Hybrid analytical H-norm optimization approach for dynamic vibration absorbers

Conventionally, single-targeted H∞ or H2 optimization methods are adopted to determine the optimal parameters of different Dynamic Vibration Absorbers (DVAs) individually. A generic analytical framework for various DVAs considering a dual-target of H∞ and H2 norms is lacking. Addressing these issues, a hybrid analytical H∞-H2 optimization approach is proposed, leading to closed-form optimal solutions characterized by equal-height fixed points and conditional minimum H2-norms, combining the advantages of H∞ and H2 solutions. The proposed method is completely based on arbitrary filter coefficients of the targeted transfer function. Therefore, it can be generically applied for various DVAs. With the proposed method, the analytical optimal parameters of Negative-Stiffness Inerter-based Tuned Mass Systems (NS-ITMSs) are obtained based on an extended generic representation model considering multiple parameters. In extension, the method is illustratively applied on three complicated DVAs, including a Lever-type Inerter-based Vibration Absorber with Negative Stiffness (NS-LIVA) considering a leverage effect, a Piezoelectric Shunt Damping System (PSDS) considering an electro-mechanical coupling effect, and a Negative-Stiffness Tuned Viscous Mass Damper (NS-TVMD) for vibration isolator considering a transmissibility target. The closed-form solutions for these advanced DVAs are obtained for engineering reference. Furthermore, this method can be extended for more complicated energy dissipation or harvesting techniques.