## 5 Simulation Results and Discussion  
Four structural configurations consisting of passive, semi-active, hybrid active and semi-active hybrid control devices were considered for investigating the efficacy of the SHMD device for the vibration control of high-rise structures. Figure 12 summarises the peak and rms (displacement and acceleration) responses at every floor. The results of the evaluation for the different performance criteria \(J_{1},J_{2},..,J_{12}\) are presented in Figure 13.  
The results indicate that, for approximately the same damper strokes, the SHMD-equipped structure is able to achieve similar performance as the ATMD-equipped one, while clearly outperforming the passive and semi-actively controlled alternative. With reference to Figures 13 and 14, it is evident that the SHMD device requires much less energy and actuation demands for achieving the aforementioned performance increase. As a matter of fact, the SHMD device requires approximately 26% of the total energy required by the ATMD device (1245 kJ compared to 4863 kJ). This is due to the large control effort and consequently the large amount of energy required to be added by the active actuators (approximately 4125 kJ or 82% of the total required active energy) in order to effectively accelerate the mass so that sufficient control force is provided in order to overcome the \"braking\" force acted by the passive component of the ATMD. Conversely, in the SHMD configuration, while the actuators are accelerating the mass, the semi-active damping component attains its minimum value, minimising the \"braking\" force needed to be counteracted by the actuators, thus requiring a lower control power (Figure 14b top). The energy required to be added in the SHMD configured structure is only 1245 kJ compared to 4125 kJ (which accounts for the 82% of the total energy required) (Figure 14). On the other hand, for energy dissipation purposes (Figure 14a,b bottom), the ATMD configuration is required to supply only a fraction (737 kJ and the remaining 18% of the total energy) of energy, while the SHMD-equipped structure requires consumption of a staggering 4600 kJ. However, since energy dissipation in the SHMD configuration occurs exclusively in the semi-active elements,  
Figure 12: Illustration of the performance of different control measures in terms of (**a**) RMS acceleration; (**b**) RMS displacement; (**c**) absolute acceleration; and (**d**) absolute displacement at different floor levels. Figure 13: (**a**) Normalised; and (**b**) non-normalised performance indices (lower index indicates better performance). the required energy depends solely on the selected semi-active device. Still, regardless of the device, the energy required for semi-active control is not expected to exceed the order of a few watts [32]. For more tolerant damper stroke limits, a lower passive damping ratio can be chosen for the ATMD which will reasonably lower the actuation demands for energy addition. On the contrary, lower damping ratios of the damping device will require the actuators to work harder in dissipating energy by decelerating the mass (and essentially work as an energy-expensive passive damper). The aforementioned arguments are illustrated in Figure 15, in which the power required by a purely active AMD device (i.e., absence of passive damping component) is investigated. As can be observed, the AMD is required to expend most of its energy for dissipation (4500 kJ as opposed to the 720 kJ required by the ATMD counterpart), while only a small fraction of that energy is required for energy addition (approximately 1100 kJ). It should be clarified that no further comparisons can be made with the purely active AMD system, as its performance is theoretically uncapped (the larger the control effort, the lower the response). Figure 14: Power and its time integral (dotted line) energy for (**a**) ATMD; and (**b**) SHMD configuration. Positive stands for energy addition and negative for energy dissipation.