Sokolova L. Solution the free vibration problems of circular cylindrical shells with variable thickness in refined formulation on the basis of spline-approximation.

Thesis is devoted to development of the effective approach to solving in refined formulation of the class of problems on the free vibrations of circular cylindrical shells with variable thickness by various conditions on the edges. The problems are described by the system of partial differential equations of 10th power with variable coefficients. The approach proposed is based on reduction of two-dimensional boundary-value problem to one-dimensional using the spline-collocation method along one coordinate. The one-dimensional eigenvalues problem obtained is solved by the stable numerical discrete orthogonalization method in combination with step-by-step search method. On the basis of the approach developed the computations of free vibrations of circular cylindrical shells with variable thickness by various conditions on the edges, depending on orthotropy of material, kind of geometry and variable thickness in one and both coordinate directions was carried out.