On the Interval Frequency Response of Cracked Beams with Uncertain Damage

This chapter addresses the frequency response of damaged beams in presence of cracks characterized by interval uncertainty, setting a correspondence between two alternative models for describing the cracks. The presence of cracks is one of the most important causes of accidents and failures in structures. The chapter provides the dynamic response in the frequency domain of a multi-cracked beam where the crack depth is assumed as an interval variable and the crack is described following both the finite element model and the continuous one. In the continuous beam model, the presence of an open crack results in a discontinuity in the slope of the beam deflection. The chapter also provides interval analytical solutions to the forced vibrations of cracked Euler–Bernoulli beams. A correspondence between the crack depth and the spring stiffness has been presented in terms of respective bounds evaluating the interval compliance function.