Piezoelectric Digital Vibration Absorbers for Multimodal Vibration Mitigation of Complex Mechanical Structures

Engineering structures are becoming lighter and more complex to accommodate the ever-increasing demand for performance and to comply with stringent environmental regulations. This trend comes with several challenges, one of which is the increased susceptibility to high-amplitude vibrations. These vibrations can be detrimental to structural performance and lifetime, and may sometimes even threaten safety. Passive and active vibration reduction techniques can provide a solution to this issue. Among the possibilities, piezoelectric damping is an attractive option, due to its compact and lightweight character, its reduced cost and its tunability. This technique uses the ability of a piezoelectric transducer to transform part of its mechanical energy into electrical energy. The converted energy can then be dissipated by connecting a shunt circuit to the transducer. However, the difficulty of realizing such circuits limits the broad applicability of piezoelectric shunting.

This doctoral thesis investigates the potential of replacing the electrical circuit comprising classical components such as resistors and inductors by a digital unit and a current source, thereby creating a digital vibration absorber (DVA). Virtually any circuit can be emulated with a digital controller, providing this approach with an extreme versatility for vibration mitigation of complex mechanical structures. In this regard, the DVA is first analyzed in terms of power consumption and stability of the controlled system. Then, effective and easy-to-use tuning approaches for the control of multiple structural modes either with passive electrical circuits or a DVA are proposed, namely a passivity-based tuning of shunt circuits, a modal-based synthesis of electrical networks interconnecting multiple piezoelectric transducers, and a numerical norm-homotopy optimization resulting in an all-equal-peak design. These techniques are eventually applied and adapted to real-life structures with potentially complex dynamics. Specifically, effective vibration mitigation is demonstrated on structures exhibiting nonlinear behaviors and high modal density.