Dependence of strain amplitude on loss mechanisms in plate resonators

Piezoelectric elements are used in a variety of applications such as optical modulators, microactuators, and certain types of transducers and resonant sensors, where it is necessary to know the maximum amplitude obtainable. Conduction, dielectric, and viscous losses all limit the amplitude. We consider high frequency crystal plates in the one-dimensional approximation. By the use of a complex piezoelectric coupling coefficient incorporating all three loss mechanisms, the limiting amplitude of the fundamental mode is found. Examples are given for AT, BT, and SC quartz cuts, along with lithium niobate and lead titanate ceramic. The influence of electrode mass loading on amplitude is also determined, along with the magnitude of the interfacial stress. The stress levels can attain significant levels.