Enhanced coupling of piezoelectric micromachined ultrasonic transducers with initial static deflection

The enhancement of the vibration amplitude of a clamped circular piezoelectric micromachined ultrasonic transducer (pMUT) with static deflection has been theoretically and numerically investigated for the first time. Using Fourier series expansion of the classic plate theory with in-plane time-dependent piezoelectric stress, the first harmonic motion equation of a pMUT plate with initial displacement was derived. An analytical solution based on a novel Green´s function approach was detailed, where additional plate deflection due to the synergy between the static deflection and the applied AC voltage was theoretically predicted and confirmed using Finite Element Modeling (FEM). This unprecedented demonstration opens up new opportunities for understanding pre-deflected pMUTs and implementing optimized designs.