Flutter Instability of Cracked Rotating Non-Uniform Beams Subjected to Distributed Follower Force

In this paper, the effect of an open edge crack on the instability of rotating non-uniform beams subjected to uniform distributed tangential compressive load is studied. The local stiffness due to the presence of crack is considered in the global stiffness matrix of the structure using the finite element method. The cracked beam element is modeled as two equal sub-beam elements connected by a massless rotational spring. Based on the fracture mechanics, the strain energy release rate and the stress intensity factors are employed to investigate the stiffness of the rotational spring. Then, the modified shape functions are developed to reflect the crack stiffness in the finite element analysis. To validate the accuracy of the finite element model and results obtained, comparisons have been made between the results obtained and those available in the literature. The effects of several parameters, including the linear and nonlinear thickness variations, angular velocity, crack location and size, on the instability of cracked rotating non-uniform cantilevers are also examined. The results show that the location of crack significantly influences the critical magnitude of the follower force that destabilizes the cantilevers. In addition, geometric non-uniformity reduces the stability of the cracked cantilevers. For the same amount of cantilever mass, different patterns of mass distribution result in different stability diagrams.