Abstract
We have used linear response measurements to explore the frequency shift and peak height of the natural frequency resonance of single cantilevers in a nonlinear state versus driver frequency as the bifurcation frequency is approached. Analytical calculations of these properties for a single Duffing resonator are in good agreement in terms of softening of the natural frequency-pump difference frequency and the diverging of its peak amplitude. The deviation of the natural frequency from the analytical curve that is observed for a short cantilever can be ascribed to a large amplitude effect, which, as yet, cannot be explained by simple modifications of the Duffing equation.
