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

Invariant slow manifolds of an Atomic Force Microscope system under the Derjaguin-Muller-Toporov forces and a slow harmonic base motion

“…Hence, for f = 0.55, the contact and the non contact slow manifolds will be both visited during a period of the base displacement. This solution is geometrically a periodic burster and physically corresponds to a tapping mode of the AFM [3]. The confirmation that the solutions of the nondimensional Eq.…”

“…An enhanced understanding of these vibrations is central to the correct interpretation of the AFM outputs. Lakrad [3] and Khadraoui et al [4] studied the nonlinear dynamics of the AFM under the Lennard-Jones force between the tip and the sample. The micro-cantilever was subject to an imposed slow harmonic displacement of its base.…”

“…They computed the slow manifolds in order to explain the occurrence of the contact, noncontact and tapping modes of the AFM. The present paper follows the same workflow than [3] but in the presence of the Derjaguin-Muller-Toporov (DMT) interaction forces between the tip and the sample. The AFM is modelled by a single degree-of-freedom lumped linear system subject to a slow harmonic base displacement.…”

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

“…These dynamic bifurcations rule the contact time between the tip and the sample and they determine the operational mode of the AFM: contact, noncontact and tapping modes, respectively. This work uses a continuous model of the AFM system and it can be viewed as a continuation of a previous paper by Lakrad [15] where a lumped mass model was used. The present paper is organized as follows: in section 2 we derive a continuous nonlinear model of the microcantilever under the LJ force and the base displacement using the Hamilton principle.…”