Dynamic Responses of an Atomic Force Microscope Interacting with Samples

The objective of this paper is to formulate the equations of motion and to analyze the vibrations of an atomic force microscope (AFM), which contains a piezoelectric rod coupling with a cantilever beam, and the tip mass interacting with samples. The governing equations of the AFM system are formulated completely by Hamilton’s principle. The piezoelectric rod is treated as an actuator to excite the cantilever beam via an external voltage. The repulsive forces between the tip and samples are modeled by the Hertzian, the Derjaguin-Müller-Toporov, and Johnson-Kendall-Roberts models in the contact region. Finally, numerical results are provided to illustrate the coupling effects between the piezoelectric actuator and the cantilever beam and the interaction effects between the tip and samples on the dynamic responses.