Innovative negative-stiffness inerter-based mechanical networks

This paper presents the optimal design for novel negative-stiffness non-traditional inerter-based dynamic vibration absorbers called NS-NIDVAs. The underlying idea of negative-stiffness inerter-based mechanical networks (NS-IMNs) was inspired by the negative-stiffness technology concept. Firstly, the non-dimensional mathematical models for NS-NIDVAs are established considering the harmonic force excitation case, and then the dimensionless frequency response functions of the primary structure are computed for optimization purposes. Therefore, a dynamic stability analysis was conducted in order to determine the allowable boundary on negative stiffness variable. Moreover, the Extended Fixed Points Technique (EFPT) has been proposed as an optimal calibration procedure taking in account the undamped system case. In order to ensure a trade-off among the invariant points of the primary structure's FRFs, a constraint equation was added to the EFPT's optimality approach. It was proved that the allowable negative stiffness solution computed by the constraint equation is in accordance with that provided by the Routh-Hurwitz stability criterion. The short optimal explicit functions revealed that the NSNIDVA-C4 has a similar optimal tuning magnitude as the NS-NIDVA-C6 and C3, with the devices providing the same dynamic performance. In view of this dynamic characteristic, the H infinity performance measure is computed for both NS-NIDVAs devices considering a practical application mass ratio range. When the NS-NIDVA-C4's performance is compared to the other passive high-performance devices, an improvement of more than 50% in DMF reduction is obtained. Additionally, the NS-NIDVA-C4 can broaden the effective operating bandwidth from 46% to 82% when compared to the classic DVA. Therefore, it has been proved that NS-NIDVA-C4 has the versatility of yielding high-performance with a small physical mass of the DVA, which is the significant finding of this work.