Damage identification in plate-like structures using bending moment response power spectral density

In this article, a new damage-sensitive parameter based on bending moment response power spectral density (MSD) is presented for damage identification in two-dimensional plate-like structures. The total energy or the average output power under the bending MSD graph quantified by the zero order moment of the response spectral density, known as mean square value (MSV), is implemented as a principal response parameter. Damage indices (DIs) derived from MSV, namely relative changes in MSV, mean square value curvature (MSVC), normalized damage index, and relative root mean square error (RRMSE) are then used to detect and localize structural damage. The effectiveness of this approach is illustrated by comparing the results with those obtained from existing and well-established techniques, namely relative changes in natural frequencies, modal flexibilities, uniform load surfaces, and changes in curvatures, such as mode shape curvatures, modal flexibility curvatures, and uniform load surface curvatures. The significant advantage of the proposed technique is that both input-output and output-only damage identification problems can be treated. For the latter condition, the only assumption made is that the forcing function is stationary, ergodic white noise. The methods are illustrated on a simply supported RC rectangular plate subjected to simulated damage cases. Artificial damage simulating local stiffness degradation is introduced to the plate in terms of the material modulus at selected locations in the finite element (FE) model. The modal properties obtained from FE-based modal analyses of this plate for different damage condition states are used to generate the bending moment frequency response functions and MSD at simulated measurement grid points. Subsequently, MSV is computed for undamaged and damaged states from which the appropriate damage indices are obtained. The DIs obtained using different algorithms are used to identify and localize both single and multiple damage conditions.