Abstract:
A technique, inspired by Skudrzyk's mean value theory, for determining the severity of single cracks in uniform beams having arbitrary intermediate and boundary conditions is presented. It is based on a weighted average of eigenfrequency shifts of higher-order modes---modes 2 and higher---and does not require knowledge of the details of the structure. Starting from an analysis of a uniform beam with a midspan crack, a closed-form expression---valid for all ranges of crack compliance--- for the eigenfrequency shifts of higher-order modes was obtained. It was shown that the mode averaged eigenfrequency shifts for arbitrarily located cracks on uniform beams are given by this same analytical expression and are, hence, independent of crack location. Finally, Skudrzyk's mean value theory was invoked to extend this approach to truly complex beam assemblies. It was shown that the mode averaged response of complex beams is reasonably close to that of their equivalent simple structures thereby making the use of deterministic models in determining the magnitude of cracks unnecessary. [Work supported by ONR.]