Optimization of Passive Vibration Damping of Rotor Blade Structures using Shunted Piezoelectric Elements

This work concerns the numerical simulation and the optimization of vibration attenuation of a rotor blade structure equipped with shunted piezoelectric patches. Firstly, a finite element formulation of the coupled electromechanical problem of an elastic structure equipped with piezoelectric patches is introduced. Its originality lies in the fact that the electrical state of the system is fully described by only a couple of variables per piezoelectric patches, namely the electric charge contained in the electrodes and the voltage between the electrodes. The second part of the work is devoted to the introduction of a reduced order model by expanding the solution onto the normal modes of the electro-mechanical problem with all patches short circuited. It is shown that the classical effective electromechanical coupling factors naturally appear as the main coupling parameters in this reduced order model. The proposed approach is finally applied to vibration reduction by means of a resonant shunt system to a rotor blade structure. An optimization of the piezoelectric patches dimensions as well as their position is also proposed in order to maximize the damping effect.