Vibration analysis of a cracked rotating tapered beam using the p-version finite element method

Vibration characteristics of cracked rotating tapered beam are investigated by the p-version finite element method. In the present formulation, the shape functions enriched with the shifted Legendre orthogonal polynomials are employed to represent the transverse displacement field within the rotating tapered beam element. The crack element stiffness matrix and the p-version finite element model of the structural system are obtained by using fracture mechanics and the Lagrange equation, respectively. The common integral terms appeared in the rotating tapered beam element matrices are derived in analytical forms so as to speed up the generation of these matrices during the implementation of the present method. Comparisons have been made for several configurations between results obtained by the present method with those available in literature, and the proposed method shows excellent accuracy and convergence. The effects of crack location, crack size, rotating speed and hub radius on vibration characteristics of a cracked rotating tapered beam are investigated. The mode shapes of the cracked rotating tapered beam are also obtained and analyzed with the spatial wavelet transform approach to detect the slight perturbation at the crack position. The present method is of general applicability and can be applied to investigate vibration of arbitrarily continuous non-uniform rotating beams.