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.

This work presents a numerical analysis of the structural vibration control using piezoelectric materials in extension and shear mode connected to active-passive electric circuits composed of resistance, inductance and voltage source. For that, a finite element model for sandwich beams with three elastic or piezoelectric layers was developed. A modeling of the electric circuit dynamics and its coupling to the structure with piezoelectric elements was also done. A harmonic analysis of the resulting equations was performed to yield a preliminary evaluation of the effects caused by the electric circuit components on the structure. It was observed that the passive circuit components not only lead to a dynamic vibration absorber effect but also to an amplification of the control authority in case of actuation using the voltage source. Using the standard methodology for the design of dynamic vibration absorbers, expressions were derived for the resistance and inductance values that optimize the passive vibration control performance of the system. A numerical analysis of the passive vibration control was performed for cantilever beams with extension and shear piezoelectric ceramics showing satisfactory results. Then, an analysis of the control authority was carried out for the same structures aiming at an active-passive vibration control. The active control was achieved using a Linear Quadratic Regulator optimal feedback strategy to evaluate the voltage applied to the circuit. A comparison between the obtained results show that hybrid active-passive control is always superior to the purely active or purely passive control for both cases studied, with extension and shear piezoelectric ceramics.

This work presents a numerical analysis of the structural vibration control using piezoelectric materials in extension mode connected to active-passive electric circuits composed of resistance, inductance and voltage source. For that, a finite element model for sandwich beams with three elastic or piezoelectric layers was developed. A modeling of the electric circuit dynamics and its coupling to the structure with piezoelectric elements was also done. A harmonic analysis of the resulting equations was performed to yield a preliminary evaluation of the effects caused by the electric circuit components on the structure. It was observed that the passive circuit components not only lead to a dynamic vibration absorber effect but also to an amplification of the control authority in case of actuation using the voltage source. Using the standard methodology for the design of dynamic vibration absorbers, expressions were derived for the resistance and inductance values that optimize the passive vibration control performance of the system. An analysis of the effect of uncertainties of piezoelectric and dielectric constants of piezoelectric ceramic and resistance and inductance components of the shunt circuit on the passive and active-passive control performance for a cantilever beam structure was performed. The objective of this analysis was to quantify robustness and sensitivity of the proposed control. Then, an optimization study of the values of resistance and inductance of the shunt circuit as a function of the maximum control voltage to be applied on a plate with several piezoelectric actuators was performed. Finally and also for the plate structure, an analysis of uncertainties in the stiffness of the adhesive interface between structure and piezoelectric actuators and their effects on the performance of passive control and active-passive was performed.

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