Passive and Switched Stiffness Vibration Controllers Using Fluidic Flexible Matrix Composites

This paper investigates passive and semi-active vibration control using fluidic flexible matrix composites $(F2MC)$⁠. $F2MC$ tubes filled with fluid and connected to an accumulator through a fixed orifice can provide damping forces in response to axial strain. If the orifice is actively controlled, the stiffness of $F2MC$ tubes can be dynamically switched from soft to stiff by opening and closing an on/off valve. Fiber reinforcement of the $F2MC$ tube kinematically relates the internal volume to axial strain. With an open valve, the fluid in the tube is free to move in or out of the tube, so the stiffness is low. With a closed valve, however, the high bulk modulus fluid resists volume change and produces high axial stiffness. The equations of motion of an $F2MC$-mass system are derived using a 3D elasticity model and the energy method. The stability of the unforced dynamic system is proven using a Lyapunov approach. A reduced-order model for operation with either a fully open or fully closed valve motivates the development of a zero vibration (ZV) controller that suppresses vibration in finite time. Coupling of a fluid-filled $F2MC$ tube to a pressurized accumulator through a fixed orifice is shown to provide significant passive damping. The open-valve orifice size is optimized for optimal passive, skyhook, and ZV controllers by minimizing the integral time absolute error cost function. Simulation results show that the optimal open valve orifice provides a damping ratio of 0.35 compared with no damping in closed-valve case. The optimal ZV controller outperforms optimal passive and skyhook controllers by 32.9% and 34.2% for impulse and 34.7% and 60% for step response, respectively. Theoretical results are confirmed by experiments that demonstrate the improved damping provided by optimal passive control $F2MC$ and fast transient response provided by semi-active ZV control.