Fixed-Point Optimization of a Network of Active Tuned Inerter Dampers for Multimodal Vibration Suppression

Many engineering structures exhibit multiple vibration modes that require simultaneous attenuation, whereas conventional single-mode tuning strategies may lose effectiveness because of modal coupling and competing mode-wise design requirements. This article proposes a multimodal vibration suppression framework based on a network of active tuned inerter dampers (ATIDs) implemented through a collocated actuator–sensor pair. Each resonator in the ATID network is assigned to a target mode, and a sequential fixed-point tuning procedure is derived to determine the corresponding controller parameters. An equivalent mechanical model is also established, showing that the controller can be interpreted as a network of springs, dashpots, and inerters, which provides physical insight into its stability mechanism. Numerical simulations and experiments on a two-degree-of-freedom structure demonstrate that the proposed method can effectively suppress multiple resonances while allowing the attenuation level of each mode to be adjusted through the associated resonator gain.