Abstract
This paper is concerned with the stability analysis and design of the n-DOF (n-degree-of-freedom) mass-chain vibration systems containing both semi-active and passive mechanical controllers. Based on Lyapunov's stability theory, sufficient conditions are derived for the n-DOF vibration system containing a semi-active switched inerter and a passive mechanical network with the first-order admittance to be globally asymptotically stable. Furthermore, the optimization designs of a quarter-car vibration control system and a three-storey building vibration system are conducted together with the derived stability results, and the instability cases contradicting the stability conditions are presented for illustration. The optimization and simulation results show that the combination of semi-active and passive mechanical controllers in vibration systems can clearly enhance system performances in comparison with the conventional semi-active or passive control. The novelty of this paper is that the stability problem of a general n-DOF vibration system that simultaneously contains a semi-active controller and a first-order passive controller is investigated for the first time, where such a system combines the advantages of both semi-active and passive mechanical controllers. The investigations and results can provide an essential foundation for further exploring the stability problems of more general systems, and can be applied to the controller designs of many vibration systems in practice.