Abstract:

An approximate 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 sum over 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 is obtained. This result is used to derive an expression, consisting of a weighted sum of eigenfrequency shifts over a fixed frequency band, that is independent of structural details that are further than half a wavelength away from crack. This sum is valid for arbitrarily located cracks on uniform beams and, if evaluated over an appropriate band, is shown to be independent of boundary conditions and beam length. Finally, Skudrzyk's mean value theory is invoked to extend this approach to truly complex beam assemblies. Analytical predictions agree well with computational results. [Work supported by ONR.]