Calibration of Digital Shunts for Piezoelectric Vibration Control

Flexible structures with low modal damping can be sensitive to excessive vibrations, often dominated by the response near a single vibration mode. An effective technique for damping vibrations of small flexible structures is by piezoelectric shunt damping, where a piezoelectric transducer is attached locally to the structure and connected to an electrical circuit to dissipate energy and thereby reduce vibrations.

The present thesis investigates the calibration of piezoelectric shunts targeting a single vibration mode when limited information is available about the structure and the piezoelectric transducer, using only a minimum number of experimental measurements for the calibration. The work is divided into three parts: the development of calibration expressions; a discussion of the implementation and parameter estimation using so-called digital shunt units; and the experimental validation on a composite blade.

In the first part, a theoretical framework is developed for the calibration of piezoelectric shunts targeting a single vibration mode. A residual mode correction is introduced so that explicit calibration expressions, derived for single-degree-offreedom systems, can be applied directly for damping of flexible structures with multiple vibration modes. The influence of dielectric losses on the shunt calibration is shown to be significant for shunts with low electromechanical coupling factors and high dielectric losses, and a correction term is included in the calibration expression to retain effective damping. Additional corrections are finally proposed to account for both shunt interaction and residual modes in the tuning of multiple shunts targeting the same vibration mode.

In the second part, the implementation of an often-used digital shunt unit is considered as a replacement for analog components in an electrical shunt circuit. It is demonstrated that the device can be used both for the estimation of the modal parameters needed for calibration and to implement the shunt circuit. A new modal parameter estimation technique is presented based on two local extrema in the dynamic capacitance. Finally, a new hybrid analog-digital shunt is proposed, combining the robustness of passive resonant shunts with analog components and the flexibility of digital shunt units.

In the third part, the proposed calibration corrections and modal parameter estimation methods are validated experimentally for the damping of a composite blade. The digital shunt unit is used both for modal parameter estimation and the subsequent shunt implementation. The examples demonstrate the accuracy of the proposed calibration method for a range of electromechanical coupling factors and the practicality of using digital shunt units for implementation of piezoelectric shunts.