Flutter control mechanisms of central buckles and cross slings for double-main-span suspension bridges in operation

With the increasing application of multi-main-span suspension bridge systems in long-span bridge engineering, flutter control in the completed operational state has become a critical aerodynamic concern. However, existing studies have predominantly focused on single-main-span suspension bridges or on the construction stages of multi-span systems, while the flutter mechanisms and control effectiveness of structural countermeasures in completed double-main-span suspension bridges (DMSBs) remain insufficiently understood. In particular, the aerodynamic control mechanisms of central buckles and cross slings under strong multimodal coupling conditions have not yet been clearly elucidated. To address these issues, this study investigates the flutter behavior and control mechanisms of a DMSB in its completed state using the Practical Modality-Driven Flutter Analysis (PMDFA) method, supported by full-bridge aeroelastic model tests. Two single-main-span suspension bridges (SMSBs) with different span lengths are additionally established for comparison, enabling a systematic examination of the distinctive modal characteristics and flutter mechanisms associated with multi-main-span configurations. The results indicate that the DMSB exhibits significantly more complex dynamic characteristics than SMSBs, with both an antisymmetric torsional mode (A-1-S-T) and a symmetric torsional mode (S-1-S-T) capable of governing flutter, accompanied by pronounced multimodal coupling. Since both dominant torsional modes deform symmetrically within each individual span, central buckles exert only a limited influence on modal properties and aerodynamic damping balance, resulting in negligible improvement in flutter performance. In contrast, cross slings induce a highly nonlinear evolution of structural dynamics and flutter behavior. As their installation position approaches the middle tower, stiffness redistribution and enhanced inter-span coupling lead to frequency inflection, modal competition, and the emergence of coupled torsional modes (Low/High A-1-S-T). This modal splitting causes a sharp deterioration in flutter performance and the formation of a low-performance plateau over a range of configurations. Overall, the flutter performance of the DMSB is predominantly governed by the A-1-S-T mode, while localized dominance of the S-1-S-T mode may occur near specific cross-sling configurations. An optimal cross-sling arrangement is identified near the middle region of the span, yielding an improvement of approximately 15.5% in the flutter critical wind speed compared with the original configuration. The findings reveal that flutter control in DMSBs is governed by modal symmetry, stiffness redistribution, and multimodal aerodynamic damping reallocation, rather than by isolated changes in individual modal frequencies. This study provides a mechanistic basis for the mechanism-driven design and optimization of flutter countermeasures in multi-main-span suspension bridges.