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Vibrations of cylindrical shells with circumferential cracks

An approximate method for the vibration analysis of stepped shells accounting for the influence of cracks located at re-entrant corners of steps is presented. Introducing the additional compliance function it is shown that the flexibility of the shell near cracks can be prescribed by means of the compliance of the structure. The latter is coupled with the stress intensity factor, which is known from the linear elastic fracture mechanics. Theoretical analysis is developed for circular cylindrical shells, provided the shell wall has an arbitrary number of steps and circular cracks of constant depth. Various combinations of end conditions are considered.