The use of viscous dampers to mitigate cable vibrations on cable-stayed bridges is very popular. A viscous damper attached to a stay cable results in complex mode shapes. Such complexity could affect the dynamic stability of the cable under wind action, yet it is neglected in conventional galloping analysis. A general framework to investigate the problem of galloping of a stay cable with an attached viscous damper is therefore developed. Aerodynamic forces on the complex modes are considered, including aeroelastic coupling between the modes. A numerical example for an ice-accreted stay cable with a damper shows that conventional galloping analysis overestimates the critical wind speed for galloping occurrence. The complexity of the mode shapes gives rise to the cable being more unstable than ignoring it by treating the mode shapes as real.
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