4.3.1. Viscous Damper

First, the motion-based design of the viscous damper under uncertainty conditions was performed. The design problem of this viscous damper may be formulated as follows:

$$\begin{aligned} \text{find } \boldsymbol{\Theta} &= c\_{d,v} \text{ to minimize } f(\boldsymbol{\Theta}) = c\_{d,v} \\ \text{subject to} & \begin{cases} c\_{\min} < c\_{d,v} < c\_{\max} \\ \beta\_s(\boldsymbol{\Theta}) \ge \beta\_t = 1.35. \end{cases} \end{aligned} \tag{21}$$

As result of the optimization process, the damping coe fficient, *cd*,*v*, was obtained. The optimum value obtained was *cd*,*<sup>v</sup>* = 1.06 × 10<sup>5</sup> sN/m. The reliability index for this solution was, β*s*(θ) = 1.37, which met the design requirements. Figure 6 shows the maximum displacement at the mid-span of the cable damped by the viscous damper for the di fferent elements of the sample.

**Figure 6.** Maximum displacement at the mid-span of the stay cable damped by the viscous damper for the di fferent elements of the sample.
