Performance evaluation for inerter-based dynamic vibration absorbers

• Six inerter-based dynamic vibration absorbers (IDVAs) are proposed.
• Both H-infinity and H2 performances are investigated.
• Adding an inerter alone to traditional DVA (TDVA) negligibly improves H2 performance.
• Adding an inerter alone to TDVA does not improve H-infinity performance.
• Adding an inerter and a spring to TDVA significantly improve the performances.

This paper is concerned with the H∞ and H2 optimization problem for inerter-based dynamic vibration absorbers (IDVAs). The proposed IDVAs are obtained by replacing the damper in the traditional dynamic vibration absorber (TDVA) with some inerter-based mechanical networks. It is demonstrated in this paper that adding one inerter alone to the TDVA provides no benefits for the H∞ performance and negligible improvement (less than 0.32% improvement over the TDVA when the mass ratio less than 1) for the H2 performance. This implies the necessity of introducing another degree of freedom (element) together with inerter to the TDVA. Therefore, four different IDVAs are proposed by adding an inerter together with a spring to the TDVA, and significant improvement for both the H∞ and H2 performances is obtained. Numerical simulations in dimensionless form show that more than 20% and 10% improvement can be obtained for the H∞ and H2 performances, respectively. Besides, for the H∞ performance, the effective frequency band can be further widened by using inerter.