Study on the structural damage detection method using the flexibility matrix

The flexibility matrix finds extensive application in detecting damage in civil and mechanical engineering structures, a focus explored in-depth within this paper. This study meticulously examines distinct components of the flexibility matrix, namely the proposed Diagonal of the Flexibility Matrix Vector (DFV) and a singular row/column of the flexibility matrix (RFV). Both DFV and RFV can be represented uniquely as a specialized form-a weighted combination of the Hadamard product of two mode shapes. Sensitivity analysis reveals that DFV undergoes a sharp change in proximity to damage, establishing it as a dependable indicator for pinpointing damage locations. Conversely, this characteristic is not consistently observed with RFV. The results of numerical simulations conducted on a 16-story frame structure corroborate the outcomes of the sensitivity analysis, underscoring the efficacy of DFV not only in localizing damage but also in gauging its severity. To illustrate the potential and limitations of DFV/RFV in practical scenarios, damage localization for the I-40 Bridge is provided.