  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 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 device performance.
