Evolution of Natural Frequencies of Longitudinal Vibrations of a Bar as Its Cross-Section Defect Increases

Abstract

We study the evolution of characteristics of natural longitudinal vibrations of a circular bar in the case of increasing defect in its cross-section. It is shown that, in the limit case where the defect separates the bar into two independent fragments, the natural frequencies of the initially defect-free bar pass into the natural frequencies of its separate parts. The respective evolution of the natural modes of vibrations is observed. The evolution predicted by the theoretical analysis can be observed experimentally by using the resonance method and constantly increasing the defect till the final separation of the bar into two parts.