## 3 Overview on Antiresonance Assignment through the Active or Semi-Active Tuned Mass Dampers
### The Semi-Active Tuned Mass Damper  
Semi-active TMDs (SATMDs), as represented in Figure 5, have the distinctive feature that a variable stiffness (\(k_{sa}\)) or damper (\(c_{sa}\)) allows adapting the TMD properties to ensure a better tuning than passive TMDs. In the case of the simultaneous use of passive and active variable springs (obtained through the force exerted by an actuator), a small control effort is required whenever the passive part of the TMD is tuned to the frequency to be absorbed, while the active part is adopted to perform adaptation, increasing robustness or accomplishing secondary tasks to optimize performances. Adjustable dampers are also used in SATMDs by employing variable- orifice hydraulic dampers or dampers based on magnetorheological fluids. Just a small amount of energy is required to modulate the damping of such devices; therefore, lower power requirements with respect to ATMDs are required. This technique is very promising, especially in civil engineering applications, which is the field where SATMDs have found more use due to the lower-frequency contents of the excitations. In the seminal work [33], the SATMD is compared with the passive TMD and the ATMD, demonstrating the small amount of energy required to adapt damping while ensuring similar performances for the ATMD. Additionally, SATMDs offer reliability, robustness, and cost-effectiveness comparable to passive TMDs. The design of SATMDs, with time-varying damping, through the optimal control theory has been proposed in [34], and its actual effectiveness to reduce the steady-state response of a SDOF primary structure under harmonic excitation has been assessed. In [35], a magnetorheological damper is used to design a SATMD for a SDOF structure subject to seismic inputs. The magnetorheological SATMD outperforms the classical TMD in the seismic induced vibration suppression. Single and multiple SATMDs with variable stiffness are proposed in [36] for the control of SDOF and MDOF primary structures. The devices are effective when they have a low damping ratio and the excitation frequency can be tracked. Semiauctive vertical and pendulum TMDs have been proposed in [37], where the authors exploit a variable stiffness pendulum TMD based on the magnetic induction principle to tackle the frequency detuning that occurs due to the changes in the operating environment of the main structures that arise in long-term operations. A phase control algorithm for the SATMD is proposed in [38]. The idea is inspired by the power flow theory proposed in [39], i.e., the best performances of the TMD are achieved when it remains at a phase lag of \(-90^{\circ}\) to the structure. The algorithm proposed in [38] relies on detecting whenever the phase lag of the TMD is not equal to \(-90^{\circ}\) with respect to the structure and to brings it back through the application of a semi-active variable friction force that slows down the TMD mass block velocity. The effectiveness of the approach is validated through the simplified SDOF model of the Taipei 101 skyscraper. The performances of SATMD with varying damping for SDOF structures subject to various type of loads have been studied in [40], leading to significantly superior perfor  
Figure 5: Sketch of a SATMD. mances of the SATMD with respect to the passive TMD regardless of the type of excitations and providing also cost advantages over the ATMD [41]. SATMDs composed by magneto-sensitive rubber have been studied in [42; 43] for the vibration isolation of an infinite-dimensional flexible foundation subject to harmonic excitation varying in a prescribed frequency range. In [41], inspired by the idea of the fully-active virtual absorber (see Section 4.5) introduced in [44], a SATMD is designed by simultaneously exploiting a linear actuator in parallel with the spring of a passive undamped TMD. The idea is that the actuator sets a virtual TMD with programmable characteristic frequency in such a way that an antiresonance is assigned regardless of the precise knowledge of the dynamics of the primary structure.