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.