The dynamic behavior of an atomic force microscope cantilever probe is studied for dual frequency excitation. By using the Euler-Bernoulli beam equation with a multi-mode approximation, the system is modeled with base excitation and tip-sample interaction forces obtain from molecular dynamics simulations. The dynamic response of the cantilever probe is simulated for a range of separation distance values and analyzed using Poincare´ sections, bifurcation diagrams, and spectral analysis. The response of the cantilever probe is found to display a qualitative change when influenced by surface forces. The frequency component at half of the fundamental frequency provides an effective way to monitor the amount of force that the probe is applying to the surface of the sample. With this frequency component, an amplitude modulation operation mode is proposed in order to maintain near-grazing behavior during imaging.

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