Modal optimization and filtering in piezoelectric microplate resonators

A systematic design procedure to tailor the modal response of micro-resonators based on flexible plates with piezoelectric films is demonstrated. Sensors/actuators were designed by optimizing the surface electrode shapes in the plane dimensions. A numerical finite element procedure, which considers the effective surface electrode covering the piezoelectric film as a binary function on each element, has been implemented. Two design goals are considered: (i) optimized response (actuation or sensing) in a given mode; (ii) implementation of a modal transducer by filtering specific modes. For a given mode in a plate with arbitrary boundary conditions, our calculations allowed us to predict the top electrode layout reaching higher displacement in resonance than any other electrode design for the same structure. Microcantilevers and microbridges were fabricated and their modal response characterized by laser Doppler vibrometry. In comparison to a conventional square-shaped electrode, our experiments show that the implemented designs can increase the response in any desired resonant mode and simultaneously attenuate the contributions from other unwanted modes, by simply shaping the surface electrodes. Enhancement ratios as high as 42 dB, relative to a full-size electrode case, are demonstrated. The limitations imposed by the fabrication are also discussed.