The ability to reduce flexural vibrations of lightweight structures has been a goal for many researchers. A type of transducer-controller system that accomplishes this is a piezoelectric patch connected to an electrical impedance, or shunt. The piezoelectric patch converts the vibrational strain energy of the structure to which it is bonded into electrical energy. This converted electrical energy is then modified by the shunt to influence to mechanical response. There are many types of shunt circuits which have demonstrated effective control of flexural systems. Of interest in this work is the negative capacitance shunt, which has been shown to produce significant reduction in vibration over a broad frequency range. A negative capacitance circuit produces a current that is 180̊ out of phase from a traditional, passive capacitor. In other words, the voltage of the capacitor decreases as charge is added. The negative capacitance shunt consists of a resistor and an active negative capacitance element. By adding a resistor and negative capacitor to the electrical domain, the shunt acts as a damper and negative spring in the mechanical domain. The performance of the negative capacitance shunt can be increased through proper selection of the shunt's electrical components. Three aspects of component selection are investigated: shunt efficiency, maximum suppression, and stability. First, through electrical modeling of the shunt-patch system, the components can be chosen to increase the efficiency of the shunt for a given impedance. Second, a method is developed that could be utilized to adaptively tune the magnitude of resistance and negative capacitance for maximum control at a given frequency. Third, with regard to stability, as the control gain of the circuit is increased, by adjusting the circuit parameters, there is a point when the shunt will become unstable. A method to predict the stability of the shunt is developed to aid in suppression prediction. The negative capacitance shunt is also combined with a periodic piezoelectric patch array to modify the propagating wave behavior of a vibrating structure. A finite element method is utilized to create models to predict both the propagation constant, which characterizes the reduction in propagating waves, and the velocity frequency response of a full system. Analytical predictions are verified with experimental results for both a 1- and 2-D periodic array. Results show significant attenuation can be achieved with a negative capacitance shunt applied to a piezoelectric patch array. Three electromechanical aspects are developed: design for maximum suppression, more accurate stability prediction, and increased power-output efficiency. First, a method is developed that may be used to adaptively tune the magnitude of resistance and negative capacitance for maximum suppression. Second, with regard to stability, a method is developed to predict the circuit components at which the circuit will obtain a stable output. Third, through electrical modeling of the shunt-patch system, the components are chosen to increase the power output efficiency of the shunt circuit for a given impedance. The negative capacitance shunt is also combined with a periodic piezoelectric patch array to modify the propagating wave behavior of a vibrating structure. Analytical predictions are verified with experimental results for both a 1- and 2-D periodic array. Results show significant attenuation can be achieved with a negative capacitance shunt applied to a piezoelectric patch array.