Passive and active vibration isolation systems using inerter

This paper presents a theoretical study on passive and active vibration isolation schemes using inerter elements in a two degree of freedom (DOF) mechanical system. The aim of the work is to discuss basic capabilities and limitations of the vibration control systems at hand using simple and physically transparent models. Broad frequency band dynamic excitation of the source DOF is assumed. The purpose of the isolator system is to prevent vibration transmission to the receiving DOF. The frequency averaged kinetic energy of the receiving mass is used as the metric for vibration isolation quality. It is shown that the use of inerter element in the passive vibration isolation scheme can enhance the isolation effect. In the active case, a feedback disturbance rejection scheme is considered. Here, the error signal is the receiving body absolute velocity which is directly fed to a reactive force actuator between the source and the receiving bodies. In such a scheme, the so-called subcritical vibration isolation problems exist. These problems are characterised by the uncoupled natural frequency of the receiving body larger than the uncoupled natural frequency of the source body. In subcritical vibration isolation problems, the performance of the active control is limited by poor stability margins. This is because the stable feedback gain is restricted in a narrow range between a minimum and a maximum. However, with the inclusion of an inerter in the isolator, one of the two stability margins can be opened. This enables large, theoretically unlimited negative feedback gains and large active damping of the receiving body vibration. A simple expression for the required inertance is derived.