The Effects of Fatigue Cracks on Free Torsional Vibration of Shafts Free

The effect of a single-edge fatigue crack on the torsional vibration of shafts is investigated. A generalized variational principle is used to formulate the equation of motion and associated boundary conditions for the free vibration of a nonrotating shaft with a fatigue crack of arbitrary size and location. The fatigue crack is introduced in the form of a single-edge crack. The stress and strain of the cracked shaft are determined by introducing a crack function and a displacement function into the shaft’s compatibility relations. The crack function is designed to have the maximum value at the cracked section and decay exponentially away from the crack along the shaft’s longitudinal direction. A displacement function is constructed to modify the in-plane displacement and its slope near the single-edge crack. The natural response of the free-free shaft is calculated through a Galerkin procedure. The results indicated a clear change in the natural frequencies of the cracked nonrotating shaft.