Numerical Solution of the Problem on Free Axisymmetrical Oscillations of a Hollow Ortotropic Cylinder under Various Adjustment Of End-Faces

摘要

Problem on natural oscillations of anisotropic hollow cylinder under various boundary conditions of its end-faces is considered on the basis of spatial theory of elasticity a numerical- analytical approach to the study of the formulated problem has been proposed. The original partial equations of the theory of elasticity, using the finite-differenca approximation on the radial coordinate, are reduced to the problem for eigen values for the systems of ordinary differential equations of high order. The problem is decided by the steady-state numerical method of discrete orthogonalization parallel with the method of the step-by-step search. The calculation results are presented for the case of ortotropic material of the cylinder for different kinds of boundary conditions on its end-faces.