Electrode configuration for vibrating beam transducers

A transducer comprising a substantially solid piezoelectric beam having a natural resonant frequency and a longitudinal axis that extends between two opposed clamped ends;

• and a plurality of electrodes mounted by the beam for causing the beam to vibrate by producing forces directed along the longitudinal axis, at least one of the electrodes defining means for increasing the tendency of the beam to vibrate in a predetermined flexure mode at the natural resonant frequency, to the exclusion of harmonic frequencies, said means comprising a configuration of said at least one electrode that varies as a function of longitudinal position along the beam such that when a voltage difference is applied between the electrodes, the longitudinal force produced by the electrodes as a function of longitudinal position, approximates a longitudinal strain versus longitudinal position profile of the predetermined flexure mode at the natural resonant frequency.