Structural Vibration Control Using Extension and Shear Active-Passive Piezoelectric Networks Including Sensitivity to Electrical Uncertainties

Active-Passive Piezoelectric Networks (APPN) integrate active voltage sources with passive resistance-inductance shunt circuits to a piezoelectric patch. This technique allows to simultaneously passively dissipate vibratory energy through the shunt circuit and actively control the structural vibrations. This work presents an analysis of active-passive damping performance of beams with extension and shear APPN. A coupled finite element model with mechanical and electrical degrees of freedom is developed and used to design passive and active control parameters. Then, stochastic modeling and analyses of two cantilever beam configurations, with extension and shear APPN, are performed to evaluate the effect of uncertainties in circuit components on passive and active-passive vibration control. Results show that active-passive shunt circuits can be very interesting since they may combine an adequate passive control performance with an increase of active control authority when a control voltage is applied to the circuit. For the extension configuration, vibration amplitude reductions of up to 22 dB and 28 dB are obtained for passive and active-passive cases, respectively. Considering relative dispersions of 10% for the resistance and inductance values, the passive and active-passive amplitude reductions are found to be in the ranges 16-24 dB and 27-28 dB, respectively. For the shear configuration, increases in the active control authority of up to 29 dB due to a properly tuned resonant circuit are observed. When subjected to uncertainties in the resistance and inductance values, with 10% relative dispersions, the control authority increase is in the range of 6-29 dB.