\({\mathcal {H}}_{2}\) optimization and numerical study of inerter-based vibration isolation system helical spring fatigue life

This paper presents an optimization and numerical analysis of vibration-induced fatigue in a two degree-of-freedom inerter-based vibration isolation system. The system is comprised of a primary, e.g. source body, and a secondary, e.g. receiving body, mutually connected through an isolator. The isolator includes a spring, a dashpot and an inerter. Inerter is a mechanical device which produces a force proportional to relative acceleration between its terminals. A broadband frequency force excitation of the primary body is imposed throughout the study. The goal of the proposed optimization is to prolong the fatigue life of the ground connecting helical spring of the secondary body. The optimization is based on minimizing separately the displacement and velocity amplitudes. Both optimization criteria are compared with regard to spring fatigue life improvement for fair benchmark comparison. The inerter-based optimized systems, in which the \({\mathcal {H}}_{2}\) index of the receiving body is minimized, are also compared with the optimized systems without inerter. Notable improvements are observed in inerter-based systems due to the inclusion of an optimally tuned inerter in the isolator. The proposed analytical vibration fatigue method optimization results are compared with the finite element method results, and a very good agreement is observed. Most accurate helical spring deflection and stress correction factors are discussed and determined. Furthermore, the inerter concept is successfully implemented into finite element-based dynamic solution.