Invariant slow manifolds of an Atomic Force Microscope system under the effects of Lennard-Jones forces and a slow harmonic base motion

We study the nonlinear vibrations of an AFM system, modeled as a linear mass-spring-damper system, under the Lennard-Jones forces and an imposed harmonic base displacement. The frequency of this latter is very low with respect to the natural fundamental frequency of the system. The invariant slow manifolds of the system are approximated and their bifurcations are investigated. It is shown that two dynamic saddle-node bifurcations, during one period of the base oscillation, of the contact and the noncontact invariant slow manifolds are responsible for triggering the tapping mode. It is also shown that these dynamic bifurcations govern the contact time between the probe and the sample during the tapping mode. (C) 2015 Elsevier B.V. All rights reserved.