Analytical research on the dynamic performance of semi-active inerter-based vibration isolator with acceleration-velocity-based control strategy

A semi-active inerter-based vibration isolator with semi-active inerter is presented in this paper; the inertance of the semi-active inerter is hierarchically adjusted between two values: the maximum inertance and minimum inertance. On the basis of the mechanical property of the semi-active inerter, two acceleration-velocity-based control strategies are proposed, which are the relative-acceleration-relative-velocity (RARV) control strategy and the relative-acceleration-absolute-velocity (RAAV) control strategy. The dynamic responses of the semi-active inerter-based vibration isolator with the two control strategies are obtained using the averaging method and further checked by the numerical results. Four performance indices are defined to evaluate the isolation performance of the semi-active inerter-based vibration isolator: maximum dynamic displacement, maximum transmissibility, isolation frequency band, and transmissibility in the higher isolation frequency band. The solving process to determine the four performance indices is investigated in detail in the paper. The results show that for the semi-active inerter-based vibration isolator, the maximum dynamic displacement and transmissibility are smaller than the passive one; the latter two performance indices fall in between the value when the maximum inertance and minimum inertance are achieved for the passive one. In addition, the isolation performance of the semi-active inerter-based vibration isolator with the two control strategies are compared based on the four performance indices.