VIBRATIONAL RESPONSE OF A BEAM WITH A BREATHING CRACK

Abstract

Fatigue cracks often exist in structural members that are subjected to repeated loading, which will certainly lower the structural integrity. Many studies have been carried out on the dynamic response of fatigue cracks, in an attempt to nd viable vibration methods for non-destructive inspection and health monitoring. The crack models used in these analyses fall largely into two categories: (1) open crack models and (2) opening and closing or breathing crack models. Most researchers have used open crack models in their studies and have claimed that the change in natural frequency might be a parameter used to detect the presence of cracks [1}4]. However, the assumption that cracks are always open in vibration is not realistic because compressive loads may close the cracks. Recently, increasing e!orts have focused on vibration analysis using opening and closing models to simulate a fatigue crack, as in Crespo et al. [5] and Prime and Shevitz [6]. Their fatigue crack model considers the bilinear behavior of an elastic crack and ignores the crack surface interference during fatigue. In their model, the structure has only two characteristic sti!ness values: a larger value corresponding to the state of crack closing and a smaller value for crack opening. This fatigue crack model, however, only represents an idealized situation in which the crack has two perfectly #at surfaces and can only exist in the fully open or fully closed states. In reality, partial crack closure often occurs due to (1) roughness interference, (2) wedging by corrosion or wear debris, and (3) elastic constraint on the wake of the plastic zone. Therefore, the sti!ness of a structure containing a real fatigue crack may change continuously with time as the load oscillates. A more general approach, employing many terms of a Fourier series to simulate the continuous