Dynamic stability of a cracked pipe conveying fluid and resting on a Pasternak elastic foundation

Pipeline transport is used worldwide in many sectors of the economy. Its main advantages are continuity of transport, large transportation volumes, small energy consumption, safety, reliability and high environmental benefits. However, the safety problems of pipes attract much interest in science and industry. This paper deals with a cracked pipe with a static scheme of a simply supported beam. It rests along its entire length on a Pasternak elastic foundation. The flowing fluid is considered non-compressible and heavy. The Galerkin method is employed to approach the problem numerically. Conclusions are drawn based on the influence of the crack and the parameters of the Pasternak elastic foundation on the critical flow velocity of the fluid.