Mixed Nonlinear Response and Transition of Nonlinearity in a Piezoelectric Membrane

Nonlinearities play a critical role in the dynamics of mechanical resonators, enhancing sensitivity and enabling signal manipulation. Understanding the parameters affecting nonlinearities is crucial for developing strategies to counteract their effects or manipulate them for improved device performance. This study investigates the impact of fabrication-induced curvature on the dynamics of zinc-oxide-based piezoelectric micromachined ultrasonic transducers (PMUTs). Our experiments reveal that these devices exhibit hardening, softening, and mixed nonlinear responses with varying initial static displacements. Notably, PMUTs with an almost flat initial static displacement exhibit hardening nonlinearity, while those with a curved initial static displacement show softening nonlinearity. An exotic mixed nonlinear response is observed for intermediate static displacement. We attribute the observed nonlinear response to the interplay between static displacement induced quadratic nonlinearity and midplane-stretching induced cubic nonlinearity. We provide a theoretical formulation for the dynamics of the devices, which explains the experimental results and highlights the nonlinear responses and their dependence on the initial static displacement. Our findings underscore the significance of nonlinearities in the dynamics of mechanical resonators and suggest ways to optimize the device performance.