DYNAMIC RESPONSE OF A BEAM WITH A CRACK SUBJECT TO A MOVING MASS

An iterative modal analysis approach is developed to determine the effect of transverse cracks on the dynamic behavior of simply supported undamped Bernoulli-Euler beams subject to a moving mass. The presence of crack results in higher deflections and alters the beam response patterns. In particular, the largest deflection in the beam for a given speed takes longer to build up, and a discontinuity appears in the slope of the beam deflected shape at the crack location. Crack effects become more noticeable as crack depth increases. The effect of the inertia force due to the moving mass is, in general, qualitatively similar and additive to the effect of the crack. The exact effect of crack and mass depends on the speed, time, crack size, crack location, and the moving mass level. Other approximate methods, namely a stationary mass model and a single iteration technique, are also evaluated. The stationary mass approach is useful for light moving masses (<20% of beam mass) and cracks at mid-span. For other cases, the errors can be unacceptably large. The results of the single-iteration approximation are quite close to the iterative modal analysis approach, which indicates that this approximate solution is an excellent tool for the analysis of the moving mass problem.