A passive electric controller for multimodal vibrations of thin plates

A dynamic passive controller for thin plate vibrations is here presented. The vibrations damping is obtained by uniformly distributing an array of piezoelectric elements on the host plate, and by interconnecting their terminals via a passive electric circuit. The use of an electric network having the same structure as the plate equations (i.e., plate analog network) assures a multiresonant and broad band electromechanical coupling. The governing equations of the proposed network are derived by paralleling the Lagrangian functional of a discretized Kirchhoff-Love plate with that of a lumped, lossless and reciprocal circuit. A possible realization of the plate analog network is also proposed under the form of a circuit constituted by capacitors, inductors and transformers only. The appropriate insertion of optimized resistors in the found analog circuit allows for effecting multimodal damping of forced oscillations. The efficiency of the proposed strategy is validated through the analysis of a realistic simply supported plate. Exact solutions are computed for interesting mechanical disturbances.