Modal Identification of a Superimposed Structure: The Crossing of the Mosque–Cathedral of Córdoba

The Gothic–Renaissance crossing of the Mosque–Cathedral of Córdoba constitutes one of the most structurally complex sectors of the monument owing to the coexistence of Islamic and Christian construction systems developed over several centuries. Accurately reproducing the mechanical interaction between these successive construction phases remains a major challenge in the numerical assessment of historically superimposed heritage structures. This study presents the first three-dimensional finite element (FE) model of the crossing, explicitly representing the interfaces between the Gothic–Renaissance intervention and the surrounding Islamic structure through frictional contact elements implemented in OpenSees 3.7.2. The model incorporates the principal structural components of the crossing, including the masonry walls and piers, ribbed vaults, dome, buttresses and adjacent Islamic arcades. Mesh and material sensitivity analyses were performed to quantify the influence of the principal modelling parameters on the predicted dynamic response and to establish an efficient and reliable numerical model. The results showed that the first three natural frequencies vary by less than 0.7% with mesh refinement, whereas ±10% variations in density or Young’s modulus modify the predicted frequencies by approximately 5% without altering the modal hierarchy. The first three vibration modes correspond to two dominant translational modes (2.01 Hz and 2.52 Hz) followed by a torsional mode (3.14 Hz), demonstrating that the crossing and the surrounding Islamic structure behave as a single integrated structural system rather than as independent construction phases. Higher vibration modes reveal localized deformation mechanisms concentrated in the buttresses, whose modal behavior is consistent with the historical strengthening interventions that modified their stiffness.