**6. Conclusions**

This study proposed a synthetic approach to design and implement 2DOFs TMDs for damping the bending and torsional modes of suspension bridges. For verifying the effectiveness of the concept model, we cast the parameter optimization of the 2DOFs TMDs conceptual model as a control problem with decentralized static output feedback for minimizing the response of the bridge deck. The optimized frequency ratios play a significant role in the TMD structural parameter design. For designing the expected modes of the 2DOFs TMDs, the graphical approach is introduced to arrange flexible beams properly according to the exact constraints. Based on the optimized frequency ratios, the dimensions of TMDs are determined by the compliance matrix method. The proposed design has been simulated and implemented successfully on a suspension bridge mock-up. Based on the presented results and interpretations, the main findings are summarized as follows:


**Author Contributions:** All authors discussed and agreed upon the idea and made scientific contributions. The original idea of the article was provided by F.M. and he also designed the methodology, realized its MATLAB program, and wrote the manuscript; J.W., Y.X. and Y.M. provided with the support of the entire study and revised the manuscript; J.Y. gave suggestions in the theoretical analyses and tests. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Science and Technology Research Project of State Grid (Research on Key Technologies for Improving Impact Resistance of Suspension Spanning Frame, Grant No. 5442GC180003).

**Acknowledgments:** The authors thank André Preumont of Active Structures Laboratory from Université Libre de Bruxelles, Brussels, Belgium for his kind guidance and suggestions in the whole research process; and thank the colleagues of FMRL lab from Beihang University, Beijing, China for the realization of the experimental set-up. The reviewers are very much acknowledged.

**Conflicts of Interest:** The authors declare no conflict of interest.
