Free vibrations of thick layered cylindrical shells

Two approaches to the calculation of closed thick layered cylindrical shells are developed. They are based on division of the cylindrical shell across its thickness by concentric circumferential surfaces into a series of constituent cylindrical shells. Satisfying the contact conditions on the surfaces between constituent shells, it is possible to determine the frequency of free bending vibrations of the initial shell with a sufficient accuracy. In the first approach, the distribution of unknown functions across the shell thickness is sought on the basis of an analytical solution to the corresponding system of differential equations; in the second one, the distribution is assigned by polynomial approximation functions.