Damage localization in ambient vibration by constructing proportional flexibility matrix

Damage localization approaches based on changes of flexibility constitute an important technique for damage detection. Construction of flexibility matrix with output-only data is still unfathomed, and this makes flexibility-based approaches not applicable in ambient vibration. An algorithm is presented to construct a Proportional Flexibility Matrix (PFM) from a set of arbitrarily-scaled modal shapes and modal frequencies. By scaling and redistributing the mass of real structure, a dummy structure is obtained. The ratios among the modal masses of the real and dummy structures can be deduced, and then the PFM is constructed. PFMs for the pre-damaged and post-damaged structure are employed to do damage localization by the Damage Locating Vector (DLV) method. To make the two flexibilities comparable, a normalization scheme of mass matrix is presented. A numerical example shows that a small number of measured modes can produce PFMs with sufficient accuracy to correctly locate the damage employing the DLV method.