Abstract
In this study, H∞ optimization is conducted for a tuned inerter damper (TID) with negative stiffness device (denoted as TID_NSD) subjected to harmonic support excitation. The study shows that there are still two nonzero-frequency fixed points independent of the damping of the TID_NSD; therefore, the optimum tuning frequency and damping ratio for the TID_NSD are, respectively, derived based on the well-known fixed points theory. By imposing the zero-frequency fixed point having the same amplitude as the other two nonzero-frequency fixed points, the optimum negative stiffness ratio, which makes the primary system with a TID_NSD remain stable, is obtained. Moreover, the role of a negative stiffness device of a TID_NSD system in response control of a single degree-of-freedom (SDOF) structure is evaluated through parametric study. Also, a numerical analysis is conducted on both a SDOF and multiple DOFs structure to validate the feasibility of the derived formulas by simulations with real earthquake records. Numerical results demonstrate that the maximum displacement and the maximum absolute acceleration of the structure equipped with TID_NSD system are reduced by increasing the absolute value of negative stiffness ratio. The results also show that the optimally designed TID_NSD system outperforms the optimally designed TID system in terms of the displacement and absolute acceleration mitigation control. The closed-form solutions proposed in this study can be useful for the optimal design of the structure equipped with TID_NSD.
Highlights
Kun Ye and Patrice NyangiH∞ optimization is conducted for a tuned inerter damper (TID) with negative stiffness device (denoted as TID_NSD) subjected to harmonic support excitation
E related results indicated that both a negative stiffness device and an inerter could efficiently decrease the H∞ norm
The time histories of the maximum displacement and absolute acceleration of the primary system are illustrated in Figure 5 when both the TID_NSD and the tuned inerter damper (TID) systems are subjected to a selected earthquake record (LA16). e succeeding parameters have been adopted in the numerical analysis: μ = 0.1, βopt = 1.41, λopt = 0.36, and θopt = − 0.71 for the TID_NSD system; μ = 0.1, βopt = 0.83, and λopt = 0.25 for the TID system
Summary
H∞ optimization is conducted for a tuned inerter damper (TID) with negative stiffness device (denoted as TID_NSD) subjected to harmonic support excitation. Numerical results demonstrate that the maximum displacement and the maximum absolute acceleration of the structure equipped with TID_NSD system are reduced by increasing the absolute value of negative stiffness ratio. Eir findings supported the reason why a TID is more commonly adopted in vibration control systems It can be noted from the above-reported research works that the use of inerter, negative stiffness device, or inerter and negative stiffness concurrently could improve the performance of DVAs. to the best of the authors’ knowledge, the optimal design and performance benefits of DVAs with a dual combination between inerter and negative stiffness device have not been widely investigated.
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