  In this work, we present the effects of stochastic force generated by white
noise on the nonlinear dynamics of a circular silicon nitride membrane. By
tuning the membrane to the Duffing nonlinear region, detected signals switching
between low- and high- amplitudes have been observed. They are generated by
noise-assisted random jumps between bistable states at room temperature and
exhibit high sensitivity to the driving frequency. Through artificially heating
different mechanical vibration modes by external input of white noise, the
switching rate exhibits exponential dependence on the effective temperature and
follows with Kramer's law. Furthermore, both the measured switching rate and
activation energy exhibit sensitivity to the width of the hysteresis window in
nonlinear response and the driving force, which is in qualitative agreement
with the theoretical descriptions. Besides, white noise-induced hysteresis
window squeezing and bifurcation point shifting have also been observed, which
are attributed to the stochastic force modulation of the spring constant of the
membrane. These studies are essential for the generation and manipulation of
stochastic switching effects, paving the way to explore new functions based on
probability distributions in nanomechanical resonators.
