Premature jump-down mimicks nonlinear damping in nanoresonators

Recent experiments on nano-resonators in a bistable regime use the `jump-down' point between states to infer mechanical properties of the membrane or a load, but often suggest the presence of some nonlinear damping. Motivated by such experiments, we develop a mechanical model of a membrane subject to a uniform, oscillatory load and linear damping. We solve this model numerically and compare its jump-down behaviour with standard asymptotic predictions for a one-dimensional Duffing oscillator with strain stiffening. We show that the axisymmetric, but spatially-varying, problem can be mapped to the Duffing problem with coefficients determined rationally from the model's Partial Differential Equations. However, we also show that jump-down happens earlier than expected (i.e.~at lower frequency, and with a smaller oscillation amplitude). Although this premature jump-down is often interpreted as the signature of a nonlinear damping in experiments, its appearance in numerical simulations with only linear damping suggests instead that indicate that the limitations of asymptotic results may, at least sometimes, be the cause. We therefore suggest that care should be exercised in interpreting the results of nano-resonator experiments.