Stiffness Shaping for Zero Vibration Fluidic Flexible Matrix Composites

This paper studies semi-active vibration control using Fluidic Flexible Matrix Composites (F²MC) as variable stiffness structures. The apparent stiffness of F²MC tubes can be changed using a variable orifice valve. With fiber reinforcement, the volume inside the tube may change with external load. With an open valve, the liquid is free to move in or out of the tube, so the apparent stiffness will not changed. When the valve is closed, the high bulk modulus liquid is confined, which resists the volume change and causes the apparent stiffness of the tube to increase. The equations of motion of an F²MC-mass system is derived using a 3D elasticity model and the energy method. A reduced order model is then developed for fully-open or fully-closed valves. A Skyhook valve that cycles the valve between open and closed, asymptotically decays the vibration. A Zero Vibration (ZV) Stiffness Shaping technique is introduced to suppress the vibration in finite time. A sensitivity analysis of the ZV Stiffness Shaper studies the robustness to parameteric uncertainties.