Theoretical study and experimental verification of equivalent structural stiffness damage simulation using local added mass

This study clarifies the theoretical basis and applicability of using local added mass to simulate structural stiffness reduction. Starting from the characteristic equation of undamped free vibration, the contribution of local stiffness and mass modifications to the global eigenvalue problem is formulated explicitly, and the quantitative relationship between the stiffness-reduction coefficient and the equivalent added-mass increment coefficient is re-derived at the element level. An independent stiffness-reduction finite element model is introduced as a benchmark, followed by laboratory modal tests on a simply supported steel beam. The numerical comparison shows that the modal responses of the direct stiffness-reduction and equivalent added-mass models are nearly identical for the investigated cases. In the numerical-experimental comparison, the first natural frequency shows the closest agreement, with a maximum relative error of approximately 0.70%, while the corresponding MAC values remain above 0.97 for the first three modes. Larger discrepancies in higher-order frequencies are associated with their greater sensitivity to modelling and experimental uncertainties. The results demonstrate that distributed local added mass provides a nondestructive, controllable, and repeatable means of reproducing the principal dynamic effects associated with prescribed local stiffness reduction under the conditions considered in this study.