###### Abstract
The extension of passive solid and liquid dampers to adaptive and active vibration dampers has also been extensively investigated scientifically and is partly applied in practice [21; 22; 23]. In the case of liquid dampers, the apparent low density of the moving damper mass (e.g., water \(\rho=1000\) kg/m\({}^{3}\)) compared to conventional solid dampers (e.g., steel \(\rho=7850\) kg/m\({}^{3}\)) results in a considerable disadvantage in terms of the space required at the installation site of the damper. For example, a 5 MW offshore wind turbine with a 112 m steel tube length has a diameter of 5.5 m at the tower head [24]. The total vibrating mass of such a wind turbine is approx. 560 tons and it consists of the head mass (nacelle, hub, and rotor blades) with approx. 435 tons and the kinetically equivalent tower mass with approx. 125 tons. If the ratio of the damper mass to the vibrating mass of the main system is 5%, which is common in the design of vibration absorber systems, the required damper mass results in 28 tonnes, which corresponds in the case of a fluid damper to approx. 28 m\({}^{3}\) of horizontally moving (active) fluid mass. To achieve the desired bidirectional vibration damper effect, at least two liquid dampers must be installed in the two possible vibration directions, resulting in a total space requirement of 56 m\({}^{3}\) at the tower head of a wind turbine. Assuming an available tower diameter of 5.5 m, the total floor space is just 23.76 m\({}^{2}\) and the horizontal section of the liquid dampers would have to be at least 2.36 m high. Thus, it is evident that even if liquid dampers offer several advantages compared to solid dampers, their application to real structures often fails because of the limited available installation space in the case of vibration-prone slender high-rise structures such as, e.g., wind turbines. Compared to liquid dampers, the installation space required for the moving mass of pendulum dampers is, in principle, significantly smaller due to the raw density of steel. However, the very low fundamental natural frequency in the range of approx. 0.20 Hz usually found in on- and offshore wind turbines requires a very large pendulum length of approx. 6.21 m. Hence, the space gained by the small steel pendulum mass compared to the fluid mass of liquid dampers is compensated by the very long pendulum lengths. The optimal tuning of vibration absorbers is, in the first step, performed to a single selected resonant frequency of the main system by applying the optimization equations according to [PERSON] [4]. The two optimization parameters (natural frequency and damping) of the vibration damper result solely from the selected mass ratio \(\mu=m_{A}/m_{H}\) (active damper mass \(m_{A}\) to the kinetically equivalent mass of the main system in the considered vibration mode). As an example: With a resonance frequency of the forced-excited main system of \(f_{H}=1\) Hz and \(\mu=0.05\), the optimum natural frequency of the damper results in \(f_{A,opt}=0.95\) Hz, and the optimum Lehr damping ratio to \(\zeta_{A,opt}=13\%\). Once the damper is optimally tuned, vibration reductions of up to 95% can be achieved over the entire frequency range of interest. However, in the case of coupled vibration modes (not well separated) and tuning of multiple dampers to a single selected vibration mode, a state space optimization method is preferably applied to determine the optimal absorber parameters [14; 15]. Lately, newer types of solid-body vibration absorbers, with ball or cylinder-shaped damper masses, have been investigated in quite a bit of detail. They consist of a cylindrical- or spherical-shaped container which allows a rolling movement of the damper mass. The combination of the cylinder-shaped mass and container can be described as a tuned solid roll damper (TSRD) which is used for unidirectional vibration damping.