Optimized design and placement of piezoelectric transducers for micromechanical structures subject to membrane stress

This paper reports on the optimization of the design of piezoelectric transducer elements integrated on doubly-clamped micro-beam resonators. We report and emphasize the often forgotten influence of membrane stresses on defining the dimensions and optimal position of the piezoelectric transducer patches. The study is based on the shift of the inflection line (i.e., points of zero curvature) of the fundamental mode of vibration as a result of (excessive) membrane-stresses. The above is analysed theoretically using numerical models and is confirmed by impedance measurements and optical measurements of fabricated doubly-clamped beam resonators.