Hybrid Analytical Optimal Approach and Comparative Analyses for Tuned Viscous Mass Damper with Negative Stiffness (TVMDNS)

Tuned viscous mass damper with negative stiffness (TVMDNS) has higher damping efficiency and broadband characteristics for vibration control by utilizing dual benefits of the inerter and negative stiffness. And single-performance H_∞ or H₂ optimal methods are adopted to determine the optimal parameters of TVMDNS individually. However, the vibration mitigation performance of the TVMDNS under high-frequency or resonance excitation based on H_∞ optimization is lesser than H₂ optimization, and quasi-static or low-frequency displacement response based on H₂ optimization will be greater than H_∞ optimization. An analytical strategy considering a dual-performance of H_∞ and H₂ norms is lacking at present.

For this reason, closed-form expressions are derived for the control of structural displacement responses based on hybrid H₂/H_∞ optimal approach. The vibration mitigation performance of the TVMDNS is evaluated considering harmonic, stochastic, and impulsive excitation using different optimal methods.

The initial static responses and ultra-low-frequency in hybrid H₂/H_∞ optimal methods are between H₂ and H_∞ optimal design, and the high-frequency and resonance dynamic responses are also between those, which indicates an excellent and balanced control performance combining the advantages of H₂ and H_∞ solutions. And the global vibration control can be achieved by this dual-performance-based optimal strategy.

When designing the specific TVMDNS, hybrid H₂/H_∞ optimal design can be considered as the best choice for its compatibility and high adaptability for complex stochastic excitation. Furthermore, this approach can be extended for various topology connection forms of inerter and negative stiffness system for energy dissipation or vibration control.