A nonlinear saturating amplifier circuit for piezoelectric vibration control of flexible mechanical system

This work investigates the vibration control properties of a saturating shunt circuit for piezoelectric vibration control. The circuit is realized as a saturating operational amplifier that takes the induced piezoelectric voltage as input. Furthermore, an inductor and resistor are placed in series. Using complexification-averaging, an analytical form of the frequency response is derived by approximating the saturation by an arctangent. It is found that the vibration damping properties are similar to that of the piezo-electric nonlinear energy sink (NES) shunt circuit that consists of a cubic multiplication of the piezoelectric voltage. These properties are 1) Saturation of the host structure amplitude 2) an efficient quasi-periodic vibration regime, and 3) the appearance of an isolated response curve (IRC). The difference is that for the saturating circuit, the isolated response appears to the right of the host structures’ resonance, while for the NES circuit, it results in an IRC to the left of this resonance. The analytical frequency response is compared to Runge-Kutta simulation for arctangent and non-smooth saturation, showing good agreement.