CHANGES IN THE NATURAL FREQUENCIES OF REPEATED MODE PAIRS INDUCED BY CRACKS IN A VIBRATING RING

The presence of cracks in solid structures can be detected by measurin g changes in the natural frequencies of appropriate vibration modes. I n the present work a simple energy-based model of a vibrating ring is presented to estimate the effect of a crack on the frequencies of repe ated mode pairs. Introduction of a crack breaks the symmetry of the st ructure, causing the frequencies of the degenerate modes to split to a measurable extent. A simple expression is derived that relates the sp lit in frequency to the frequency of the modes in the un-cracked ring, the dimensions of the ring and the crack length. The treatment is ext ended to the case of a ring that is not perfectly symmetrical prior to the introduction of a crack. In the latter case, when the crack is sm all, the mode pairs have a preferred orientation determined by the ini tial asymmetry. As the crack grows the mode pairs rotate to become ali gned with the axis defining the location of the crack. (C) 1998 Academ ic Press.