Optimization of TMDs for multimode vortex-induced vibration control of flexible structures with closely spaced modes

Previous research on optimizing tuned mass dampers (TMDs) for vortex-induced vibration (VIV) control has generally assumed that VIV is governed by a single mode. For structures that may exhibit VIVs across multiple modes, a separate TMD can be designed for each mode based on this assumption. However, in structures with closely spaced modes, the VIV response within the lock-in range of a specific mode can be influenced by both the dominant mode and other secondary modes due to TMD attachments, making the single-mode assumption inaccurate and the TMDs designed based on this assumption ineffective. This study provides a comprehensive investigation into the modal coupling phenomenon in the VIV responses of flexible structures with TMD attachments. The equations of motion for a general flexible structure-TMDs system are established, accounting for both the resonant mode and non-resonant secondary modes of the primary structure. It is demonstrated that TMD attachments can induce modal coupling in the VIV responses of various structures. The strength of these modal coupling effects is significantly influenced by the proximity of the frequencies of adjacent modes and the mass of the TMDs. A decoupling criterion is derived, demonstrating that modal coupling can be mitigated by appropriately positioning the TMDs. A novel procedure is proposed for determining TMD parameters for multimode VIV control in flexible structures with closely spaced modes, which ensures that each TMD primarily affects its target mode by strategically placing the TMDs, thereby minimizing the modal coupling effects resulting from their installation.