Analysis and optimisation for inerter-based isolators via fixed-point theory and algebraic solution

This paper is concerned with the problem of analysis and optimisation of the inerter-based isolators based on a “uni-axial” single-degree-of-freedom isolation system. In the first part, in order to gain an in-depth understanding of inerter from the prospective of vibration, the frequency responses of both parallel-connected and series-connected inerters are analysed. In the second part, three other inerter-based isolators are introduced and the tuning procedures in both the H∞ optimisation and the H2 optimisation are proposed in an analytical manner. The achieved H2 and H∞ performance of the inerter-based isolators is superior to that achieved by the traditional dynamic vibration absorber (DVA) when the same inertance-to-mass (or mass) ratio is considered. Moreover, the inerter-based isolators have two unique properties, which are more attractive than the traditional DVA: first, the inertance-to-mass ratio of the inerter-based isolators can easily be larger than the mass ratio of the traditional DVA without increasing the physical mass of the whole system; second, there is no need to mount an additional mass on the object to be isolated.