New Mathematical Model for Coupled Vibration Analysis of High-Rise Buildings via Aeroelastic Wind Tunnel Testing

High-rise buildings with closely spaced translational natural frequencies in orthogonal directions are susceptible to modal coupling. This study established a theoretical framework for wind-induced coupled vibration of high-rise buildings by introducing an equivalent trajectory rotation mechanism. By modeling the rotation of the instantaneous motion direction in the horizontal plane, new coupled equations of motion are derived, in which the coupling arises naturally from the Coriolis-type inertial forces associated with the trajectory rotation rate. This formulation provides a clear physical interpretation of modal interaction and reveals the intrinsic source of energy transfer between along-wind and across-wind responses. Based on the proposed theory, a mathematical model for characterizing the coupling effect and a corresponding decoupling strategy were developed. To validate the model, wind tunnel tests were performed on a multi-degree-of-freedom (MDOF) aeroelastic model exhibiting pronounced coupling and a two-degree-of-freedom (2DOF) reference model without any coupling. The experimental results demonstrate that the MDOF model exhibits bidirectional energy transfer, multi-peak spectral characteristics, and trajectory rotation, all of which are accurately reproduced by the proposed theoretical model. Moreover, the decoupled responses obtained from the MDOF model exhibited a strong agreement with the normalized responses of the 2DOF model, confirming the effectiveness of the proposed decoupling strategy. Collectively, the theoretical derivation, physical interpretation, and experimental validation form a comprehensive framework for understanding, modeling, and separating coupled wind-induced vibrations in high-rise buildings, offering new insights into structural analysis, wind-resistant design, and system identification.