Longitudinal vibrations of a cross-cracked cantilever beam. Part 1. Small vibrations

Based on the analysis of solutions to differential equations of longitudinal vibrations of a macroelastic body whose nonlinearity is due to "breathing" of the damaged material under tension-compression cycling, we estimate the suitability of the deformation-cycle characteristic of a body under free and forced vibrations for the diagnostics of fatigue damage in structural elements. We consider the following problems: the construction of a simplified model of longitudinal vibrations of mechanical elements with cross cracks, the investigation of free vibrations of a cracked body including resistance forces, the forced vibrations of a cracked body taking into account a perturbation force including and excluding resistance forces, and the study of vibrations of a beam with resistance different from the linear one. We show that the presence of a macrocrack is responsible for the occurrence of representative higher harmonics in the deformation-cycle spectrum. They can serve as a sensitive and efficient vibration-diagnostic parameter to detect cracks in structural elements. © 1999 Kluwer Academic/Plenum Publishers.