We study nanomechanical resonators with frequency fluctuations due to diffusion of absorbed particles. The diffusion depends on the vibration amplitude through inertial effect. We find that, if the diffusion coefficient is sufficiently large, the res
onator response to periodic driving displays bistability. The lifetime of the coexisting vibrational states scales exponentially with the diffusion coefficient. It also displays a characteristic scaling dependence on the distance to bifurcation points.
We propose a scheme to measure the mass of a single particle using the nonlinear response of a 2D nanoresonator with degenerate eigenmodes. Using numerical and analytical calculations, we show that by driving a square graphene nanoresonator into the
nonlinear regime, simultaneous determination of the mass and position of an added particle is possible. Moreover, this scheme only requires measurements in a narrow frequency band near the fundamental resonance.
