Robustness of a multimodal piezoelectric damping involving the electrical analogue of a plate

Abstract

Multimodal passive damping of a mechanical structure can be implemented by a coupling to a secondary structure exhibiting similar modal properties. When considering a piezoelectric coupling, the secondary structure is an electrical network. A suitable topology for such a network can be obtained by a finite difference formulation of the mechanical equations, followed by a direct electromechanical analogy. This procedure is applied to the Kirchhoff-Love theory in order to find the electrical analogue of a clamped plate. The passive electrical network is implemented with inductors, transformers and the inherent capacitance of the piezoelectric patches. The electrical resonances are tuned to approach those of several mechanical modes simultaneously. This yields a broadband reduction of the plate vibrations through the array of interconnected piezoelectric patches. The robustness of the control strategy is evaluated by introducing perturbations in the mechanical or electrical designs. A non-optimal tuning is considered by way of a uniform variation of the network inductance. Then, the effect of local or boundary modifications of the electromechanical system is observed experimentally. In the end, the use of an analogous electrical network appears as an efficient and robust solution for the multimodal control of a plate.