Nonlinear vibrations of microcantilevers subjected to tip-sample interactions: Theory and experiment

Improvement of microcantilever-based sensors and actuators chiefly depends on their modeling accuracy. Atomic force microscopy (AFM) is the most widespread application of microcantilever beam as a sensor, which is usually influenced by the tip-sample interaction force. Along this line of reasoning, vibration of AFM microcantilever probe is analyzed in this paper, along with analytical and experimental investigation of the influence of the sample interaction force on the microcantilever vibration. Nonlinear integropartial equation of microcantilever vibration subject to the tip-sample interaction is then derived and multiple time scales method is utilized to estimate the tip amplitude while it is vibrating near the sample. A set of experiments is performed using a commercial AFM for both resonance and nonresonance modes, and the results are compared with the theoretical results. Hysteresis, instability and amplitude drop can be identified in the experimental curves inside the particle attraction domain. They are likely related to the interaction force between the tip and sample as well as the ever-present water layer during the experiments. A fair agreement is observed between the theoretical simulations and experimental findings, which obviously demonstrates the effectiveness and applicability of the developed model.