Doctoral thesis presented by Boris Lossouarn

Multimodal vibration damping of structures coupled
to their analogous piezoelectric networks

Submitted September the 16th 2016 to the thesis committee:

Corrado MAURINI δ'Alembert, UPMC, Paris Rapporteur
Elie LEFEUVRE IEF, Université Paris Sud, Paris Rapporteur
Olivier ALLIX LMT, ENS Cachan Examinateur
Andrea BERGAMINI EMPA, Dübendorf, Suisse Examinateur
Kenneth A. CUNEFARE IAL, Georgia Tech, Atlanta, USA Examinateur
Mathieu AUCEJO LMSSC, Cnam Paris Co-encadrant de thèse
Jean-François DEÜ LMSSC, Cnam Paris Directeur de thèse


Structural vibrations can be reduced by benefiting from the electromechanical coupling that is offered by piezoelectric materials. In terms of passive damping, piezoelectric shunts allow converting the vibration energy into electrical energy. Adding an inductor in the circuit creates an electrical resonance due to the charge exchanges with the piezoelectric capacitance. By tuning the resonance of the shunt to the natural frequency of the mechanical structure, the equivalent of a tuned mass damper is implemented.

This strategy is extended to the control of a multimodal structure by increasing the number of piezoelectric patches. These are interconnected through an electrical network offering modal properties that approximate the behavior of the structure to control. This multi-resonant network allows the simultaneous control of multiple mechanical modes. An adequate electrical topology is obtained by discretizing the mechanical structure and applying the direct electromechanical analogy. The analogous network shows inductors and transformers, whose numbers and values are chosen according to the frequency band of interest.

After focusing on the design of suitable magnetic components, the passive control strategy is applied to the damping of one-dimensional structures as bars or beams. It is then extended to the control of thin plates by implementing a two-dimensional analogous network.