Effects of a slow harmonic displacement on an Atomic Force Microscope system under Lennard-Jones forces

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

Effects of a slow harmonic displacement on an Atomic Force Microscope system under Lennard-Jones forces

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