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In this paper, the dynamic stability of a rotating cantilever pipe conveying fluid with a crack and tip mass is investigated by numerical method. That is, the effects of the rotating the rotating angular velocity, the mass ratio, the crack and tip mass on the critical flow velocity for flutter instability of system are studied. The equations of motion of rotating pipe are derived by using the extended Hamilton's principle. The crack section of pipe is represented by a local flexibility matrix connecting two undamaged pipe segments. The crack is assumed to be in the first mode of fracture and always opened during the vibrations. Finally, the stability maps of the cracked rotating pipe system as a rotating angular velocity and mass ratio β are presented.

The dynamic stability and natural frequency of elastically restrained pipe conveying fluid with the attached mass and crack are investigated in this paper. The pipe system with a crack is modeled by using extended Hamilton's principle with consideration of bending energy. The crack on the pipe system is represented by a local flexibility matrix and two undamaged beam segments are connected. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. From the governing equations, the influence of attached mass, its position and crack on the dynamic stability of elastically restrained pipe system is presented. Also, the critical flow velocity for the flutter and divergence due to the variation in the position and stiffness of supported spring is studied. Finally, the critical flow velocities and stability maps of the cracked pipe conveying fluid with the attached mass are obtained by the changing parameters.