Vibration and stability of a cracked translating beam

The vibration and stability characteristics of a cracked beam translating b etween fixed supports are investigated. Using Hamilton's principle and elem entary fracture mechanics, the equations of motion for the beam are develop ed. Throughout this analysis it is assumed that the crack is shallow and al ways remains open, i.e., crack closure and the associated impact conditions are not considered. In order to restrict attention to the open crack scena rio, parameter regimes corresponding to (1) a fully open crack, (2) a fully closed crack, and (3) a partly open-partly closed crack are clearly identi fied. For parameter values in regime (1), the free vibration characteristic s are studied via an eigenanalysis. This shows that the natural frequencies (Im(lambda)) and stability characteristics (Re(lambda)) fluctuate as the c rack translates along with the beam between the two supports. For the shall ow cracks being considered, the fluctuations are attributed primarily to th e localized drop in the mass per unit length (occurring at the crack) rathe r than from the increased flexibility. Furthermore, the magnitudes of these fluctuations are shown to vary with both the axial transport speed and the crack depth and are mapped in the control parameter space. Implications fo r the free and forced vibration problems are discussed. (C) 2000 Academic P ress.