## 5 Conclusions  
This paper introduced a novel single tube semi-active tuned liquid gas damper (SATLGD) for suppressing horizontal vibrations of tower-like structures. The special feature of the presented SA-TLGD is its lack of any vertical tube sections, which lead to a great advantage regarding the required installation space in slender vibration-prone structures, e.g., wind turbines. The horizontal orientated single tube is partially filled with a fluid and sealed at both ends. A large deformable elastic membrane with neglectable stiffness is used as the interface between fluid and air, and the resulting gas spring provides the restoring force and frequency tuning parameter, respectively. The equations of motion were derived for both a SDOF-main system with a single SA-TLGD and a MDOF-main system with multiple SA-TLGDs attached. Modal tuning of the single SA-TLGD attached to a SDOF-main system was presented by the application of [PERSON]'s formulas considering a harmonic force and seismic excitation. Optimal tuning of multiple SA-TLGDs attached to a MDOF-main system was achieved by minimizing the frequency domain-based quadratic performance index in state space representation. It was shown that the adjustment of the SA-TLGDs vibration frequency is simply achieved by separating the bulk gas volume \(V_{0}\) at the left and right tube sections into a series of gas chambers \(V_{0i}\) all connected via controllable valves. Depending on the desired optimal vibrating frequency a specific size of gas volume is initiated through the utilized control software, which opens or closes the appropriate number of valves. In addition, the magnitude of the fluid damping is properly adjusted by varying the diameter of several controllable orifices that are built into the fluid stream. The achievable damping effectiveness of the introduced SA-TLGDs were evaluated considering two different application examples. The first example was a SDOF-wind turbine with a single optimally tuned SA-TLGD attached. In this example, the vibration absorber was optimally tuned to the most critical fundamental mode of the force excited SDOF-main system and a frequency shift of \(\pm 5\%\) of the main systems' fundamental frequency was assumed. The mass ratio was chosen with \(\mu=1\%\). It was shown that the achievable reduction in the maximum tower head displacement resulted as almost \(70\%\) and that the assumed light structural damping ratio of \(\zeta_{S,eff}=4.9\%\) could be increased to the effective damping ratio of \(\zeta_{S,eff}=4.9\%\) by the installed optimally tuned SA-TLGD. To avoid detuning due to the assumed frequency shift the SA-TLGD was equipped with a total of three gas volumes \(V_{01}\), \(V_{02}\), and \(V_{03}\) at each side of the sealed tube and optimal tuning was achieved by setting the appropriate size of the gas volume via controllable valves. The second example was a scaled MDOF-shear frame structure with two optimally tuned SA-TLGDs in parallel connection installed on the top floor of the structure. The mass ratio was chosen with \(\mu=4\%\) (includes the total fluid mass of both installed SA-TLGDs). The two vibration absorbers were tuned to the most critical fundamental vibration mode of the MDOF-main system, and it was shown that a vibration reduction in the maximum horizontal 3 rd floor displacement of almost \(90\%\) could be achieved. The assumed light structural damping ratio of \(\zeta_{S1}=1\%\) of the fundamental mode could be increased to the effective damping ratio \(\zeta_{S1,eff}=8.6\%\) by the installed optimally tuned SA-TLGDs. It is concluded that the presented SA-TLGDs achieve a high reduction in the maximum force vibration amplitudes of tower-like structures and that its semi-active functionality enables the possibility of re-adjustment any time during the operation of the damper. Hence, SA-TLGDs can best account for the expected frequency shifts that occur in real structures and, thus, provide the favored optimal performance over the total operation life of vibration-prone structures.