A uniqueness result on crack location in vibrating rods

Abstract

The inverse problem of locating a single crack in an elastic beam in axial vibration from the knowledge of spectral data is considered. By modeling the crack with a local compliance, the diagnostic problem becomes a inverse eigenvalue problem with discontinuity. It is found that knowledge of the highest part of the spectrum suffices to determine uniquely the position of the crack. The uniqueness result comes essentially from the fact that the spectrum of the cracked rod separates in to two asymptotic classes which depend on the location of the damage. A series of dynamic tests performed on two steel rods with a crack of different depth showed that the expected asymptotic separation of the spectrum can be detected and measured experimentally for relatively low frequency in the case of rather severe levels of damage.

Keywords:

• Detection of cracks
• axially vibrating beams
• inverse eigenvalue problems with discontinuities

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Notes

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