Resettable-inertance inerter: A semiactive control device for energy absorption

Semiactive control systems are based on formerly passive mechanical devices whose characteristics are adjusted in real time by active means. They can be classified into variable-damping dampers, variable-stiffness springs, and variable-inertance inerters. Similarly to the case of variable-stiffness, two possibilities are devised for inerters: independently-variable inertance, where inertance can increase or decrease continuously at any instant of time, and resettable-inertance, where it can increase only at instants where relative velocity is zero. By duality with resettable-stiffness springs, a resettable-inertance inerter (RII) is composed of an inerter that can suddenly be disconnected from the vibrating system and blocked in order to eliminate kinetic energy. Studies on independently-variable inertance have been carried out recently, but there are still no studies on resettable inertance. This paper presents an analytical numerical study on RII, for an energy-based control law, through the mathematical model of a mechanical implementation. By simulation of a numerical example that considers a SDOF system with three different devices, the performance is demonstrated for energy absorption and vibration reduction. Moreover, closed-form expressions for the equivalent-linear inertance, stiffness, and damping are found for the resettable devices and validated through the numerical example. Main conclusion is that RII adds equivalent damping without dynamically stiffening the structure. Besides, the absorbed energy can be dissipated and/or harvested in time intervals in which the RII is uncoupled from the structure.