Abstract
We focus in this paper on the modeling and dynamical analysis of a tapping mode atomic force microscopy (AFM). The microbeam is subjected to a low frequency harmonic displacement of its base and to the Lennard-Jones (LJ) forces at its free end. Static and modal analysis are performed for various gaps between the tip of the microbeam and a sample. The Galerkin method is employed to reduce the equations of motion to a fast-slow dynamical system. We show that the dynamics of the AFM system is governed by the contact and the noncontact invariant slow manifolds. The tapping mode is triggered via two saddle-node bifurcations of these manifolds. Moreover, the contact time is computed and the effects of the base motion amplitude and the initial gap are discussed.
Highlights
The Atomic Force Microscope (AFM) is a scanning probe microscope that is used as a nano-scale tool for manipulation and characterization in nanosciences [1]
We developed a mathematical model of an AFM microbeam subjected to a slow harmonic base motion and Lennard-Jones forces
It was shown that the fundamental natural frequency near the contact mode is the most affected by the intermolecular interactions
Summary
The classical beam theory based on the Euler-Bernoulli assumptions is used to develop a continuous model of an AFM probe, of length L, operating in air.
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