Coupled vibration response of a shaft with a breathing crack

The accurate and detailed knowledge of the local flexibility which is introduced by a crack into a structure may be used in damage diagnosis. This paper investigates the variation of the local flexibility of cracked shafts under harmonic type of loadings causing tensional as well as compressional stresses around the crack faces in a periodic manner which inevitably lead to the opening and closure of the crack, i.e. the breathing mechanism. Time-dependent nonlinear finite element method (FEM) is adopted to analyze various crack sizes as well as time-dependent axial, bending and torsional types of loading. Special boundary conditions are adopted between crack faces to avoid penetration along the contact area and simultaneously permit the existence of stick or slip contact zones according to Coulomb׳s law. Deflection differences at the loaded edge between uncracked and cracked shaft are used for the computation of the local flexibilities. Apart from the computation of the diagonal terms of local flexibility matrix intensive emphasis is given to its off-diagonal coefficients which cause the coupling of motion between different degrees of freedom and thus may affect considerably the overall vibrational behavior of the shaft.