Analytical study on the effects of flexural rigidity and negative stiffness in the optimal tuning of inerter-based damper for cable vibration mitigation

The control performances of inerter-based dampers on stay cables, usually governed by relevant damper parameters (such as inertance, stiffness, and damping coefficients), are sensitive to parameter variation around the optimal range. Further given these inerter-based dampers amplify the vibration amplitude at the damper location, the effects of cable’s flexural rigidity, which is often ignored in previous studies, are examined in this study. The results suggest an approximate 10% increase in all three design parameters (i.e., inertance, stiffness, and damping coefficients) is required to achieve optimal control compared with the case ignoring the flexural rigidity. In addition, the potential combination of inerter-based dampers with negative stiffness elements is also discussed in this study, which offers a more flexible layout and enhances multi-mode cable vibration control performance. Consequently, the tuning procedures are updated, and the revised optimal tuning formulas taking account of both the cable’s flexural rigidity and the introduction of negative stiffness are presented in this paper.