Optimization of a vibration isolator containing an inerter-like element

This study investigates the performance of a group of vibration isolators which are variants of systems existing in the literature. The isolators in question are meant to isolate systems/structures from dynamic support/base motion. The isolators consist of inertia elements, springs and dashpots (dampers) and differ among themselves in the number of springs and dashpots. The idea for the isolators studied was derived from inerter, which is a two-terminal inertia element put forward fairly recently. The isolation systems under study here have only one terminal but the arragement of inertia elements resembles those of an inerter. The isolators studied here are called inerter-like because of the difference in the number of terminals. The performance metric for a vibration isolator is the transmissibility of base displacement to the system to be protected from vibration. The objective of the study is to minimize transmissibility for all isolator configurations, seven in total, in the group and to determine the best configuration among all, for operation in a given frequency band. Minimization of transmissibility was carried out with MATLAB optimization tools, fMincone and the genetic algorithm. Constraints were prescribed for the values of modal damping ratios and for static compression (or tension, depending on the case) of the springs under the weight of the main mass. Several isolator configurations successfully reduced transmissibility values below 20% at all frequencies within a band while complying with all the constraints. It was shown that inerter systems, being systems with multiple degrees of freedom, reduce transmissibility values more successfully compared to systems with a single degree of freedom, namely, systems with a single spring and a damper.