Vibration Testing for Detecting Internal Corrosion∗ Habib Ammari

The vibration behavior of structures can be characterized in terms of resonance frequencies and mode shapes which describe properties of the tested object in a global way but do not in general provide information about structural details. Following an asymptotic formalism, in much the same spirit as the work in [3] and recent text [1], we develop a simple method to address the inverse problem of identifying an internal corrosive part of small Hausdorff measure in a pipeline by vibration analysis. The viability of our reconstruction method is documented by a variety of numerical results from synthetic, noiseless and noisy data.