Optimal Placement and Design of Multi-Unit Passive Vibration Control Systems: TMD, TLCD, and STLCD Strategies for MDOF Structures

This doctoral thesis investigates multi-unit passive vibration control systems for multi-degree-of-freedom (MDOF) structures. A multi-unit configuration consists of control units distributed across the structural system and tuned to distinct vibration modes, so that the dynamic behavior of the structure is addressed through a coordinated and spatially distributed control action.Within this framework, the multi-unit concept is examined for the mass-based Tuned Mass Damper (TMD) and for liquid-based configurations, namely the Tuned Liquid Column Damper (TLCD) and the Sliding Tuned Liquid Column Damper (STLCD), the latter incorporating a sliding mechanism that broadens the applicability of liquid-based control in relatively stiff structures. The corresponding multi-unit control strategies, denoted as Multi-Tuned Mass Damper (M-TMD), Multi-Tuned Liquid Column Damper (M-TLCD), and Multi-Sliding Tuned Liquid Column Damper (M-STLCD), are established. The governing equations of the MDOF structure equipped with each configuration are formulated in compact block-matrix form. For the M-TLCD and M-STLCD configurations, this compact formulation retains the nonlinear damping behavior associated with the liquid motion in each unit.To address the expanded design space inherent to multi-unit configurations, the thesis proposes a sequential optimization procedure operating in a coupled time–frequency framework. At each stage, the procedure determines the optimal tuning parameters and floor allocation of a single unit with reference to the configuration resulting from the previously installed devices, while explicitly retaining the nonlinear liquid-related behavior in the case of M-TLCD and M-STLCD systems.The effectiveness of the proposed framework is assessed through comparative numerical analyses conducted on three- and six-story MDOF case-study structures under broadband and recorded seismic excitations, confirming the ability of the optimized multi-unit systems to engage the relevant vibration modes and to achieve spatially distributed mitigation effects.