elasticity theory. Using the spline-approximation and collocation, the original partial equations of elasticity theory are reduced to the problem for eigenvalues for the high-order systems of ordinary differential equations by the radial coordinate. The problems are solved by the steady-state numerical method of discrete orthogonalization with incremental search. The calculation results are presented for the case of an isotropic inhomogeneous cylinder for different boundary conditions on its end-faces.