## 5 Results  
This section focuses on presenting the kinematics at the top of the building. We included the time series for the two orthogonal directions, for the displacement as well as the acceleration. These are the typical quantities of interest for the design. Baseline results characterize the motion of the structure under wind loading, without any AMD. The broad-band excitation is caused by naturally turbulent wind. For this, engineers typically consider a 10-minute time frame, as that is deemed statistically stationary and representative for relevant actions on structures [48]. The initial time phase of 45 s (as seen in Figure 10) represents the initiation phase, with these values being discarded for the quantitative evaluation. Specific metrics are evaluated and shown in Table 3. The along-wind response is comparable, with the TMD and TSD performing similarly, at approximately \begin{table}
\begin{tabular}{c l l l l} \hline \hline
**System** & **Property** & **Symbol** & **Unit** & **Weak Bending** & **Strong Bending** \\ \hline \multirow{8}{*}{**Structure**} & Height & \(H\) & [m] & 180 \\  & Width & \(W\) & [m] & 30 \\  & Depth & \(D\) & [m] & 45 \\  & Total mass & \(m\) & \(\times 10^{3}\) kg] & 39,875 \\  & Equivalent density & \(\rho\) & [kg/m\({}^{3}\)] & 164 \\  & Mode shape number & i & [\(-\)] & 1 2 \\  & Eigenfrequency & \(f\) & [Hz] & 0.20 & 0.23 \\  & Value of the mode shape at the AMD & \(\eta\) & [\(-\)] & 0.94 & 0.96 \\  & Generalized modal mass of the mode shape & \(m^{*}\) & [\(\times 10^{3}\) kg] & 10,144 & 12,698 \\  & Damping ratio & \(\zeta\) & [\%] & 1.00 & 1.00 \\  & Mass & \(m\) & [\(\times 10^{3}\) kg] & 180 \\  & Frequency & \(f\) & [Hz] & 0.20 & 0.23 \\  & Stiffness & \(k\) & [kg/s\({}^{2}\)] & 280,321 & 371,690 \\
**TMD**1,3 & Damping ratio & \(\zeta\) & [\%] & 7.61 & 6.96 \\  & Damping & \(c\) & [kg/s] & 34,215 & 36,031 \\  & Total mass ratio & \(\mu_{tot}\) & [\%] & 0.45 \\  & Modal mass ratio & \(\mu_{mod}\) & [\%] & 1.57 & 1.32 \\  & Length & \(L\) & [m] & 9.50 & 7.00 \\  & Width & \(W\) & [m] & 3.00 & 2.30 \\  & Resting water height & \(h_{0}\) & [m] & 1.57 & 1.12 \\  & Location of screens & \(x\) & [\(-\)] & \((0.4,0.6)L\) \\  & Solidity ratio of screens & \(S\) & [\(-\)] & 0.32 & 0.30 \\  & Mass per unit & \(m_{N}\) & [\(\times 10^{3}\) kg] & 45 & 18 \\
**TSD**1,4 & Number of TSD units & \(N\) & [\(-\)] & 4 & 10 \\  & Total mass & \(m_{uv}\) & [\(\times 10^{3}\) kg] & 180 \\  & Total mass ratio & \(\mu_{tot}\) & [\%] & 0.45 \\  & Modal mass ratio & \(\mu_{mod}\) & [\%] & 1.57 & 1.32 \\  & Effective mass per unit & \(m_{eff,N}\) & [\(\times 10^{3}\) kg] & 33 & 13 \\  & Effective mass & \(m_{eff}\) & [\(\times 10^{3}\) kg] & 135 \\  & Total mass ratio & \(\mu_{tot}\) & [\%] & 0.34 \\  & Modal mass ratio & \(\mu_{mod}\) & [\%] & 1.17 & 0.99 \\  & Damping ratio with screens & \(\zeta\) & [\%] & 5.59 & 4.88 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Setup of the interacting systems—tructure and AMDs—using the definitions based on the structure-attached coordinate system. \(\pm 5\,\%\) relative of each other. For the cross-wind direction, the TSD performs at around 25 % worse than a TMD under these settings. Both AMDs improve the structural response by mitigating deflections up to 50 %. We mention that such devices aim to perform well for excitation forces near the natural vibration of the underlying construction. However, this load case is broad-banded, so less efficiency is to be expected. Figure 10: Time series of the kinematics of the top point under turbulent wind loading. Time series are accompanied by a quantitative statistical evaluation. As an additional metric, we define a maximum value based upon derived quantities, instead of the sample maximum.