Vibration analysis for isolation system with inerter

Fundamental analysis of vibration system with inerter is carried out in this paper based on a "uni-axial" single-degree-of-freedom isolation system. The condition that force and displacement transmissibilities are identical is derived for all passive isolators composed of springs, dampers and inerters. Specifically, the inerter in parallel connection and the one in series connection are analyzed in terms of the invariant points and isolating bandwidth of the considered transmissibilities. It is analytically demonstrated that both the parallel-connected and the series-connected inerters can effectively lower the invariant points and enlarge the isolating bandwidth. It is also shown that the series-connected inerter can depict some mixed-behaviours between the configuration with only a spring and the configuration with a parallel connection of a spring and an inerter, due to its inherent property of the physical structure. The weakness of isolation at high frequency caused by inerter is also analytically demonstrated.