Design of Single Degree-of-freedom Optimally Passive Vibration Isolation System

In this paper, a new design method for the system stiffness and damping coefficient of Single Degree-OfFreedom (SDOF) vibration isolation system is presented. By appropriately selecting the state variables and applying the optimal control theory to the corresponding active vibration isolation system, one could obtain the optimal control force, which is the linear combination of the relative displacement and relative velocity. Accordingly, the passive devices, e.g. a pair of re-selected spring and damper, could entirely replace the obtained optimal control force. The newly designed passive system is called as the optimally passive vibration isolation system. Compared with the original passive vibration isolation system and the corresponding semi-active on-off control system, the excellent performance of the optimally passive vibration isolation system are illustrated through some performance indices, such as the transmissibility, the effective values to sine excitation and random excitation.