Non-axisymmetric vibrations of stepped cylindrical shells

Vibrations of stepped circular cylindrical shells with cracks are studied. The shell under consideration is sub-divided into multiple segments separated by the locations of thickness variations. It is assumed that at the boundary of these segments circumferential surface cracks with are located. The influence of circular cracks with constant depth on the vibration of the shell is prescribed with the aid of a matrix of local flexibility. The latter is related to the coefficient of the stress intensity known in the linear fracture mechanics. Numerical results are obtained for various crack models including those, where the shell with a crack is simulated geometrically as a two-stepped shell with small length of the intermediate section. Shells with various combinations of boundary conditions can be analyzed by the proposed method. The influences of the shell thicknesses, locations of step-wise variations of the thickness and other parameters on the natural frequencies are examined. The results can be used for the approximate evaluation of dynamic parameters of simply supported or clamped cylindrical shells with cracks and flaws.