An efficient finite element formulation for passive vibration attenuation using shunt piezoelectric patches

Abstract eng:
This paper concerns the numerical simulation of the vibrations of an elastic mechanical structure equipped with several piezoelectric patches, with applications to control, sensing and reduction of vibrations. Firstly, a finite element formulation of the coupled electromechanical problem is introduced, whose originality is that provided a set of non restrictiveassumptions, the system electrical state is fully described by a very few global discrete unknowns: only a couple of variables per piezoelectric patches, namely (1) the electric charge contained in the electrodes and (2) the voltage between the electrodes. A reduced order model (ROM) of the problem is then introduced, by means of a modal expansion. This leads to show that the classical efficient electromechanical coupling factors (EEMCF) naturally appear as the main parameters that master the electromechanical coupling in the ROM. Finally, the above results are applied in the case of a cantilever beam whose vibrations are reduced by means of a resonant shunt. The proposed finite element formulation enables to compute the system EEMCF as well as its frequency response that are compared to experimental results, showing an excellent agreement.

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